We provide a logical matrix semantics and a Gentzen-style sequent calculus for the first-degree entailments valid in W. T. Parry’s logic of Analytic Implication. We achieve the former by introducing a logical matrix closely related to that inducing paracomplete weak Kleene logic, and the latter by presenting a calculus where the initial sequents and the left and right rules for negation are subject to linguistic constraints.

We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics is defined (...) in terms of a \-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints. (shrink)

The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part of a (...) larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004). The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts). Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians. The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction. Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses. This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation. Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – but also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated. In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions. This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed. (shrink)

Indian Philosophy has reached across the globe. It is popular for its practical way towards life. Study of Indian philosophy should be part of all streams of education. Film is effective tool of communication. It attracts all generations and makes strong impression in the mind. Film is always considered as an effective tool in Pedagogy. Philosophy deals with abstract concepts, their correlation and logical reasoning. It deals with the complex problem of reality. People have notion that philosophy is a dry (...) and theoretical subject. Students can understand complex philosophical ideas if they are demonstrated through films. There are films based on biographies of philosophers, life picture of great people, incidences in life of philosophers. But it can attract only limited number of audience. Some popular Hollywood films have amalgamation of science fiction, super natural elements, fantastic story guided by some philosophical principles. Such films attract audience from different strata. Viewer is totally captivated by extra ordinary super natural and fictional elements in the film. As a result, certain philosophical principles are taught to audience without their conscious effort. (Kantāsammita upadeśa) Teaching philosophy with the means of such films can be definitely effective tool in Pedagogy. Such practise will not only create liking for Indian Philosophy but will result in effective understanding of complex ideas. It can create awareness that Indian Philosophy is embraced across the globe, there are no boundaries for philosophical deliberations and there are certain common threads in different philosophical schools. Paper will take example of popular movie ‘Matrix’ to explain the principles of Advaita Vedānta. The Matrix is a 1999 science fiction film written and directed by The Wachowskis, starring Keanu Reeves, Laurence Fishburne, Carrie-Anne Moss, Hugo Weaving, and Joe Pantoliano. It states the journey of hero of the film ‘Neo’ who is aspiring for reality. He is struggling between illusory world and the real world which is presented through the means of science fiction. This paper will analyse Matrix from the perspective of Advaita Vedānta. Māyā projects the illusory world (vikṣepa) in place of Brahman (āvaraṇa). Film portrays digital world as illusory world. One sees this world as real due to limitations of body, mind and intellect. Neo goes to the real world and realises his true nature. True reality is beyond senses and sense objects (atindrīya). Concepts of Advaita Vedānta can be explained with this film. Such movies can be shown to students along with Vedanta discourses. Paper will explore ‘Film and Philosophy’ as an effective pedagogical model. (shrink)

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures (...) are given. Specifically, a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)

In this paper we consider the logics L(i,n) obtained from the (n+1)-valued Lukasiewicz logics L(n+1) by taking the order filter generated by i/n as the set of designated elements. In particular, the conditions of maximality and strong maximality among them are analyzed. We present a very general theorem that provides sufficient conditions for maximality between logics. As a consequence of this theorem, it is shown that L(i,n) is maximal w.r.t. CPL whenever n is prime. Concerning strong maximality (...) (i.e. maximality w.r.t. rules instead of only axioms), we provide algebraic arguments in order to show that the logics L(i,n) are not strongly maximal w.r.t. CPL, even for n prime. Indeed, in such case, we show that there is just one extension between L(i,n) and CPL obtained by adding to L(i,n) a kind of graded explosion rule. Finally, using these results, we show that the logics L(i,n) with n prime and i/n < 1/2 are ideal paraconsistent logics. (shrink)

In 2016, Béziau introduces a restricted notion of paraconsistency, the so-called genuine paraconsistency. A logic is genuine paraconsistent if it rejects the laws $\varphi,\neg \varphi \vdash \psi$ and $\vdash \neg (\varphi \wedge \neg \varphi)$. In that paper, the author analyzes, among the three-valued logics, which of them satisfy this property. If we consider multiple-conclusion consequence relations, the dual properties of those above-mentioned are $\vdash \varphi, \neg \varphi$ and $\neg (\varphi \vee \neg \varphi) \vdash$. We call genuine paracomplete logics (...) those rejecting the mentioned properties. We present here an analysis of the three-valued genuine paracomplete logics. A very natural twist structures semantics for these logics is also found in a systematic way. This semantics produces automatically a simple and elegant Hilbert-style characterization for all these logics. Finally, we introduce the logic LGP which is genuine paracomplete is not genuine paraconsistent, not even paraconsistent and cannot be characterized by a single finite logical matrix. (shrink)

Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices (which he called quasi-matrices), in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlev’s hierarchy, also proposing weaker six-valued systems in which the (T) axiom was replaced by the deontic (D) axiom. In this (...) paper, we propose even weaker systems, by eliminating both axioms, which are characterized by eight-valued non-deterministic matrices. In addition, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary (deterministic) logical matrices would be possible for all those Ivlev-like systems. We will show that finite deterministic matrices do not characterize any of them. (shrink)

The Belnap–Dunn logic is a well-known and well-studied four-valued logic, but until recently little has been known about its extensions, i.e. stronger logics in the same language, called super-Belnap logics here. We give an overview of several results on these logics which have been proved in recent works by Přenosil and Rivieccio. We present Hilbert-style axiomatizations, describe reduced matrix models, and give a description of the lattice of super-Belnap logics and its connections with graph theory. (...) We adopt the point of view ofAlgebraic Logic, exploring applications of the general theory of algebraization of logics to the super-Belnap family. In this respect we establish a number of new results, including a description of the algebraic counterparts, Leibniz filters, and strong versions of super-Belnap logics, as well as the classification of these logics within the Leibniz and Frege hierarchies. (shrink)

In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces (...) naturally a non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras. (shrink)

We look at extensions (i.e., stronger logics in the same language) of the Belnap–Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap–Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterise the reduced algebraic models of these new logics and prove a completeness result for the first and last element of the chain stating that both logics are determined (...) by a single finite logical matrix. We show that the last logic of the chain is not finitely axiomatisable. (shrink)

Developing a suggestion of Wittgenstein, I provide an account of truth tables as formulas of a formal language. I define the syntax and semantics of TPL (the language of Tabular Propositional Logic), and develop its proof theory. Single formulas of TPL, and finite groups of formulas with the same top row and TF matrix (depiction of possible valuations), are able to serve as their own proofs with respect to metalogical properties of interest. The situation is different, however, for groups (...) of formulas whose top rows differ. For them I provide (i) a tree-style system of ‘row tree proofs’, which is shown to be sound and complete, and (ii) an alternative, re-writing strategy. (shrink)

The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements of (...) subsets so there is a dual concept of logical entropy which is the normalized counting measure on distinctions of partitions. Thus the logical notion of information is a measure of distinctions. Classical logical entropy naturally extends to the notion of quantum logical entropy which provides a more natural and informative alternative to the usual Von Neumann entropy in quantum information theory. The quantum logical entropy of a post-measurement density matrix has the simple interpretation as the probability that two independent measurements of the same state using the same observable will have different results. The main result of the paper is that the increase in quantum logical entropy due to a projective measurement of a pure state is the sum of the absolute squares of the off-diagonal entries ("coherences") of the pure state density matrix that are zeroed ("decohered") by the measurement, i.e., the measure of the distinctions ("decoherences") created by the measurement. (shrink)

A Symbol doesn't explain, says Jung. In fact it is beyond the dichotomy of the binary logic, that wants the limiting and restrictive diktat of the tertium non datur to be perpetuated so as to be obliged to choose between two possibilities being anyway on the same nomological axis.

The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...) Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (shrink)

We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the A(Si) and i,±1 N Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of quantum mechanics. In detail we (...) realize a bare bone skeleton of quantum mechanics recovering all the basic foundations of this theory on an algebraic framework. We give proof of the quantum like Heisenberg uncertainty relations using only the basic support of the Clifford algebra. In addition we demonstrate the well known phenomenon of quantum Mach Zender interference using the same algebraic framework, as well as we give algebraic proof of quantum collapse in some cases of physical interest by direct application of the theorem that we derive to elaborate the i,±1 N algebra. We also discuss the problem of time evolution of quantum systems as well as the changes in space location, in momentum and the linked invariance principles. We are also able to re-derive the basic wave function of standard quantum mechanics by using only the Clifford algebraic approach. In this manner we obtain a full exposition of standard quantum mechanics using only the basic axioms of Clifford algebra. We also discuss more advanced features of quantum mechanics. In detail, we give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR paradox only using the Clifford algebra. By using the same approach we also derive Bell inequalities. Our formulation is strongly based on the use of idempotents that are contained in Clifford algebra. Their counterpart in quantum mechanics is represented by the projection operators that, as it is well known, are interpreted as logical statements, following the basic von Neumann results. Von Neumann realized a matrix logic on the basis of quantum mechanics. Using the Clifford algebra we are able to invert such result. According to the results previously obtained by Orlov in 1994, we are able to give proof that quantum mechanics derives from logic. We show that indeterminism and quantum interference have their origin in the logic. Therefore, it seems that we may conclude that quantum mechanics, as it appears when investigated by the Clifford algebra, is a two-faced theory in the sense that it looks from one side to “matter per se”, thus to objects but simultaneously also to conceptual entities. We advance the basic conclusion of the paper: There are stages of our reality in which we no more can separate the logic ( and thus cognition and thus conceptual entity) from the features of “matter per se”. In quantum mechanics the logic, and thus the cognition and thus the conceptual entity-cognitive performance, assume the same importance as the features of what is being described. We are at levels of reality in which the truths of logical statements about dynamic variables become dynamic variables themselves so that a profound link is established from its starting in this theory between physics and conceptual entities. Finally, in this approach there is not an absolute definition of logical truths. Transformations , and thus … “redefinitions”…. of truth values are permitted in such scheme as well as the well established invariance principles, clearly indicate . (shrink)

Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.

In this work I propose a theory of evolution as a process of unfolding. This theory is based on four logically concatenated principles. The principle of evolutionary order establishes that the more complex cannot be generated from the simpler. The principle of origin establishes that there must be a maximum complexity that originates the others by logical deduction. Finally, the principle of unfolding and the principle of actualization guarantee the development of the evolutionary process from the simplest to the most (...) complex. These logical principles determine the existence of a virtual ideological matrix that contains the sequence of the preformed and folded morphogenetic fields. In this manner, the evolutionary process consists of the sequential unfolding and actualization of these fields, which is motorized by a process of teleologization carried out by the opening consciousness of the forms included in the fields of the ideological matrix. This theory leads to a radical change of perspective regarding the materialist worldview, and places life at the center of the evolutionary process as an activity carried out by a consciousness that seeks to fulfill a purpose by actualizing its own potentialities. (shrink)

In the 20th century, the term “media logic” was introduced to denote the influence of independent mass media on political systems and other institutions. In recent years the idea has been reworked and labeled “mediatization” to widen the framework by including new media and new areas of application. In Section Two the paper discusses different conceptualizations. It is argued that even if they bring new insights, they cannot be unified into one concept, and that they also lack a consistent definition (...) of digital media. Section three provides a definition of digital media in order to identify new trajectories made possible by these media, which have led into a new media matrix built around the internet and mobile devices. It will be argued that the new media matrix cannot be understood from a point of view defined by the framework of 20th century mass media because digital media open new trajectories and because in the new matrix the previously existing media have had to transform themselves. (shrink)

This chapter is concerned with plural discourse in the grammatical sense. The goal of the chapter is to urge the value of the event analysis of the matrix of action sentences in thinking about logical form in plural discourse about action. Among the claims advanced are that: -/- 1. The ambiguity between distributive and collective readings of plural action sentences is not lexical ambiguity, either in the noun phrase (NP) or in the verb phrase (VP), but an ambiguity tracing (...) to the scope of the event quantifier introduced by the action verb. 2. This allows us to analyze collective action sentences in a way that commits us only to individual agents acting when we say that groups act, without denying that there are groups as such or that we talk about them as such. 3. Intermediate readings, that seem to be neither purely distributive nor purely collective, can be explained in terms of the same apparatus. (shrink)

Description In this paper, we propose an advanced mathematical framework centered around the Energy Number Field (E), which fundamentally avoids the conventional concept of zero by introducing a neutral ele- ment, νE. Through this approach, we redefine core mathematical constructs, including limits, continuity, differentiation, integration, and series summation, ensuring they operate seamlessly within a zero-less paradigm. We address and redefine matrix operations, topology, metric spaces, and complex analysis, aligning them with the principles of E. Additionally, we explore non-mappable properties (...) of energy numbers in the context of symmetry groups, non-standard fields, fractional calculus, and non-Euclidean geometries. By employing νE as the central element, our framework resolves conventional zero-related sin- gularities and computational anomalies, offering a novel perspective that bridges advanced mathematical theories with practical applications in physics, computational algorithms, and topological transforma- tions. This work paves the way for future research to experimentally validate these formulations and explore potential applications in advanced physics, quantum mechanics, and beyond. (shrink)

One of the primary, if not most critical, difficulties in the design and implementation of autonomous systems is the black-boxed nature of the decision-making structures and logical pathways. How human values are embodied and actualised in situ may ultimately prove to be harmful if not outright recalcitrant. For this reason, the values of stakeholders become of particular significance given the risks posed by opaque structures of intelligent agents (IAs). This paper explores how decision matrix algorithms, via the belief-desire-intention model (...) for autonomous vehicles, can be designed to minimize the risks of opaque architectures. Primarily through an explicit orientation towards designing for the values of explainability and verifiability. In doing so, this research adopts the Value Sensitive Design (VSD) approach as a principled framework for the incorporation of such values within design. VSD is recognized as a potential starting point that offers a systematic way for engineering teams to formally incorporate existing technical solutions within ethical design, while simultaneously remaining pliable to emerging issues and needs. It is concluded that the VSD methodology offers at least a strong enough foundation from which designers can begin to anticipate design needs and formulate salient design flows that can be adapted to the changing ethical landscapes required for utilisation in autonomous vehicles. (shrink)

Jung's interpretative "matrix" seems to offer us the possibility to frame the social phenomenology concerning the loss of sense, with the consequent load of experience of widespread awkwardness, in a context of epoch-making, progressive, "one-dimensional" reduction of the symbolic. -/- This seems to us the fundamental matrix of the disastrous, schizoid conflict of the present day society: on one side a literalism in keeping with the logics of power and control, disheartening any possibility of individual and collective (...) development and wellbeing; on the other side the absolute impossibility to keep together the fragments of this vision of the world, anachronistic as it appears by now, in an epoch-making realizing of what could be defined as the violence of the "monotheism" of the reason. -/- The pervasive social influence we are subjected to and we suffer even in the ephemeral shelter of our privacy speaks the language of literalism, rejects the oxygenating receptiveness to the metaphor, prefers the poor inclusive significance of the meaning to the deeper (and potentially enlivening source of psychic welfare) but embarrassing liberty of the sense. (shrink)

Some of the most enduring skeptical arguments invoke stories of deception -- the evil demon, convincing dreams, an envatted brain, the Matrix -- in order to show that we have no first-order knowledge of the external world. I confront such arguments with a dilemma: either (1) they establish no more than the logical possibility of error, in which case they fail to threaten fallible knowledge, the only kind of knowledge of the external world most of us think we have (...) anyway; or (2) they defeat themselves because they must grant us empirical knowledge or justified beliefs of the very kind they must also entirely deny us. Either way they pose no significant threat. (shrink)

In recent decades, perspectivism has developed into an independent epistemological research program. Perspectivism is based on the idea of perspective as an attempt to elucidate an object from a multitude of factors. Perspectivists are concerned with reconstructing and explaining these factors, identifying the conditioning of epistemic acts, using concepts such as “position”/“point of view,” “gaze,” “angle of view,” “horizon,” “focus,” “picture,” “relativity,” and “context”. Although these concepts are part of the perspectivist's toolkit, their content and interrelationship have not yet been (...) critically and comprehensively analyzed. The purpose of this article is to clarify the conceptual basis of perspectivism as an epistemological program, which began in the works of F. Kaulbach (1990) and W. Stegmaier (2008). For this purpose, a systematic conceptual analysis will be carried out, a detailed presentation of the logical content of perspectivist notions and their reduction into a single coherent model, which can become the conceptual basis of perspectivism. Perspectivist concepts constitute a “population” or matrix of the concept “epistemic situation”. Being consistently expounded and correlated in a conceptual model, they can be used as a tool for a detailed analysis of epistemic situations and their results (theories, positions, views, etc.). The final part of the article will formulate a number of significant implications of the new programmatic understanding of perspectivism: the status of perspectivist concepts, the distinction of perspectivism from similar epistemological programs, and the challenges for its further development. (shrink)

Although there are several monistic and dualistic approaches to the mind-body problem on the basis of classical or quantum mechanics, thus far no consensus exists about a solution. Recently, the Elementary Process Theory (EPT) has been developed: this corresponds with a fundamentally new disciplinary matrix for the study of physical reality. The purpose of the present research was to investigate the mind-body problem within this newly developed disciplinary matrix. The main finding is that the idea of a duality (...) of body and mind has to be rejected as an incomplete representation of reality: in the universe of the EPT, man hás to be a trinity of body, spirit and soul, where ‘body’, ‘spirit’ and ‘soul’ are names for distinct physical things. The mind is then a mere idea that arises from (self-)experience, but without onto-logical connotation. In addition a mechanism for mental causation, which implies a principle of choice, is rigorously formulated. The main conclusion is that a fundamentally new physicalist approach to the mind-body problem, according to which man has a free will, has been formulated strictly within the language of the EPT. Further physical research is then required to describe how the interaction between body, spirit and soul is to be understood in terms of fundamental interactions. In addition, further philosophical-theological research has to establish whether the presently discussed trinity and the trinities of body, spirit and soul mentioned in the Bible and the Vedic texts are one and the same thing. -/- Edit: a revised version of this preprint has been published as a book chapter. (shrink)

The aim of this article is to investigate the reception of Husserl’s theory of meaning by Ajdukiewicz and Blaustein, two members of the analytically-oriented Lvov-Warsaw School, who, in different ways, were attracted to and confronted with Husserl’s phenomenology. The discussed hypothesis is that Ajdukiewicz’s interpretation of Logical Investigations, and his original theory of meaning influenced both Blaustein’s critical reading of Husserl’s theory of intentionality and his account of meaning-intention. After outlining the central elements of “First Logical Investigation” the paper shows (...) how it is interpreted by Ajdukiewicz in his Lvov lectures on logic and in his directival theory of meaning. What emerges is a psychological-descriptive interpretation of Husserl’s concept of meaning, and a reconsideration of his theory of intentionality within the inferential structure of beliefs in premises that motivates a person who speaks a language to believe in conclusions of a certain form. This leads Ajdukiewicz to his own original conventionalist account of meaning which is based on the identification of three main directives of meaning that represent the matrix of a given language, i.e., the grid in which each meaning finds its place. These elements allow one to demonstrate how Ajdukiewicz’s interpretation resonates in Blaustein’s critique of Husserl in his early writings, where, in addition to a psychological-descriptive reading of phenomenology we also find a conventionalist conception of meaning acts and signitive presentations. According to Blaustein, a sign can represent an object only through the conventions arising from the directives of meaning that belong to a given natural language. (shrink)

The new phase of science evolution is characterized by totality of subject and object of cognition and technology (high-hume). As a result, forming of network structure in a disciplinary matrix modern are «human dimensional» natural sciences and two paradigmal «nuclei» (attraktors). As a result, the complication of structure of disciplinary matrix and forming a few paradigm nuclei in modern «human dimensional» natural sciences are observed. In the process of social verification integration of scientific theories into the existent system (...) of mental and valued options of spiritual culture takes place. The attribute of classical science – ethics neutrality of scientific knowledge becomes an unattainable ideal. One of the trends in the evolution of theoretical epistemology is the study of migration mechanisms of generation of scientific knowledge from the sphere of its own logic and methodology of science in the field of sociology - the consideration of this process, as the resulting system of interactions of social structures and institutions. Ensuing ideas and settings become the dominant worldview of philosophical and technological civilization. -/- . (shrink)

The new phase of science evolution is characterized by totality of subject and object of cognition and technology (high-hume). As a result, forming of network structure in a disciplinary matrix modern are «human dimensional» natural sciences and two paradigmal «nuclei» (attraktors). As a result, the complication of structure of disciplinary matrix and forming a few paradigm nuclei in modern «human dimensional» natural sciences are observed. In the process of social verification integration of scientific theories into the existent system (...) of mental and valued options of spiritual culture takes place. The attribute of classical science – ethics neutrality of scientific knowledge becomes an unattainable ideal. One of the trends in the evolution of theoretical epistemology is the study of migration mechanisms of generation of scientific knowledge from the sphere of its own logic and methodology of science in the field of sociology - the consideration of this process, as the resulting system of interactions of social structures and institutions. Ensuing ideas and settings become the dominant worldview of philosophical and technological civilization. -/- . (shrink)

Thomas Kuhn's philosophy brought a series of important ways of interpreting scientific practice, where history came to be understood as a significant part of this dynamic. In his 1962 “The Structure of Scientific Revolutions”, Kuhn provided us with some important concepts such as paradigm, normal science, anomalies and extraordinary science. From then on, science was no longer seen only as a logical structure related to discovery – but it was suggested that scientific changes occurred due to an increase in unresolved (...) problems that were sometimes ignored; contrary to what a science standardized by Popper's falsificationism could propose. Science in its normal period would be extremely traditionalist, remaining faithful to its paradigm and ignoring a series of problems – the paradigm being, among various ways of describing such a term, as a matrix of models. After many ignored and unresolved problems, a crisis can set in and from this process new paradigms can emerge: note that this dynamic can be related to a historical process within science. (shrink)

The Covid-19 pandemic raises the need for an ethical framework addressing unique questions of airborne infectious disease. In particular, are you ethically obliged to wear a face mask? If so, why and when? The Respiratory Ethics Framework (REF) herein derives answers from ethical norms. Always covering coughs and sneezes just in case you might be infectious is an ethical norm. But if you are infectious with an airborne illness, you are probably spreading germs even with every breath and vocalization. Therefore, (...) given that respiratory covering should be done to prevent spreading germs, you should wear a mask if you believe you are infectious because it also provides covering while breathing and vocalizing. REF is grounded in the non-harm principle. Why should we avoid spreading infections to others? Because they can cause bodily physical harm and we should act to prevent causing such harm to others without justifiable reason. Under REF, the magnitude of your obligation to mask is proportional to the magnitude of risk you pose to others by way of airborne germs. This functional relationship is logically modeled and visually mapped with a decision matrix in this essay. (shrink)

The paper aims to add contextual dependence to the new directival theory of meaning, a functional role semantics based on Kazimierz Ajdukiewicz’s directival theory of meaning. We show that the original formulation of the theory does not have a straight answer on how the meaning of indexicals and demonstratives is established. We illustrate it in the example of some problematic axiomatic and inferential directives containing indexicals. We show that the main reason why developing the new directival theory of meaning in (...) this direction is difficult is that the theory focuses on the notion of a sentence (and not the notion of an utterance). To add the latter notion to the theory, we introduce the idea of admissible contextual distribution being an interpretation of the hybrid expression view on indexicals and demonstratives. We argue that this idea introduces a small but important modification to the concept of language matrix and gives way to define two distinct concepts of meaning: for an expression type and for a use of an expression type. (shrink)

By pure calculus of names we mean a quantifier-free theory, based on the classical propositional calculus, which defines predicates known from Aristotle’s syllogistic and Leśniewski’s Ontology. For a large fragment of the theory decision procedures, defined by a combination of simple syntactic operations and models in two-membered domains, can be used. We compare the system which employs `ε’ as the only specific term with the system enriched with functors of Syllogistic. In the former, we do not need an empty name (...) in the model, so we are able to construct a 3-valued matrix, while for the latter, for which an empty name is necessary, the respective matrices are 4-valued. (shrink)

In this paper we present a characterization of hyper-connexivity by means of a relating semantics for Boolean connexive logics. We also show that the minimal Boolean connexive logic is Abelardian, strongly consistent, Kapsner strong and antiparadox. We give an example showing that the minimal Boolean connexive logic is not simplificative. This shows that the minimal Boolean connexive logic is not totally connexive.

This paper presents a semantical analysis of the Weak Kleene Logics Kw3 and PWK from the tradition of Bochvar and Halldén. These are three-valued logics in which a formula takes the third value if at least one of its components does. The paper establishes two main results: a characterisation result for the relation of logical con- sequence in PWK – that is, we individuate necessary and sufficient conditions for a set.

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The (...) case of QmbC, the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called QLFI1o is also studied, which is equivalent to the quantified version of da Costa and D'Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and QLFI1o with a standard equality predicate is also considered. (shrink)

In this paper the system IL for relative interpretability is studied.

We intoduce a novel extension of Description Logics (DLs) of typicality by means of probabilities able to represent and reason about typical properties and defeasible inheritance in DLs.

In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order (...) to philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we show that mbC, a logic of formal inconsistency based on classical logic, may be enhanced in order to express the basic ideas of an intuitive interpretation of contradictions as conflicting evidence. (shrink)

We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on trees are sound and (...) complete for the basic positive distributive substructural logic $\mathsf {B}^+$, that collection frames on multisets are sound and complete for $\mathsf {RW}^+$ (the relevant logic $\mathsf {R}^+$, without contraction, or equivalently, positive multiplicative and additive linear logic with distribution for the additive connectives), and that collection frames on sets are sound for the positive relevant logic $\mathsf {R}^+$. The completeness of set frames for $\mathsf {R}^+$ is, currently, an open question. (shrink)

This chapter focuses on alternative logics. It discusses a hierarchy of logical reform. It presents case studies that illustrate particular aspects of the logical revisionism discussed in the chapter. The first case study is of intuitionistic logic. The second case study turns to quantum logic, a system proposed on empirical grounds as a resolution of the antinomies of quantum mechanics. The third case study is concerned with systems of relevance logic, which have been the subject of an especially detailed (...) reform program. Finally, the fourth case study is paraconsistent logic, perhaps the most controversial of serious proposals. (shrink)

Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences of (...) a flaw. However, since different programs and machines can interact with (or be nested into) one another, we need to account for different kind of errors, and this calls for an evaluation of systems with multiple contaminating values. In this paper, we make steps toward these evaluation systems by considering two logics, HYB1 and HYB2, whose semantic interpretations account for two contaminating values beside classical values 0 and 1. In particular, we provide two main formal contributions. First, we give a characterization of their relations of (multiple-conclusion) logical consequence—that is, necessary and sufficient conditions for a set Δ of formulas to logically follow from a set Γ of formulas in HYB1 or HYB2 . Second, we provide sound and complete sequent calculi for the two logics. (shrink)

Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”.

The aim of this paper is to provide a proof-theoretic characterization of relevant logics including fusion and fission connectives, as well as Ackermann’s truth constant. We achieve this by employing the well-established methodology of labelled sequent calculi. After having introduced several systems, we will conduct a detailed proof-theoretic analysis, show a cut-admissibility theorem, and establish soundness and completeness. The paper ends with a discussion that contextualizes our current work within the broader landscape of the proof theory of relevant (...) class='Hi'>logics. (shrink)

In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalise to partial and paraconsistent (...) class='Hi'>logics once the right set-up is chosen. Our logic L4 has a semantics that also underlies Belnap’s [4] and is related to the logic of bilattices. L4 is in focus most of the time, but it is also shown how results obtained for L4 can be transferred to several variants. (shrink)

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by (...) at least some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that (...) none of them discusses our main question. This is why we finally turn to the analysis of the truth-conditions for conjunction and disjunction in infectious logics, employing the framework of plurivalent logics, as discussed by Priest. In doing so, we arrive at the interesting conclusion that —in the context of infectious logics— conjunction is conjunction, whereas disjunction is not disjunction. (shrink)

We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and (...) Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions. (shrink)

This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent (...) case, we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate. (shrink)

In this paper we propose a very general de nition of combination of logics by means of the concept of sheaves of logics. We first discuss some properties of this general definition and list some problems, as well as connections to related work. As applications of our abstract setting, we show that the notion of possible-translations semantics, introduced in previous papers by the first author, can be described in categorial terms. Possible-translations semantics constitute illustrative cases, since they provide (...) a new semantical account for abstract logical systems, particularly for many-valued and paraconsistent logics. (shrink)