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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. 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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  5. 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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  6. 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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  7. Proof Terms for Classical Derivations.Restall Greg - manuscript
    I give an account of proof terms for derivations in a sequent calculus for classical propositional logic. The term for a derivation δ of a sequent Σ≻Δ encodes how the premises Σ and conclusions Δ are related in δ. This encoding is many–to–one in the sense that different derivations can have the same proof term, since different derivations may be different ways of representing the same underlying connection between premises and conclusions. However, not all proof terms for a sequent Σ≻Δ (...)
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  8. The Orthologic of Epistemic Modals.Wesley H. Holliday & Matthew Mandelkern - manuscript
    Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form ‘p, but it might be that not p’ appears to be a contradiction, 'might not p' does not entail 'not p', which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. Some theories predict that (...)
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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. In Quest of Universal Logic: A brief overview of formal logic's evolution.Arman Kashef - manuscript
    As a result of trying to distinguish between what we do not know as humans and what we do know, concepts such as dialectic were formed. On this basis, logic was developed to monitor arguments' validity and provide methods for creating valid complex arguments. This work provides a brief overview of such topics and studies the development of formal logic and its semantics. In doing so, we enter the territory of propositional logic and predicate logic. In the next edition, we (...)
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  12. 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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  13. 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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  14. 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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  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. 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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  17. 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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  18. 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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  19. 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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  20. 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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  21. 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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  22. Montague's Paradox without Necessitation.T. Parent - manuscript
    Some such as Dean (2014) suggest that Montague's paradox requires the necessitation rule, and that the use of the rule in such a context is contentious. But here, I show that the paradox arises independently of the necessitation rule. A derivation of the paradox is given in modal system T without deploying necessitation; a necessitation-free derivation is also formulated in a weaker system that is not even complete with respect to truth-functional validities.
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  23. Modest versus Ultra-Modest Dialetheism.T. Parent - manuscript
    Jc Beall is known for defending modest dialetheism; this is the view that there are dialetheia, but only in the form of “spandrels” arising otherwise reasonable semantic terminology (e.g., the Liar paradox). Beall also regards his view as modest in partaking of a deflationary view of truth, a view where ‘true’ is a device of disquotational inference which expresses no “substantive property.” Beall supports deflationism by an appeal to Ockham’s razor; however, the premise that ‘true’ is always disquotational is found (...)
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  24. Intensionality from Self-Reference.T. Parent - manuscript
    If a semantically open language has no constraints on self-reference, one can prove an absurdity. The argument exploits a self-referential function symbol where the expressed function ends up being intensional in virtue of self-reference. The prohibition on intensional functions thus entails that self-reference cannot be unconstrained, even in a language that is free of semantic terms. However, since intensional functions are already excluded in classical logic, there are no drastic revisionary implications here. Still, the argument reveals a new sort of (...)
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  25. 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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  26. The Theory of Relations, Complex Terms, and a Connection Between λ and ε Calculi.Edward N. Zalta - manuscript
    This paper introduces a new method of interpreting complex relation terms in a second-order quantified modal language. We develop a completely general second-order modal language with two kinds of complex terms: one kind for denoting individuals and one kind for denoting n-place relations. Several issues arise in connection with previous, algebraic methods for interpreting the relation terms. The new method of interpreting these terms described here addresses those issues while establishing an interesting connection between λ and ε calculi. The resulting (...)
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  27. 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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  28. 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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  29. Logical Characterisation of Possibilistic and Probabilistic Descriptions of Events in Description Logics.Farshad Badie - forthcoming - Bulletin of the Section of Logic.
    Description Logics (DLs) are a family of formal knowledge representation formalisms and the most well-known formalisms in semantics-based systems. The central focus of this research is on logical-terminological characterisation/analysis of possibilistic and probabilistic descriptions of events in DLs. Based on a logical characterisation of the concept of `being', this paper conceptualises events within DLs world descriptions. Accordingly, it deals with the concepts of `possibility of events' and `probability of events'. The main goal of this research is to investigate how possible (...)
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  30. Los monstruos kaplanianos y la lógica de los demostrativos.Tomas Barrero - forthcoming - Ideas y Valores. Revista Colombiana de Filosofía.
    ¿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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  31. Peirce’s Triadic Logic and Its (Overlooked) Connexive Expansion.Alex Belikov - forthcoming - Logic and Logical Philosophy:1.
    In this paper, we present two variants of Peirce’s Triadic Logic within a language containing only conjunction, disjunction, and negation. The peculiarity of our systems is that conjunction and disjunction are interpreted by means of Peirce’s mysterious binary operations Ψ and Φ from his ‘Logical Notebook’. We show that semantic conditions that can be extracted from the definitions of Ψ and Φ agree (in some sense) with the traditional view on the semantic conditions of conjunction and disjunction. Thus, we support (...)
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  32. Characterizing existence of a measurable cardinal via modal logic.G. Bezhanishvili, N. Bezhanishvili, J. Lucero-Bryan & J. van Mill - forthcoming - Journal of Symbolic Logic:1-15.
    We prove that the existence of a measurable cardinal is equivalent to the existence of a normal space whose modal logic coincides with the modal logic of the Kripke frame isomorphic to the powerset of a two element set.
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  33. 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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  34. 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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  35. Twist-Valued Models for Three-Valued Paraconsistent Set Theory.Walter A. Carnielli & Marcelo E. Coniglio - forthcoming - Logic and Logical Philosophy:1.
    We propose in this paper a family of algebraic models of ZFC based on the three-valued paraconsistent logic LPT0, a linguistic variant of da Costa and D’Ottaviano’s logic J3. The semantics is given by twist structures defined over complete Boolean agebras. The Boolean-valued models of ZFC are adapted to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. This allows for inconsistent sets w satisfying ‘not (w = w)’, where ‘not’ stands for the paraconsistent negation. Finally, our (...)
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  36. Logics of Formal Inconsistency Enriched with Replacement: An Algebraic and Modal Account.Walter Carnielli, Marcelo E. Coniglio & David Fuenmayor - forthcoming - 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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  37. 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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  38. Sorites, Curry and Suitable Models.Bruno Da Ré & Paula Teijeiro - forthcoming - Logic and Logical Philosophy:1.
    In this paper we present two new approaches for dealing with semantic paradoxes and soritical predicates based on fuzzy logic. We show that both of them have conceptual advantages over the more traditional Łukasiewicz approach, and that the second one even avoids standard proofs of ω-nconsistency.
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  39. Doing without action types.Hein Duijf, Jan Broersen, Alexandra Kuncová & Aldo Iván Ramírez Abarca - forthcoming - Review of Symbolic Logic:1-31.
    This paper explores the analysis of ability, where ability is to be understood in the epistemic sense—in contrast to what might be called a causal sense. There are plenty of cases where an agent is able to perform an action that guarantees a given result even though she does not know which of her actions guarantees that result. Such an agent possesses the causal ability but lacks the epistemic ability. The standard analysis of such epistemic abilities relies on the notion (...)
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  40. Logical Nihilism and the Logic of ‘prem’.Andreas Fjellstad - forthcoming - Logic and Logical Philosophy:1.
    As the final component of a chain of reasoning intended to take us all the way to logical nihilism, Russell (2018) presents the atomic sentence ‘prem’ which is supposed to be true when featuring as premise in an argument and false when featuring as conclusion in an argument. Such a sentence requires a non-reflexive logic and an endnote by Russell (2018) could easily leave the reader with the impression that going non-reflexive suffices for logical nihilism. This paper shows how one (...)
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  41. 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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  42. ‘Or both’: A note on the alleged exclusivity of disjunction in English.Kaave Lajevardi - forthcoming - Analysis.
    I make a point concerning the construction ‘A or B or both’ in English, to the effect that if the connective ‘or’ is understood exclusively across the board then this familiar construction cannot convey the intended inclusive sense of disjunction. If we take ‘or’ inclusively, ‘A or B or both’ has the function of emphasizing that the disjunction is inclusive; taking ‘or’ exclusively, it does nothing.
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  43. Belnap-Dunn Semantics for the Variants of BN4 and E4 which Contain Routley and Meyer’s Logic B.Sandra M. López - forthcoming - Logic and Logical Philosophy:29-56.
    The logics BN4 and E4 can be considered as the 4-valued logics of the relevant conditional and (relevant) entailment, respectively. The logic BN4 was developed by Brady in 1982 and the logic E4 by Robles and Méndez in 2016. The aim of this paper is to investigate the implicative variants (of both systems) which contain Routley and Meyer’s logic B and endow them with a Belnap-Dunn type bivalent semantics.
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  44. Sequent Calculi and Interpolation for Non-Normal Modal and Deontic Logics.Eugenio Orlandelli - forthcoming - Logic and Logical Philosophy:1.
    G3-style sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are studied. For each calculus we prove that weakening and contraction are height-preserving admissible, and we give a syntactic proof of the admissibility of cut. This implies that the subformula property holds and that derivability can be decided by a terminating proof search whose complexity is in Pspace. These calculi are shown to be equivalent to the axiomatic ones and, therefore, they are (...)
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  45. The Nonarithmeticity of the Predicate Logic of Strictly Primitive Recursive Realizability.Valery Plisko - forthcoming - Review of Symbolic Logic:1-30.
    A notion of strictly primitive recursive realizability is introduced by Damnjanovic in 1994. It is a kind of constructive semantics of the arithmetical sentences using primitive recursive functions. It is of interest to study the corresponding predicate logic. It was argued by Park in 2003 that the predicate logic of strictly primitive recursive realizability is not arithmetical. Park’s argument is essentially based on a claim of Damnjanovic that intuitionistic logic is sound with respect to strictly primitive recursive realizability, but that (...)
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  46. Chisholm's Modal Paradox(es) and Counterpart Theory 50 Years On.Murali Ramachandran - forthcoming - Logic and Logical Philosophy:1.
    Lewis’s [1968] counterpart theory (LCT for short), motivated by his modal realism, made its appearance within a year of Chisholm’s modal paradox [1967]. We are not modal realists, but we argue that a satisfactory resolution to the paradox calls for a counterpart-theoretic (CT-)semantics. We make our case by showing that the Chandler–Salmon strategy of denying the S4 axiom [◊◊ψ →◊ψ] is inadequate to resolve the paradox – we take on Salmon’s attempts to defend that strategy against objects from Lewis and (...)
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  47. 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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  48. The Ontological Innocence of Schematic Logic.Oliver William Tatton-Brown - forthcoming - Logic and Logical Philosophy:1.
    This paper gives a semantics for schematic logic, proving soundness and completeness. The argument for soundness is carried out in ontologically innocent fashion, relying only on the existence of formulae which are actually written down in the course of a derivation in the logic. This makes the logic available to a nominalist, even a nominalist who does not wish to rely on modal notions, and who accepts the possibility that the universe may in fact be finite.
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  49. A "Distributive" or a "Collective" Approach to Sentences?Piotr Łukowski - forthcoming - Logic and Logical Philosophy:1.
  50. Content Implication and the Yablo’s Sequent of Sentences.Piotr Łukowski - forthcoming - Logic and Logical Philosophy:1.
1 — 50 / 969