The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlak’s rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of different perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set, in relation to the rough set, is defined as a family of sets (...) approximated by the so called lower and upper limits. The family is simultaneously considered as a family of all denotations of sharp terms representing a suitable vague term, from the agent’s point of view. Some algebraic operations on vague sets and their properties are defined. Some important conditions concerning the membership relation for vague sets, in connection to Blizard’s multisets and Zadeh’s fuzzy sets, are established as well. A classical outlook on a logic of vague sentences (vague logic) based on vague sets is also discussed. (shrink)

Abstract: Theories of rough sets and fuzzy sets are related and complementary methodologies to handle uncertainty of vagueness and coarseness, respectively. They are generalizations of classical set theory for modeling vagueness and uncertainty. A fundamental question concerning both theories is their connections and differences. There have been many studies on this topic. Topology is a branch of mathematics, whose ideas exist not only in almost all branches of mathematics but also in many real life applications. The (...) topological structure on an abstract set is used as the base, which used to extract knowledge from data. In this paper: topological structure is used to study the relation between rough sets and fuzzy sets. Membership function is used to convert from rough set to fuzzy set and vice versa. This conversion will achieve the advantages of two theories. Some examples and theories are introduced to indicate the importance of using general binary relations in the construction of rough set concepts, and indicate the relation between rough sets and fuzzy sets according to the topological spaces. (shrink)

In the article the problem of imprecise information and concepts is considered. The theory of rough sets and the theory of fuzzy sets are used to provide an original solution to this problem.

A rough fuzzy set is the result of the approximation of a fuzzy set with respect to a crisp approximation space. It is a mathematical tool for the knowledge discovery in the fuzzy information systems. In this paper, we introduce the concepts of rough standard neutrosophic sets and standard neutrosophic information system, and give some results of the knowledge discovery on standard neutrosophic information system based on rough standard neutrosophic sets.

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and (...) show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. (shrink)

In this paper, we first defined soft intervalvalued neutrosophic rough sets(SIVN- rough sets for short) which combines interval valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of soft interval valued intuitionistic fuzzy rough sets( SIVIF- rough sets). Finally an illustartive example is given to verfy the developped algorithm and to demonstrate its practicality and effectiveness.

Shared conceptualization, in the sense we take it here, is as recent a notion as the Semantic Web, but its relevance for a large variety of fields requires efficient methods of extraction and representation for both quantitative and qualitative data. This notion is particularly relevant for the investigation into, and construction of, semantic structures such as knowledge bases and taxonomies, but given the required large, often inaccurate, corpora available for search we can get only approximations. We see fuzzy description (...) logic as an adequate medium for the representation of human semantic knowledge and propose a means to couple it with fuzzy semantic networks via the propositional Łukasiewicz fuzzy logic such that these suffice for decidability for queries over a semantic-knowledge base such as “to what degree of sharedness does it entail the instantiation C(a) for some concept C” or “what are the roles R that connect the individuals a and b to degree of sharedness ε.” . (shrink)

The objective of the paper is to implement and validate diagnosis in the medical field via refined neutrosophic fuzzy logic (RNFL). As such, we have proposed a Max-Min composition (MMC) method in RNFL. This method deals with the diagnosis under certain constraints like uncertainty and indeterminacy. Further, we have considered the diagnosis problems to validate the sensitivity analysis of the novel multi attribute decision-making technique. Finally, we gave the graphical representations and compared the obtained results with other existing measures (...) in refined neutrosophic fuzzy sets. (shrink)

The short exposition of the triplet model of concepts and some definitions connected with it are given. In this model any concept may be depicted as having three characteristics: a base, a representing part and the linkage between them. The paper introduces the fuzzification of concepts in terms of the triplet model.

In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes (parameters)’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, (...) and for a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined be-tween each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life. (shrink)

The paper explicates the stages of the author’s philosophical evolution in the light of Kopnin’s ideas and heritage. Starting from Kopnin’s understanding of dialectical materialism, the author has stated that category transformations of physics has opened from conceptualization of immutability to mutability and then to interaction, evolvement and emergence. He has connected the problem of physical cognition universals with an elaboration of the specific system of tools and methods of identifying, individuating and distinguishing objects from a scientific theory domain. The (...) role of vacuum conception and the idea of existence (actual and potential, observable and nonobservable, virtual and hidden) types were analyzed. In collaboration with S.Crymski heuristic and regulative functions of categories of substance, world as a whole as well as postulates of relativity and absoluteness, and anthropic and self-development principles were singled out. Elaborating Kopnin’s view of scientific theories as a practically effective and relatively true mapping of their domains, the author in collaboration with M. Burgin have originated the unified structure-nominative reconstruction (model) of scientific theory as a knowledge system. According to it, every scientific knowledge system includes hierarchically organized and complex subsystems that partially and separately have been studied by standard, structuralist, operationalist, problem-solving, axiological and other directions of the current philosophy of science. 1) The logico-linguistic subsystem represents and normalizes by means of different, including mathematical, languages and normalizes and logical calculi the knowledge available on objects under study. 2) The model-representing subsystem comprises peculiar to the knowledge system ways of their modeling and understanding. 3) The pragmatic-procedural subsystem contains general and unique to the knowledge system operations, methods, procedures, algorithms and programs. 4) From the viewpoint of the problem-heuristic subsystem, the knowledge system is a unique way of setting and resolving questions, problems, puzzles and tasks of cognition of objects into question. It also includes various heuristics and estimations (truth, consistency, beauty, efficacy, adequacy, heuristicity etc) of components and structures of the knowledge system. 5) The subsystem of links fixes interrelations between above-mentioned components, structures and subsystems of the knowledge system. The structure-nominative reconstruction has been used in the philosophical and comparative case-studies of mathematical, physical, economic, legal, political, pedagogical, social, and sociological theories. It has enlarged the collection of knowledge structures, connected, for instance, with a multitude of theoreticity levels and with an application of numerous mathematical languages. It has deepened the comprehension of relations between the main directions of current philosophy of science. They are interpreted as dealing mainly with isolated subsystems of scientific theory. This reconstruction has disclosed a variety of undetected knowledge structures, associated also, for instance, with principles of symmetry and supersymmetry and with laws of various levels and degrees. In cooperation with the physicist Olexander Gabovich the modified structure-nominative reconstruction is in the processes of development and justification. Ideas and concepts were also in the center of Kopnin’s cognitive activity. The author has suggested and elaborated the triplet model of concepts. According to it, any scientific concept is a dependent on cognitive situation, dynamical, multifunctional state of scientist’s thinking, and available knowledge system. A concept is modeled as being consisted from three interrelated structures. 1) The concept base characterizes objects falling under a concept as well as their properties and relations. In terms of volume and content the logical modeling reveals partially only the concept base. 2) The concept representing part includes structures and means (names, statements, abstract properties, quantitative values of object properties and relations, mathematical equations and their systems, theoretical models etc.) of object representation in the appropriate knowledge system. 3) The linkage unites a structures and procedures that connect components from the abovementioned structures. The partial cases of the triplet model are logical, information, two-tired, standard, exemplar, prototype, knowledge-dependent and other concept models. It has introduced the triplet classification that comprises several hundreds of concept types. Different kinds of fuzziness are distinguished. Even the most precise and exact concepts are fuzzy in some triplet aspect. The notions of relations between real scientific concepts are essentially extended. For example, the definition and strict analysis of such relations between concepts as formalization, quantification, mathematization, generalization, fuzzification, and various kinds of identity are proposed. The concepts «PLANET» and «ELEMENTARY PARTICLE» and some of their metamorphoses were analyzed in triplet terms. The Kopnin’s methodology and epistemology of cognition was being used for creating conception of the philosophy of law as elaborating of understanding, justification, estimating and criticizing legal system. The basic information on the major directions in current Western philosophy of law (legal realism, feminism, criticism, postmodernism, economical analysis of law etc.) is firstly introduced to the Ukrainian audience. The classification of more than fifty directions in modern legal philosophy is suggested. Some results of historical, linguistic, scientometric and philosophic-legal studies of the present state of Ukrainian academic science are given. (shrink)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and (...) show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. These, provides a new interpretation of Quantum Mechanics.More exactly what we see here is "Particle-Fuzzy time" interpretation of quantum Mechanics, in contrast to some other interpretations of Quantum Mechanics like " Wave-Particle" interpretation. At the end, we propound a question about the possible solution of a paradox in Physics, the contradiction between General Relativity and Quantum Mechanics. (shrink)

Philosophers of science often assume that logically equivalent theories are theoretically equivalent. I argue that two theses, anti-exceptionalism about logic (which says, roughly, that logic is not a priori, that it is revisable, and that it is not special or set apart from other human inquiry) and logical realism (which says, roughly, that differences in logic reflect genuine metaphysical differences in the world), make trouble for both this commitment and the closely related commitment to theories being closed under logical consequence. (...) I provide three arguments. The first two show that anti-exceptionalism about logic provides an epistemic challenge to both the closure and the equivalence claims; the third shows that logical realism provides a metaphysical challenge to both the closure and the equivalence claims. Along the way, I show that there are important methodological upshots for metaphysicians and philosophers of logic. In particular, there are lessons to be drawn about certain conceptions of naturalism as constraining the possibilities for metaphysics and the philosophy of logic. (shrink)

Semantic dispositionalism is roughly the view that meaning a certain thing by a word, or possessing a certain concept, consists in being disposed to do something, e.g., infer a certain way. Its main problem is that it seems to have so many and disparate exceptions. People can fail to infer as required due to lack of logical acumen, intoxication, confusion, deviant theories, neural malfunctioning, and so on. I present a theory stating possession conditions of concepts that are counterfactuals, rather (...) than disposition attributions, but which is otherwise similar to inferentialist versions of dispositionalism. I argue that it can handle all the exceptions discussed in the literature without recourse to ceteris paribus clauses. Psychological exceptions are handled by suitably undemanding requirements (unlike that of giving the sum of any two numbers) and by setting the following two preconditions upon someone’s making the inference: that she considers the inference and has no motivating reason against it. The non-psychological exceptions, i.e., cases of neural malfunctioning, are handled by requiring that the counterfactuals be true sufficiently often during the relevant interval. I argue that this accommodates some important intuitions about concept possession, in particular, the intuition that concept possession is vague along a certain dimension. (shrink)

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and (...) more sensitive evaluations are made by a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations. (shrink)

The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite (...) to the other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)

The concept of knowledge can be modelled in epistemic modal logic and, if modelled by using a standard modal operator, it is subject to the problem of logical omniscience. The classical solution to this problem is to distinguish between implicit and explicit knowledge and to construe the knowledge operator as capturing the concept of implicit knowledge. In addition, since a proposition is said to be implicitly known just in case it is derivable from the set of propositions that are explicitly (...) known by using a certain set of logical rules, the concept of implicit knowledge is definable on the basis of the concept of explicit knowledge. In any case, both implicit and explicit knowledge are typically characterized as factive, i.e. such that it is always the case that what is known is also true. The aim of the present paper is twofold: first, we will develop a dynamic system of explicit intersubjective knowledge that allows us to introduce the operator of implicit knowledge by definition; secondly, we will show that it is not possible to hold together the following two theses: (1) the concept of implicit knowledge is definable along the lines indicated above and (2) the concept of implicit knowledge is factive. (shrink)

The main objective of the paper is to provide a conceptual apparatus of a general logical theory of language communication. The aim of the paper is to outline a formal-logical theory of language in which the concepts of the phenomenon of language communication and language communication in general are defined and some conditions for their adequacy are formulated. The theory explicates the key notions of contemporary syntax, semantics, and pragmatics. The theory is formalized on two levels: token-level and type-level. (...) As such, it takes into account the dual – token and type – ontological character of linguistic entities. The basic notions of the theory: language communication, meaning and interpretation are introduced on the second, type-level of formalization, and their required prior formalization of some of the notions introduced on the first, token-level; among others, the notion of an act of communication. Owing to the theory, it is possible to address the problems of adequacy of both empirical acts of communication and of language communication in general. All the conditions of adequacy of communication discussed in the presented paper, are valid for one-way communication (sender-recipient); nevertheless, they can also apply to the reverse direction of language communication (recipient-sender). Therefore, they concern the problem of two-way understanding in language communication. (shrink)

The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of Language Signs and the Problem of (...) Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)

Ben-Yami presents Wittgenstein’s explicit criticism of the Platonic identification of an explanation with a definition and the alternative forms of explanation he employed. He then discusses a few predecessors of Wittgenstein’s criticisms and the Fregean background against which he wrote. Next, the idea of family resemblance is introduced, and objections answered. Wittgenstein’s endorsement of vagueness and the indeterminacy of sense are presented, as well as the open texture of concepts. Common misunderstandings are addressed along the way. Wittgenstein’s ideas, (...) as is then shown, have far-reaching implications for knowledge of meaning and the nature of logic, and with them to the nature of the philosophical project and its possible achievements. (shrink)

Cognitive, or knowledge, agents, who are in some way aware of describing their own view of the world (based on their mental concepts), need to become concerned with the expressions of their own conceptions. My main supposition is that agents’ conceptions are mainly expressed in the form of linguistic expressions that are spoken, written, and represented based on e.g. letters, numbers, or symbols. This research especially focuses on symbolic conceptions (that are agents’ conceptions that are manifested in the form (...) of their symbols). I attempt to logically (and using ????LSYM) analyse symbolic conceptions in terminological systems. ????LSYM is an assertional fragment of my developed Conception Language (????L), which is utilised as a formal-logical system for representing and explicating agents’ conceptions of the world. Keywords: assertional logic; cognitive agent; knowledge agent; conception language; conception; symbol; symbolic conception. (shrink)

This paper deals with Gärdenfors’ theory of conceptual spaces. Let \({\mathcal {S}}\) be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes \(\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S}\) be given. Our main result is the construction of a classification algorithm. That is, given an element \({\tilde{A}}\in \mathcal {S},\) our algorithm classifies it into the conceptual field determined by one of the given prototypes \(\tilde{P}_i.\) The construction of our algorithm uses some physical (...) analogies and the Newton potential plays a significant role here. Importantly, the resulting conceptual fields are not convex in the Euclidean sense, which we believe is a reasonable departure from the assumptions of Gardenfors’ original definition of the conceptual space. A partitioning algorithm of the space \(\mathcal {S}\) is also considered in the paper. In the application section, we test our classification algorithm on real data and obtain very satisfactory results. Moreover, the example we consider is another argument against requiring convexity of conceptual fields. (shrink)

Buridan holds that the proper subject of psychology (i.e., the science undertaken in Aristotle’s De Anima) is the soul, its powers, and characteristic functions. But, on his view, the science of psychology should not be understood as including the body nor even the soul-body composite as its proper subject. Rather its subject is just “the soul in itself and its powers and functions insofar as they stand on the side of the soul". Buridan takes it as obvious that, even thus (...) narrowly construed, such a science is possible. To the extent that this science includes the human or intellective soul, however, Buridan’s claim regarding its possibility is far from obvious. After all, like most of his contemporaries, Buridan takes the human soul to be immaterial. Thus, he readily admits that “the intellect cannot be sensed” and its operations are likewise inaccessible to the senses. Yet, on Buridan's broadly empiricist theory of knowledge, all (human) knowledge, including knowledge of the intellect or intellective soul, takes its start in the senses. How, then, is a science of the human soul possible? What is the nature or source of our knowledge of the intellect? In this paper, I reconstruct Buridan's answer to these questions. -/- My discussion divides roughly into two parts. In the first, I set out the main elements of Buridan’s account of how we come to cognize the intellect, focusing on what he says about the genesis of our concept of the intellect. I then consider his account of our cognition of our own intellective states. As the discussion in part one make clear, Buridan holds that our concepts of intellect and of intellective states are both derived (inferentially) from subjective “experience” of our own states and rational activities. In part two, therefore, I try to elucidate Buridan’s notion of experience. Ultimately, I argue that it is a non-conceptual, non-discursive mode of self-awareness. I suggest, moreover, that it might best be understood in terms of our own notion of phenomenal consciousness. On the interpretation I advance, then, it turns out that, for Buridan, our concept of the intellect itself and, hence, the science of (human) psychology in general, is ultimately grounded in phenomenal experience of our own intellective states. (shrink)

Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the (...) epistemic process of extracting information implicit in explicitly given information) and, second, the process of establishing knowledge that a conclusion does not follow. Despite the overwhelming tendency to interpret the syllogistic as formal epistemology, it was not until the early 1970s that it occurred to anyone to think that Aristotle may have developed a theory of deductive reasoning with a well worked-out system of deductions comparable in rigor and precision with systems such as propositional logic or equational logic familiar from mathematical logic. When modern logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle's contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotle from possible charges of psychologism. They thought they saw Aristotle applying the informal axiomatic method to formal ontology, not as making the first steps into formal epistemology. They did not notice Aristotle's description of deductive reasoning. Ironically, the formal axiomatic method (in which one explicitly presents not merely the substantive axioms but also the deductive processes used to derive theorems from the axioms) is incipient in Aristotle's presentation. Partly in opposition to the axiomatic, ontically-oriented approach to Aristotle's logic and partly as a result of attempting to increase the degree of fit between interpretation and text, logicians in the 1970s working independently came to remarkably similar conclusions to the effect that Aristotle indeed had produced the first system of formal deductions. They concluded that Aristotle had analyzed the process of deduction and that his achievement included a semantically complete system of natural deductions including both direct and indirect deductions. Where the interpretations of the 1920s and 1930s attribute to Aristotle a system of propositions organized deductively, the interpretations of the 1970s attribute to Aristotle a system of deductions, or extended deductive discourses, organized epistemically. The logicians of the 1920s and 1930s take Aristotle to be deducing laws of logic from axiomatic origins; the logicians of the 1970s take Aristotle to be describing the process of deduction and in particular to be describing deductions themselves, both those deductions that are proofs based on axiomatic premises and those deductions that, though deductively cogent, do not establish the truth of the conclusion but only that the conclusion is implied by the premise-set. Thus, two very different and opposed interpretations had emerged, interestingly both products of modern logicians equipped with the theoretical apparatus of mathematical logic. The issue at stake between these two interpretations is the historical question of Aristotle's place in the history of logic and of his orientation in philosophy of logic. This paper affirms Aristotle's place as the founder of logic taken as formal epistemology, including the study of deductive reasoning. A by-product of this study of Aristotle's accomplishments in logic is a clarification of a distinction implicit in discourses among logicians--that between logic as formal ontology and logic as formal epistemology. (shrink)

Gila Sher interviewed by Chen Bo: -/- I. Academic Background and Earlier Research: 1. Sher’s early years. 2. Intellectual influence: Kant, Quine, and Tarski. 3. Origin and main Ideas of The Bounds of Logic. 4. Branching quantifiers and IF logic. 5. Preparation for the next step. -/- II. Foundational Holism and a Post-Quinean Model of Knowledge: 1. General characterization of foundational holism. 2. Circularity, infinite regress, and philosophical arguments. 3. Comparing foundational holism and foundherentism. 4. A post-Quinean model of knowledge. (...) 5. Intellect and figuring out. 6. Comparing foundational holism with Quine’s holism. 7. Evaluation of Quine’s Philosophy -/- III. Substantive Theory of Truth and Relevant Issues: 1. Outline of Sher’s substantive theory of truth. 2. Criticism of deflationism and treatment of the Liar. 3. Comparing Sher’s substantive theory of truth with Tarski’s theory of truth. -/- IV. A New Philosophy of Logic and Comparison with Other Theories: 1. Foundational account of logic. 2. Standard of logicality, set theory and logic. 3. Psychologism, Hanna’s and Maddy’s conceptions of logic. 4. Quine’s theses about the revisability of logic. -/- V. Epilogue. (shrink)

The concept of a hypersoft membership function is introduced in the extension of a soft set known as a hypersoft set, permitting it to handle complicated and uncertain information in a more powerful and flexible manner. Many academics have already become fascinated with this new area of study, leading to the development of a number of hybrid structures. This chapter develops some new hybrid hypersoft set structures by taking into account multiple fuzzy set-like settings and possibility degree-based settings collectively. (...) Additionally, numerical examples are included to clarify the concept of these structures. Researchers can utilize this work to better understand and apply a variety of mathematical ideas. (shrink)

If science disputes the validity or authenticity of religious knowledge it is because both the scientist and the rational man assume that every object of knowledge there is or can be exists as a material percept in time and space. If we assume that knowledge of material objects is definite knowledge – an assumption itself suspect considering that the latest WMAP data indicates that 95.4% of the total matter in our universe is dark matter and dark energy – all scientific (...) knowledge (confined as it is to knowledge of 4.6% of the visible universe) is definite knowledge; but because it’s knowledge is confined to a miniscule fraction of all knowledge there is or can be had in our material universe, it can scarcely be said – as Sir Bertrand Russell claims – that all definite knowledge is scientific knowledge. There are other reasons why all definite knowledge is not in the domain of science. Parts of the universe are; the universe as a whole isn’t. The sentient body is; the Self that is clothed by that body isn’t. Analysis of both these wholes reveals the possibility of the existence of a third entity that is beyond scientific knowledge. This humanity calls God. A detailed investigation not conducted but outlined here reveals that (a) Russell’s claim that science holds a monopoly of definite knowledge is false: he probably meant that science has a monopoly of objectively verifiable knowledge; (b) as objective verifiability is contingent upon objectively real existence, science’s monopoly is over entities that are objectively real; (c) all objects of knowledge are not material objects in time and space: there are objects that, because they are not percepts, are not objectively verifiable. There is nothing indefinite about knowledge of such entities. There is nothing subjective about the knowledge of such entities either: so it is not open to science to dismiss knowledge of such entities as subjective, arising from the state of mind of the observer. Space and time are aspects of objective reality and not of subjective reality. The second part of this paper briefly examines the nature of dimensions. Space, time and Self consciousness are three types of dimensions considered. The third part of this paper speaks of a concept called immutable wholes. This is a logical culmination of the paper because dimensions are the state-giving norms of the wholes that these dimensions define and characterize. Spiritual seekers make these entities (sub specie aeternitatis) objects of their realization. Such entities as the Universe as a Whole, the Self, and God belong to this class of existents. If Universe as a Whole {not parts of it (study of which is in the domain of science), no matter how large those parts are, but the whole. Only a true seeker can tell science why the whole ≠ sum of all its parts – but that would be the subject of another paper}. (shrink)

The major point in [1] chapter 2 is the following claim: “Any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction.” So, in the case we wish to save Classical Logic we should change our Computational Model. As we see in chapter two, the mentioned contradiction is about and around the concept of time, as it is in the contradiction of modified version of paradox. It is natural to (...) try fabricating the paradox not by time but in some other linear ordering or the concept of space. Interestingly, the attempts to have similar contradiction by the other concepts like space and linear ordering, is failed. It is remarkable that, the paradox is considered either Epistemological or Logical traditionally, but by new considerations the new version of paradox should be considered as either Logical or Physical paradox. Hence, in order to change our Computational Model, it is natural to change the concept of time, but how? We start from some models that are different from the classical one but they are intuitively plausible. The idea of model is somewhat introduced by Brouwer and Husserl [3]. This model doesn’t refute the paradox, since the paradox and the associated contradiction would be repeated in this new model. The model is introduced in [2]. Here we give some more explanations. (shrink)

“Neutrosophics Knowledge” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. The submitted papers should be professional, in good English and Arabic, containing a brief review of a problem and obtained results. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as (...) their interactions with different ideational spectra. (shrink)

Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than forcing their unification. In this paper, we introduce nested sequent calculi for propositional standpoint logics---proof systems that manipulate trees whose nodes are multisets of formulae---and show how to automate standpoint reasoning by means of non-deterministic proof-search algorithms. To obtain worst-case complexity-optimal proof-search, we introduce a novel technique in the context (...) of nested sequents, referred to as "coloring," which consists of taking a formula as input, guessing a certain coloring of its subformulae, and then running proof-search in a nested sequent calculus on the colored input. Our technique lets us decide the validity of standpoint formulae in CoNP since proof-search only produces a partial proof relative to each permitted coloring of the input. We show how all partial proofs can be fused together to construct a complete proof when the input is valid, and how certain partial proofs can be transformed into a counter-model when the input is invalid. These "certificates" (i.e. proofs and counter-models) serve as explanations of the (in)validity of the input. (shrink)

In the view of my philosophical position “nominal conceptualism”, cognitive/knowledge agents, who are in some way aware of expressing the world based on their mental concepts, deal with their linguistic and/or symbolic expressions. In this paper I rely on nominal conceptualism to logically characterise agents’ concept-based descriptions of the world and analyse a fundamental logical system for conception representation.

Commonplace syntactic constructions in natural language seem to generate ontological commitments to a dazzling array of metaphysical categories - aggregations, sets, ordered n-tuples, possible worlds, intensional entities, ideal objects, species, intensive and extensive quantities, stuffs, situations, states, courses of events, nonexistent objects, intentional and discourse objects, general objects, plural objects, variable objects, arbitrary objects, vague kinds and concepts, fuzzy sets, and so forth. But just because a syntactic construction in some natural language appears to invoke a new (...) category of entity, are we theoreticians epistemically justified in holding that there are such entities? This would hardly seem sufficient. To be epistemically justified, the ontology to which we theoreticians are committed must pass strict standards: the entities must be of the sort required by our best comprehensive theory of the world. The thesis of this paper is that fine-grained type-free intensional entities are like this. If the thesis is right, these entities have a special objective status perhaps not possessed by some of the other ontological categories associated with special syntactic constructions in natural language. In fact, it is plausible to hold that fine-grained type-free intensional entities provide the proper minimal framework for constructing logical and linguistic theories. In this paper my strategy will be to survey the competing conceptions of fine-grained type-free intensionality and to present arguments in support of one of them. Following this narrowing down process, I will go on to the indicated epistemological considerations. (shrink)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection of sentences, (...) above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

The topics approached in the 52 papers included in this book are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft (...) sets; LA-semihypergroups; single valued trapezoidal neutrosophic number; inclusion relation; Q-linguistic neutrosophic variable set; vector similarity measure; fundamental neutro-homomorphism theorem; neutro-isomorphism theorem; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; cloud model; Maclaurin symmetric mean; pseudo-BCI algebra; hesitant fuzzy set; photovoltaic plan; decision-making trial and evaluation laboratory (DEMATEL); Choquet integral; fuzzy measure; clustering algorithm; and many more. (shrink)

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the (...) single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. (shrink)

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper (...) is to show that a large class of non-classical logics are strong enough to formulate their own model theory in a corresponding non-classical set theory. Specifically I show that adequate definitions of validity can be given for the propositional calculus in such a way that the metatheory proves, in the specified logic, that every theorem of the propositional fragment of that logic is validated. It is shown that in some cases it may fail to be a classical matter whether a given sentence is valid or not. One surprising conclusion for non-classical accounts of vagueness is drawn: there can be no axiomatic, and therefore precise, system which is determinately sound and complete. (shrink)

“Probably Peirce’s best-known works are the first two articles in a series of six that originally were collectively entitled Illustrations of the Logic of Science and published in Popular Science Monthly from November 1877 through August 1878. The first is entitled ‘The Fixation of Belief’ and the second is entitled ‘How to Make Our Ideas Clear.’ In the first of these papers Peirce defended, in a manner consistent with not accepting naive realism, the superiority of the scientific method over other (...) methods of overcoming doubt and ‘fixing belief.’” — Robert Burch, “Charles Sanders Peirce,” entry in the Stanford Encyclopedia of Philosophy (2021 revision) -/- “Pragmatist epistemologies often explore how we can carry out inquiries in a self-controlled and fruitful way. (Where much analytic epistemology centres around the concept of knowledge, considered as an idealised end-point of human thought, pragmatist epistemology centres around the concept of inquiry, considered as the process of knowledge-seeking and how we can improve it.) So pragmatists often provide rich accounts of the capacities or virtues that we must possess in order to inquire well, and the rules or guiding principles that we should adopt. A canonical account is Peirce’s classic early paper ‘The Fixation of Belief‘. Here Peirce states that inquiry is a struggle to replace doubt with “settled belief“, and that the only method of inquiry that can make sense of the fact that at least some of us are disturbed by inconsistent beliefs, and will subsequently reflect upon which methods of fixing belief are correct is the Method of Science, which draws on the Pragmatic Maxim described above. This contrasts with three other methods of fixing belief: i) refusing to consider evidence contrary to one’s favored beliefs (the Method of Tenacity), ii) accepting an institution’s dictates (the Method of Authority), iii) developing the most rationally coherent or elegant-seeming belief-set (the A Priori Method).“ — Catherine Legg, “Pragmatism,” entry in the Stanford Encyclopedia of Philosophy (2021 revision). (shrink)

This paper aims to reassess a notion in the works of the later Husserl that is both historically important and philosophically insightful, but remains understudied, namely, that of type. In opposition to a standard reading which treats Husserl’s type presentations as pre-conceptual habits, this paper argues that these representations are a specific kind of concept. More precisely, it shows that Husserl’s account of type presentations is akin to the contemporary prototype theory of concepts. This is historically important, since the (...) predecessor of the prototype theory is usually said to be Wittgenstein. From a philosophical standpoint, the paper shows that Husserl has an innovative account of the connection between type concepts and their extension. Contrary to the standard view of extensions as sets and thus sharp entities, Husserl develops a correlationalist theory of concepts, according to which, for the specific characteristics in the structure of a concept, there are corresponding characteristics in the arrangement of its members, and vice versa. According to this theory, while sharp concepts lead to sharp extensions, vague concepts such as (proto)type concepts lead to vague extensions. The paper presents this understanding of Husserl in detail and explains its philosophical significance. (shrink)

What is it to share the same concept? The question is an important one since sharing the same concept explains our ability to non-accidentally coordinate on the same topic over time and between individuals. Moreover, concept identity grounds key logical relations among thought contents such as samesaying, contradiction, validity, and entailment. Finally, an account of concept identity is crucial to explaining and justifying epistemic efforts to better understand the precise contents of our thoughts. The key question, then, is what psychological (...) and social facts could play these roles? Elsewhere, we have argued for a specific relational model of concept identity, the connectedness model (e.g. Schroeter 2012, Schroeter and Schroeter 2014, 2015). Our aim in this chapter is to further explain the motivations behind that account, to address worries about transitivity and vagueness, and to contrast our approach with closely related accounts of concept identity developed by François Recanati and Simon Prosser. -/- What’s distinctive of our approach is that we seek to vindicate the first-person epistemic perspective of concept users. Concepts, on our account, play a crucial normative role in setting regulative ideals for the representational practices in which individual subjects participate. This focus on the normative role of concepts – as opposed to a purely causal explanatory role – motivates our approach to concept identity and our toleration of vagueness and borderline cases. (shrink)

2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and (...) they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics. (shrink)

Neutrosophic set is a new mathematical tool for handling problems involving imprecise, indetermi nacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics. Recently, we applied neutrosophic set theory to pseudo-BCI al gebras. In this paper, we study neutrosophic filters in pseudo-BCI algebras. The concepts of neutrosophic regular filter, neutrosophic closed filter and fuzzy regular filter in pseudo-BCI algebras are introduced, and some basic properties are discussed. (...) Moreover, the relationships among neutrosophic regular filter, fuzzy filters and anti-grouped neutrosophic filters are prese nted, and the results are proved: a neutrosophic filter (fuzzy filter) is a neutrosophic regular filter (fuzzy regular filter), if and only if it is both a neutrosophic closed filter (fuzzy closed filter) and an anti-grouped neutrosophic filter (fuzzy anti-grouped filter). (shrink)

Artificial Psychology (AP) is a highly multidisciplinary field of study in psychology. AP tries to solve problems which occur when psychologists do research and need a robust analysis method. Conventional statistical approaches have deep rooted limitations. These approaches are excellent on paper but often fail to model the real world. Mind researchers have been trying to overcome this by simplifying the models being studied. This stance has not received much practical attention recently. Promoting and improving artificial intelligence helps mind researchers (...) to find a holistic model of mental models. This development achieves this goal by using multiple perspectives and multiple data sets together with interactive, and realistic models. In this book, the methodology of approximate inference in psychological research from a theoretical and practical perspective has been considered. Quantitative variable-oriented methodology and qualitative case-oriented methods are both used to explain the set-oriented methodology and this book combines the precision of quantitative methods with information from qualitative methods. This is a book that many researchers can use to expand and deepen their psychological research and is a book which can be useful to postgraduate students. The reader does not need an in-depth knowledge of mathematics or statistics because statistical and mathematical intuitions are key here and they will be learned through practice. What is important is to understand and use the new application of the methods for finding new, dynamic and realistic interpretations. This book incorporates theoretical fuzzy inference and deep machine learning algorithms in practice. This is the kind of book that we wished we had had when we were students. This book covers at least some of the most important issues in mind research including uncertainty, fuzziness, continuity, complexity and high dimensionality which are inherent to mind data. These are elements of artificial psychology. This book implements models using R software. (shrink)

This paper is devoted to Plithogeny, Plithogenic Set, and its extensions. These concepts are branches of uncertainty and indeterminacy instruments of practical and theoretical interest. Starting with some examples, we proceed towards general structures. Then we present definitions and applications of the principal concepts derived from plithogeny, and relate them to complex problems.

Abilitism is an approach to the metaphysics of concepts according to which each concept consists of a managing cognitive ability coordinating other abilities (cognitive and non-cognitive) and a set of subordinate abilities associated with this managing ability. As I argue here, if we accept the abilitist approach, we can efficiently solve such puzzles in the metaphysics of concepts as the partial possession problem, the concept pluralism problem, etc. However, there are some possible objections to abilitism, concerning the abilitist (...) explanation of compositional properties of concepts, knowledge-that, an extension/intension of concepts, and the idea that concepts are constituents of thought. As I demonstrate here, these objections can be answered. (shrink)

It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so possible taking into account the logical openness relationship between observer and system. We are going to show how considering the truth-values of quantum propositions within the context of the fuzzy sets is here more useful for systemics. In conclusion (...) we propose an example of formal quantum coherence. (shrink)

Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough stud ies have already been done. There are various ways such as fuzzy, intuitionistic and neutrosophic sets to handle these uncertainties. Although these concepts can handle incomplete information in various real-world issues, they cannot address all types of uncertainty such as indeterminate and inconsistent information. Also, plithogenic sets as a generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets, which is a set whose (...) elements are characterized by many attributes’ values. In this paper, our aim is to demonstrate and review the history of fuzzy, intuitionistic and neutrosophic sets. For this purpose, we divided the paper as: section 1. History of Fuzzy Sets, section 2. History of Intuitionistic Fuzzy Sets and section 3. History of Neutrosophic Theories and Applications, section 4. History of Plithogenic Sets. (shrink)

A theistic science would have to represent the integration of all kinds of knowledge intent on explaining the whole of reality. These would include, at least, history, metaphysics, theology, formal logic, mathematics, and experimental sciences. However, what is the whole of reality that one wants to explain? :.

The so-called materially valid inferences have come to new prominence through the work of Robert Brandom. This paper introduces a fragment of a logic of concepts that does not reduce concepts to their extensions. Concept logic and ist semantics allow us to represent the conceptual knowledge used in material inferences and thus suggests a way to deal with them.

This present work is a historical analysis of the notion of truth understood as the main epistemic value. The Baden School’s views on truth are presented as gradually developing from strictly epistemological conceptions towards distinctly ontological ones. In the times of the emancipation of new sciences the focus on epistemology was an attempt to provide philosophy with its own place in human knowledge. The ontological turn followed the growth of interest in the way cognition refers to reality. The work consists (...) of four chapters which present in the historically-philosophical order the views of selected members of the Baden School: Wilhelm Windelband, Heinrich Rickert, Emil Lask and Bruno Bauch. Each of the chapters follows what is assumed to be a set of fundamental problems in the theory of truth. (shrink)