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  1. Knowledge & Logic: Towards a science of knowledge.Luis M. Augusto - manuscript
    Just started a new book. The aim is to establish a science of knowledge in the same way that we have a science of physics or a science of materials. This might appear as an overly ambitious, possibly arrogant, objective, but bear with me. On the day I am beginning to write it–June 7th, 2020–, I think I am in possession of a few things that will help me to achieve this objective. Again, bear with me. My aim is well (...)
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  2. Halfway Up To the Mathematical Infinity I: On the Ontological & Epistemic Sustainability of Georg Cantor’s Transfinite Design.Edward G. Belaga - manuscript
    Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty ordinal construction and his fundamental powerset description of the continuum, Cantor has also left to us his obsessive presumption that the universe of sets should be subjected to laws similar to those governing the set of natural numbers, including the universal principles of cardinal comparability (...)
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  3. Homo deceptus: How language creates its own reality.Bruce Bokor - manuscript
    Homo deceptus is a book that brings together new ideas on language, consciousness and physics into a comprehensive theory that unifies science and philosophy in a different kind of Theory of Everything. The subject of how we are to make sense of the world is addressed in a structured and ordered manner, which starts with a recognition that scientific truths are constructed within a linguistic framework. The author argues that an epistemic foundation of natural language must be understood before laying (...)
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  4. A Note on Logical Paradoxes and Aristotelian Square of Opposition.Beppe Brivec - manuscript
    According to Aristotle if a universal proposition (for example: “All men are white”) is true, its contrary proposition (“All men are not white”) must be false; and, according to Aristotle, if a universal proposition (for example: “All men are white”) is true, its contradictory proposition (“Not all men are white”) must be false. I agree with what Aristotle wrote about universal propositions, but there are universal propositions which have no contrary proposition and have no contradictory proposition. The proposition X “All (...)
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  5. Pragmatic Nonsense.Ricardo Peraça Cavassane, Itala M. Loffredo D'Ottaviano & Felipe Sobreira Abrahão - manuscript
    Inspired by the early Wittgenstein’s concept of nonsense (meaning that which lies beyond the limits of language), we define two different, yet complementary, types of nonsense: formal nonsense and pragmatic nonsense. The simpler notion of formal nonsense is initially defined within Tarski’s semantic theory of truth; the notion of pragmatic nonsense, by its turn, is formulated within the context of the theory of pragmatic truth, also known as quasi-truth, as formalized by da Costa and his collaborators. While an expression will (...)
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  6. The Synthetic Concept of Truth and its Descendants.Boris Culina - manuscript
    The concept of truth has many aims but only one source. The article describes the primary concept of truth, here called the synthetic concept of truth, according to which truth is the objective result of the synthesis of us and nature in the process of rational cognition. It is shown how various aspects of the concept of truth -- logical, scientific, and mathematical aspect -- arise from the synthetic concept of truth. Also, it is shown how the paradoxes of truth (...)
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  7. Introduction to Mathematical Logic, Edition 2021.Vilnis Detlovs & Karlis Podnieks - manuscript
    Textbook for students in mathematical logic. Part 1. Total formalization is possible! Formal theories. First order languages. Axioms of constructive and classical logic. Proving formulas in propositional and predicate logic. Glivenko's theorem and constructive embedding. Axiom independence. Interpretations, models and completeness theorems. Normal forms. Tableaux method. Resolution method. Herbrand's theorem.
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  8. Is Classical Mathematics Appropriate for Theory of Computation?Farzad Didehvar - manuscript
    Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...)
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  9. Introduction to CAT4. Part 3. Semantics.Andrew Thomas Holster - manuscript
    CAT4 is proposed as a general method for representing information, enabling a powerful programming method for large-scale information systems. It enables generalised machine learning, software automation and novel AI capabilities. This is Part 3 of a five-part introduction. The focus here is on explaining the semantic model for CAT4. Points in CAT4 graphs represent facts. We introduce all the formal (data) elements used in the classic semantic model: sense or intension (1st and 2nd joins), reference (3rd join), functions (4th join), (...)
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  10. Some Open Questions about Degrees of Paradoxes.Ming Hsiung - manuscript
    We can classify the (truth-theoretic) paradoxes according to their degrees of paradoxicality. Roughly speaking, two paradoxes have the same degrees of paradoxicality, if they lead to a contradiction under the same conditions, and one paradox has a (non-strictly) lower degree of paradoxicality than another, if whenever the former leads to a contradiction under a condition, the latter does so under the same condition. In this paper, we outline some results and questions around the degrees of paradoxicality and summarize recent progress.
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  11. Valuations.Jean-Louis Lenard - manuscript
    Is logic empirical? Is logic to be found in the world? Or is logic rather a convention, a product of conventions, part of the many rules that regulate the language game? Answers fall in either camp. We like the linguistic answer. In this paper, we want to analyze how a linguistic community would tackle the problem of developing a logic and show how the linguistic conventions adopted by the community determine the properties of the local logic. Then show how to (...)
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  12. Meaning, Presuppositions, Truth-relevance, Gödel's Sentence and the Liar Paradox.X. Y. Newberry - manuscript
    Section 1 reviews Strawson’s logic of presuppositions. Strawson’s justification is critiqued and a new justification proposed. Section 2 extends the logic of presuppositions to cases when the subject class is necessarily empty, such as (x)((Px & ~Px) → Qx) . The strong similarity of the resulting logic with Richard Diaz’s truth-relevant logic is pointed out. Section 3 further extends the logic of presuppositions to sentences with many variables, and a certain valuation is proposed. It is noted that, given this valuation, (...)
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  13. Gaps, Gluts, and Theoretical Equivalence.Carlo Nicolai - manuscript
    When are two formal theories of broadly logical concepts, such as truth, equivalent? The paper investigates a case study, involving two well-known variants Kripke-Feferman truth. The first, KF+CONS, features a consistent but partial truth predicate. The second, KF+COMP, an inconsistent but complete truth predicate. It is well-known that the two truth predicates are dual to each other. We show that this duality reveals a much stricter correspondence between the two theories: they are intertraslatable. Intertranslatability under natural assumptions coincides with definitional (...)
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  14. Deductively Sound Formal Proofs.P. Olcott - manuscript
    Could the intersection of [formal proofs of mathematical logic] and [sound deductive inference] specify formal systems having [deductively sound formal proofs of mathematical logic]? All that we have to do to provide [deductively sound formal proofs of mathematical logic] is select the subset of conventional [formal proofs of mathematical logic] having true premises and now we have [deductively sound formal proofs of mathematical logic].
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  15. Proof that Wittgenstein is correct about Gödel.P. Olcott - manuscript
    The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic property of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide valid the deductive inference. Conclusions of sound arguments are derived from truth preserving finite string transformations applied to true premises.
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  16. Refuting Tarski and Gödel with a Sound Deductive Formalism.P. Olcott - manuscript
    The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic value of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide the valid deductive inference. Sound deductive conclusions are the result of these finite string transformation rules.
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  17. Prolog detects pathological self reference in the Gödel sentence.P. Olcott - manuscript
    This sentence G ↔ ¬(F ⊢ G) and its negation G ↔ ~(F ⊢ ¬G) are shown to meet the conventional definition of incompleteness: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)). They meet conventional definition of incompleteness because neither the sentence nor its negation is provable in F (or any other formal system). -- .
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  18. Defining Gödel Incompleteness Away.P. Olcott - manuscript
    We can simply define Gödel 1931 Incompleteness away by redefining the meaning of the standard definition of Incompleteness: A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ). This definition construes the existence of self-contradictory expressions in a formal system as proof that this formal system is incomplete because self-contradictory expressions are neither provable nor disprovable in this formal system. Since self-contradictory expressions are neither provable nor disprovable (...)
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  19. Minimal Type Theory (MTT).Pete Olcott - manuscript
    Minimal Type Theory (MTT) is based on type theory in that it is agnostic about Predicate Logic level and expressly disallows the evaluation of incompatible types. It is called Minimal because it has the fewest possible number of fundamental types, and has all of its syntax expressed entirely as the connections in a directed acyclic graph.
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  20. Defining a Decidability Decider.Pete Olcott - manuscript
    By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that have the semantic error of Pathological self-reference(Olcott 2004). The foundation of this system requires the notion of a BaseFact that anchors the semantic notions of True and False. When-so-ever a formal proof from BaseFacts of language L to a closed WFF X or ~X of language L does not exist X is decided to be semantically (...)
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  21. Why `Might'?Giorgio Sbardolini - manuscript
    Why do we use epistemic modals like 'might'? According to Factualism, the function of 'might' is to exchange information about state-of-affairs in the modal universe. As an alternative to Factualism, this paper offers a game-theoretic rationale for epistemic possibility operators in a Bayesian setting. The background picture is one whereby communication facilitates coordination, but coordination could fail if there's too much uncertainty, since the players' ability to share a belief is undermined. However, 'might' and related expressions can be used to (...)
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  22. Formalization of dialectical logic, Separation theory of truth. Logic of cellular automata.Zhou Senhai - manuscript
    By separating the general concept of truth into syntactic truth and semantic truth, this article proposes a new theory of truth to explain several paradoxes like the Liar paradox, Card paradox, Curry’s paradox, etc. By revealing the relationship between syntactic /semantic truth and being-nothing-becoming which are the core concepts of dialectical logic, it is able to formalize dialectical logic. It also provides a logical basis for complexity theory by transferring all reasoning into a directed (cyclic/acyclic) graph which explains both paradoxical (...)
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  23. A comprehensive theory of induction and abstraction, part I.Cael L. Hasse -
    I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act as (...)
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  24. The Significance of Evidence-based Reasoning for Mathematics, Mathematics Education, Philosophy and the Natural Sciences.Bhupinder Singh Anand - forthcoming
    In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...)
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  25. Categorical Quantification.Constantin C. Brîncuș - forthcoming - Bulletin of Symbolic Logic:1-27.
    Due to Gӧdel’s incompleteness results, the categoricity of a sufficiently rich mathematical theory and the semantic completeness of its underlying logic are two mutually exclusive ideals. For first- and second-order logics we obtain one of them with the cost of losing the other. In addition, in both these logics the rules of deduction for their quantifiers are non-categorical. In this paper I examine two recent arguments –Warren (2020), Murzi and Topey (2021)– for the idea that the natural deduction rules for (...)
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  26. Carnap’s Writings on Semantics.Constantin C. Brîncuș - forthcoming - In Christian Damböck & Georg Schiemer (eds.), Rudolf Carnap Handbuch. Metzler Verlag.
    This paper is a short introduction to Carnap’s writings on semantics with an emphasis on the transition from the syntactic period to the semantic one. I claim that one of Carnap’s main aims was to investigate the possibility of the symmetry between the syntactic and the semantic methods of approaching philosophical problems, both in logic and in the philosophy of science. This ideal of methodological symmetry could be described as an attempt to obtain categorical logical systems, i.e., systems that allow (...)
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  27. AISC 2018 - Extended Abstract Pavia - December 2018.Fabrizio Calzavarini & Antonio Lieto - forthcoming - In Cristiano Chesi (ed.), AISC Proceedings, Pavia. 27100 Pavia, Province of Pavia, Italy: pp. 20-23.
    Extended abstract presented at the AISC 2018 Conference, 15th International Conference of the Italian Association of Cognitive Science, Pavia.
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  28. Tarski’s Convention T: condition beta.John Corcoran - forthcoming - South American Journal of Logic 1 (1).
    Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning (...)
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  29. Logical Form, Conditionals, Pseudo-Conditionals.Andrea Iacona - forthcoming - Logic and Logical Philosophy:1-18.
    This paper raises some questions about the formalization of sentences containing ‘if’ or similar expressions. In particular, it focuses on three kinds of sentences that resemble conditionals in some respects but exhibit distinctive logical features that deserve separate consideration: whether-or-not sentences, biscuit conditionals, and concessive conditionals. As will be suggested, the examples discussed show in different ways that an adequate formalization of a sentence must take into account the content expressed by the sentence. This upshot is arguably what one should (...)
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  30. The Logic of Hyperlogic. Part A: Foundations.Alexander W. Kocurek - forthcoming - Review of Symbolic Logic:1-27.
    Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., "Intuitionistic logic is correct" or "The law of excluded middle holds") into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical consequence (truth preservation under a classical interpretation of the (...)
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  31. Nondeterministic and nonconcurrent computational semantics for BB+ and related logics.Shay Logan - forthcoming - Journal of Logic and Computation:1-20.
    In this paper, we provide a semantics for a range of positive substructural logics, including both logics with and logics without modal connectives. The semantics is novel insofar as it is meant to explicitly capture the computational flavor of these logics, and to do so in a way that builds in both nondeterministic and nonconcurrent computational processes.
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  32. Welfarist Pluralism: Pluralistic Reasons for Belief and the Value of Truth.Andrew Reisner - forthcoming - Philosophical Topics.
    This paper outlines a new pluralistic theory of normative reasons for belief, welfarist pluralism, which aims to explain how there can be basic alethic/epistemic reasons for belief and basic pragmatic/non-alethic reasons for belief that can combine to determine what one ought to believe. The paper shows how this non-derivative first-order pluralism arises from a purely welfarist account of the foundations of theoretical normativity, thereby combining foundational pragmatism with non-derivative pluralism about normative reasons for belief. In addition, this paper outlines how (...)
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  33. The Proper Formulation of the Minimalist Theory of Truth.Thomas Schindler & Julian J. Schlöder - forthcoming - The Philosophical Quarterly.
    Minimalism about truth is one of the main contenders for our best theory of truth, but minimalists face the charge of being unable to properly state their theory. Donald Davidson incisively pointed out that minimalists must generalize over occurrences of the same expression placed in two different contexts, which is futile. In order to meet the challenge, Paul Horwich argues that one can nevertheless characterize the axioms of the minimalist theory. Sten Lindström and Tim Button have independently argued that Horwich’s (...)
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  34. Base-extension Semantics for Modal Logic.Eckhardt Timo & Pym David - forthcoming - Logic Journal of the IGPL.
    In proof-theoretic semantics, meaning is based on inference. It may be seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a ‘base’ of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems K, KT , (...)
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  35. Truth dependence against transparent truth.Susanna Melkonian-Altshuler - 2024 - Asian Journal of Philosophy 3 (1):1-17.
    Beall’s (e.g., 2009, 2021) transparency theory of truth is recognized as a prominent, deflationist solution to the liar paradox. However, it has been neglected by truth theorists who have attempted to show that a deflationist theory of truth can (or cannot) account for truth dependence, i.e., the claim that the truth of a proposition depends on how things described by the proposition are, but how these things are does not depend on the truth of the proposition. Truth theorists interested in (...)
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  36. Los monstruos kaplanianos y la lógica de los demostrativos.Tomas Barrero - 2023 - Ideas y Valores. Revista Colombiana de Filosofía 72 (181):221-244.
    ¿Cómo puede la lógica representar expresiones indéxicas como “yo”, “aquí” y “ahora”? ¿Cómo no debe representarlas? Examino estas dos preguntas a partir de la Lógica de los Demostrativos (LD) de Kaplan y su impopular prohibición de operadores monstruosos. A pesar de algunos defectos de formulación, sostengo que dicha prohibición está guiada por una poderosa visión de las relaciones lógicas de validez entre oraciones con indéxicos que desafía la concepción tradicional de consecuencia lógica como preservación de la verdad y resalta el (...)
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  37. How to Conquer the Liar and Enthrone the Logical Concept of Truth.Boris Culina - 2023 - Croatian Journal of Philosophy 23 (67):1-31.
    This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical two-valued language. (...)
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  38. A Semantics for the Impure Logic of Ground.Louis deRosset & Kit Fine - 2023 - Journal of Philosophical Logic 52 (2):415-493.
    This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of the original pure system (...)
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  39. A Deontic Logic for Programming Rightful Machines: Kant’s Normative Demand for Consistency in the Law.Ava Thomas Wright - 2023 - Logics for Ai and Law: Joint Proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence (Lingai) and the International Workshop on Logic, Ai and Law (Lail).
    In this paper, I set out some basic elements of a deontic logic with an implementation appropriate for handling conflicting legal obligations for purposes of programming autonomous machine agents. Kantian justice demands that the prescriptive system of enforceable public laws be consistent, yet statutes or case holdings may often describe legal obligations that contradict; moreover, even fundamental constitutional rights may come into conflict. I argue that a deontic logic of the law should not try to work around such conflicts but, (...)
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  40. What of multi- and interdisciplinarity? A (personal) case study.Luis M. Augusto - 2022 - Journal of Knowledge Structures and Systems 3 (2):1-3.
    An analysis of--yet another--case of academic failure in multi- and interdisciplinarity. An editorial of the Journal of Knowledge Structures & Systems.
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  41. The Form in Formal Thought Disorder: A Model of Dyssyntax in Semantic Networking.Farshad Badie & Luis M. Augusto - 2022 - MDPI AI 3:353–370.
    Formal thought disorder (FTD) is a clinical mental condition that is typically diagnosable by the speech productions of patients. However, this has been a vexing condition for the clinical community, as it is not at all easy to determine what “formal” means in the plethora of symptoms exhibited. We present a logic-based model for the syntax–semantics interface in semantic networking that can not only explain, but also diagnose, FTD. Our model is based on description logic (DL), which is well known (...)
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  42. Against Cumulative Type Theory.Tim Button & Robert Trueman - 2022 - Review of Symbolic Logic 15 (4):907-49.
    Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, the type-restrictions imposed by (...)
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  43. Logics of Formal Inconsistency Enriched with Replacement: An Algebraic and Modal Account.Walter Carnielli, Marcelo E. Coniglio & David Fuenmayor - 2022 - Review of Symbolic Logic 15 (3):771-806.
    One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...)
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  44. What Topic for off-topic in WK3?Massimiliano Carrara, Filippo Mancini & Wei Zhu - 2022 - In Bjørn Jespersen (ed.), Logically Speaking. A Festschrift for Marie Duzi. London: College Publications. pp. 113-128.
    Beall (2016) proposes to read the middle-value of Weak Kleene logic as off-topic. This interpretation has recently drawn some attention: for instance, Francez has pointed out that Beall's interpretation does not meet some important requirements to count as a truth value. Moreover, Beall is silent about what a topic (or a subject matter) is. But arguably, what is a topic? is a crucial question, and an answer is really important to fully understand his proposal. Thus, our goal here is to (...)
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  45. A Pragmatic-Semiotic Defence of Bivalence.Marc Champagne - 2022 - History and Philosophy of Logic 43 (2):143-157.
    Since Peirce defined the first operators for three-valued logic, it is usually assumed that he rejected the principle of bivalence. However, I argue that, because bivalence is a principle, the strategy used by Peirce to defend logical principles can be used to defend bivalence. Construing logic as the study of substitutions of equivalent representations, Peirce showed that some patterns of substitution get realized in the very act of questioning them. While I recognize that we can devise non-classical notations, I argue (...)
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  46. Weakly Free Multialgebras.Marcelo E. Coniglio & Guilherme V. Toledo - 2022 - Bulletin of the Section of Logic 51 (1):109-141.
    In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest in (...)
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  47. Three Ways of Being Non-Material.Vincenzo Crupi & Andrea Iacona - 2022 - Studia Logica 110:47-93.
    This paper develops a probabilistic analysis of conditionals which hinges on a quantitative measure of evidential support. In order to spell out the interpreta- tion of ‘if’ suggested, we will compare it with two more familiar interpretations, the suppositional interpretation and the strict interpretation, within a formal framework which rests on fairly uncontroversial assumptions. As it will emerge, each of the three interpretations considered exhibits specific logical features that deserve separate consideration.
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  48. Bunge y la validez de la adición.Luis Estrada González & Christian Romero-Rodríguez - 2022 - In German Guerrero-Pino (ed.), Ciencia, Realismo y materialismo. Cali, Valle del Cauca, Colombia: pp. 191-202.
    En The paradox of Addition and its dissolution (1969), Mario Bunge presenta algunos argumentos para mostrar que la Regla de Adición puede ocasionar paradojas o problemas semánticos. Posteriormente, Margáin (1972) y Robles (1976) mostraron que las afirmaciones de Bunge son insostenibles, al menos desde el punto de vista de la lógica clásica. Aunque estamos de acuerdo con las críticas de Margáin y Robles, no estamos de acuerdo en el diagnóstico del origen del problema y tampoco con la manera en la (...)
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  49. Reversing logical nihilism.Tristan Grøtvedt Haze - 2022 - Synthese 200 (3):1-18.
    Gillian Russell has recently proposed counterexamples to such elementary argument forms as Conjunction Introduction and Identity. These purported counterexamples involve expressions that are sensitive to linguistic context—for example, a sentence which is true when it appears alone but false when embedded in a larger sentence. If they are genuine counterexamples, it looks as though logical nihilism—the view that there are no valid argument forms—might be true. In this paper, I argue that the purported counterexamples are not genuine, on the grounds (...)
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  50. Bilateral Inversion Principles.Nils Kürbis - 2022 - Electronic Proceedings in Theoretical Computer Science 358:202–215.
    This paper formulates a bilateral account of harmony that is an alternative to one proposed by Francez. It builds on an account of harmony for unilateral logic proposed by Kürbis and the observation that reading the rules for the connectives of bilateral logic bottom up gives the grounds and consequences of formulas with the opposite speech act. I formulate a process I call 'inversion' which allows the determination of assertive elimination rules from assertive introduction rules, and rejective elimination rules from (...)
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