Results for 'Sequent calculus'

340 found
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  1. A cut-free sequent calculus for the bi-intuitionistic logic 2Int.Sara Ayhan - manuscript
    The purpose of this paper is to introduce a bi-intuitionistic sequent calculus and to give proofs of admissibility for its structural rules. The calculus I will present, called SC2Int, is a sequent calculus for the bi-intuitionistic logic 2Int, which Wansing presents in [2016a]. There he also gives a natural deduction system for this logic, N2Int, to which SC2Int is equivalent in terms of what is derivable. What is important is that these calculi represent a kind (...)
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  2. A Cut-Free Sequent Calculus for Defeasible Erotetic Inferences.Jared Millson - 2019 - Studia Logica (6):1-34.
    In recent years, the e ffort to formalize erotetic inferences (i.e., inferences to and from questions) has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these inferences. To fill this lacuna, we construct a calculus for (classes of) sequents that are sound and complete for two species of erotetic inferences studied by Inferential Erotetic Logic (IEL): erotetic evocation and regular erotetic implication. While an attempt has been made (...)
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  3. A Nonmonotonic Sequent Calculus for Inferentialist Expressivists.Ulf Hlobil - 2016 - In Pavel Arazim & Michal Dancak (eds.), The Logica Yearbook 2015. College Publications. pp. 87-105.
    I am presenting a sequent calculus that extends a nonmonotonic consequence relation over an atomic language to a logically complex language. The system is in line with two guiding philosophical ideas: (i) logical inferentialism and (ii) logical expressivism. The extension defined by the sequent rules is conservative. The conditional tracks the consequence relation and negation tracks incoherence. Besides the ordinary propositional connectives, the sequent calculus introduces a new kind of modal operator that marks implications that (...)
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  4. A Simple Logical Matrix and Sequent Calculus for Parry’s Logic of Analytic Implication.Damian E. Szmuc - 2021 - Studia Logica 109 (4):791-828.
    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.
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  5. A multi-succedent sequent calculus for logical expressivists.Daniel Kaplan - 2018 - In Pavel Arazim & Tomas Lavicka (eds.), The Logica Yearbook 2017. College Publications. pp. 139-153.
    Expressivism in logic is the view that logical vocabulary plays a primarily expressive role: that is, that logical vocabulary makes perspicuous in the object language structural features of inference and incompatibility (Brandom, 1994, 2008). I present a precise, technical criterion of expressivity for a logic (§2). I next present a logic that meets that criterion (§3). I further explore some interesting features of that logic: first, a representation theorem for capturing other logics (§3.1), and next some novel logical vocabulary for (...)
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  6. Stoic Sequent Logic and Proof Theory.Susanne Bobzien - 2019 - History and Philosophy of Logic 40 (3):234-265.
    This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. (...)
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  7. Uniform and Modular Sequent Systems for Description Logics.Tim Lyon & Jonas Karge - 2022 - In Ofer Arieli, Martin Homola, Jean Christoph Jung & Marie-Laure Mugnier (eds.), Proceedings of the 35th International Workshop on Description Logics (DL 2022).
    We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be obtained for extensions of description logics with special formulae that we call "role relational axioms." All sequent systems are sound, complete, and possess favorable properties such as height-preserving admissibility of common structural rules and height-preserving invertibility of rules.
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  8. A Gentzen Calculus for Nothing but the Truth.Stefan Wintein & Reinhard Muskens - 2016 - Journal of Philosophical Logic 45 (4):451-465.
    In their paper Nothing but the Truth Andreas Pietz and Umberto Rivieccio present Exactly True Logic, an interesting variation upon the four-valued logic for first-degree entailment FDE that was given by Belnap and Dunn in the 1970s. Pietz & Rivieccio provide this logic with a Hilbert-style axiomatisation and write that finding a nice sequent calculus for the logic will presumably not be easy. But a sequent calculus can be given and in this paper we will show (...)
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  9. Dual Systems of Sequents and Tableaux for Many-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - Bulletin of the EATCS 51:192-197.
    The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value (...)
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  10. Syntactic Interpolation for Tense Logics and Bi-Intuitionistic Logic via Nested Sequents.Tim Lyon, Alwen Tiu, Rajeev Gore & Ranald Clouston - 2020 - In Maribel Fernandez & Anca Muscholl (eds.), 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). pp. 1-16.
    We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without (...)
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  11. The Epsilon Calculus and Herbrand Complexity.Georg Moser & Richard Zach - 2006 - Studia Logica 82 (1):133-155.
    Hilbert's ε-calculus is based on an extension of the language of predicate logic by a term-forming operator εx. Two fundamental results about the ε-calculus, the first and second epsilon theorem, play a rôle similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of (...)
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  12. Nested Sequents for Intuitionistic Modal Logics via Structural Refinement.Tim Lyon - 2021 - In Anupam Das & Sara Negri (eds.), Automated Reasoning with Analytic Tableaux and Related Methods: TABLEAUX 2021. pp. 409-427.
    We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that are (...)
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  13. A calculus for Belnap's logic in which each proof consists of two trees.Stefan Wintein & Reinhard Muskens - 2012 - Logique Et Analyse 220:643-656.
    In this paper we introduce a Gentzen calculus for (a functionally complete variant of) Belnap's logic in which establishing the provability of a sequent in general requires \emph{two} proof trees, one establishing that whenever all premises are true some conclusion is true and one that guarantees the falsity of at least one premise if all conclusions are false. The calculus can also be put to use in proving that one statement \emph{necessarily approximates} another, where necessary approximation is (...)
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  14. Automating Reasoning with Standpoint Logic via Nested Sequents.Tim Lyon & Lucía Gómez Álvarez - 2018 - In Michael Thielscher, Francesca Toni & Frank Wolter (eds.), Proceedings of the Sixteenth International Conference on Principles of Knowledge Representation and Reasoning (KR2018). pp. 257-266.
    Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than forcing their unification. In this paper, we introduce nested sequent calculi for propositional standpoint logics---proof systems that manipulate trees whose nodes are multisets of formulae---and show how to automate standpoint reasoning by means of non-deterministic proof-search algorithms. To obtain worst-case complexity-optimal proof-search, we introduce a novel technique in the (...)
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  15. Translating Metainferences Into Formulae: Satisfaction Operators and Sequent Calculi.Ariel Jonathan Roffé & Federico Pailos - 2021 - Australasian Journal of Logic 3.
    In this paper, we present a way to translate the metainferences of a mixed metainferential system into formulae of an extended-language system, called its associated σ-system. To do this, the σ-system will contain new operators (one for each standard), called the σ operators, which represent the notions of "belonging to a (given) standard". We first prove, in a model-theoretic way, that these translations preserve (in)validity. That is, that a metainference is valid in the base system if and only if its (...)
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  16. Proof Theory of Finite-valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued (...)
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  17. Proof Theory and Semantics for a Theory of Definite Descriptions.Nils Kürbis - 2021 - In Anupam Das & Sara Negri (eds.), TABLEAUX 2021, LNAI 12842.
    This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means ‘The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown (...)
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  18. A General Schema for Bilateral Proof Rules.Ryan Simonelli - 2024 - Journal of Philosophical Logic (3):1-34.
    Bilateral proof systems, which provide rules for both affirming and denying sentences, have been prominent in the development of proof-theoretic semantics for classical logic in recent years. However, such systems provide a substantial amount of freedom in the formulation of the rules, and, as a result, a number of different sets of rules have been put forward as definitive of the meanings of the classical connectives. In this paper, I argue that a single general schema for bilateral proof rules has (...)
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  19. A Binary Quantifier for Definite Descriptions for Cut Free Free Logics.Nils Kürbis - 2021 - Studia Logica 110 (1):219-239.
    This paper presents rules in sequent calculus for a binary quantifier I to formalise definite descriptions: Ix[F, G] means ‘The F is G’. The rules are suitable to be added to a system of positive free logic. The paper extends the proof of a cut elimination theorem for this system by Indrzejczak by proving the cases for the rules of I. There are also brief comparisons of the present approach to the more common one that formalises definite descriptions (...)
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  20. Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
    This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively (...)
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  21. Uniqueness of Logical Connectives in a Bilateralist Setting.Sara Ayhan - 2021 - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2020. College Publications. pp. 1-16.
    In this paper I will show the problems that are encountered when dealing with uniqueness of connectives in a bilateralist setting within the larger framework of proof-theoretic semantics and suggest a solution. Therefore, the logic 2Int is suitable, for which I introduce a sequent calculus system, displaying - just like the corresponding natural deduction system - a consequence relation for provability as well as one dual to provability. I will propose a modified characterization of uniqueness incorporating such a (...)
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  22. Elimination of Cuts in First-order Finite-valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - Journal of Information Processing and Cybernetics EIK 29 (6):333-355.
    A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.
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  23. Non-reflexive Nonsense: Proof-Theory for Paracomplete Weak Kleene Logic.Bruno Da Ré, Damian Szmuc & María Inés Corbalán - forthcoming - Studia Logica:1-17.
    Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic `of nonsense' introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic K3W by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where no variable-inclusion conditions are (...)
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  24. A paraconsistent route to semantic closure.Eduardo Alejandro Barrio, Federico Matias Pailos & Damian Enrique Szmuc - 2017 - Logic Journal of the IGPL 25 (4):387-407.
    In this paper, we present a non-trivial and expressively complete paraconsistent naïve theory of truth, as a step in the route towards semantic closure. We achieve this goal by expressing self-reference with a weak procedure, that uses equivalences between expressions of the language, as opposed to a strong procedure, that uses identities. Finally, we make some remarks regarding the sense in which the theory of truth discussed has a property closely related to functional completeness, and we present a sound and (...)
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  25. Expanding the universe of universal logic.James Trafford - 2014 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 29 (3):325-343.
    In [5], Béziau provides a means by which Gentzen’s sequent calculus can be combined with the general semantic theory of bivaluations. In doing so, according to Béziau, it is possible to construe the abstract “core” of logics in general, where logical syntax and semantics are “two sides of the same coin”. The central suggestion there is that, by way of a modification of the notion of maximal consistency, it is possible to prove the soundness and completeness for any (...)
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  26. Intensional models for the theory of types.Reinhard Muskens - 2007 - Journal of Symbolic Logic 72 (1):98-118.
    In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to (...)
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  27. A resource-sensitive logic of agency.Daniele Porello & Nicolas Troquard - 2014 - In Ios Press (ed.), Proceedings of the 21st European Conference on Artificial Intelligence (ECAI'14), Prague, Czech Republic. 2014. pp. 723-728.
    We study a fragment of Intuitionistic Linear Logic combined with non-normal modal operators. Focusing on the minimal modal logic, we provide a Gentzen-style sequent calculus as well as a semantics in terms of Kripke resource models. We show that the proof theory is sound and complete with respect to the class of minimal Kripke resource models. We also show that the sequent calculus allows cut elimination. We put the logical framework to use by instantiating it as (...)
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  28. Takeuti's proof theory in the context of the Kyoto School.Andrew Arana - 2019 - Jahrbuch Für Philosophie Das Tetsugaku-Ronso 46:1-17.
    Gaisi Takeuti (1926–2017) is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He extensively extended Hilbert's program in the sense that he formulated Gentzen's sequent calculus, conjectured that cut-elimination holds for it (Takeuti's conjecture), and obtained several stunning results in the 1950–60s towards the solution of his conjecture. Though he has been known chiefly as a great mathematician, he wrote many papers in English and Japanese where he expressed his philosophical thoughts. In particular, (...)
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  29. Non-normal modalities in variants of linear logic.D. Porello & N. Troquard - 2015 - Journal of Applied Non-Classical Logics 25 (3):229-255.
    This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of linear logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic linear logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of Kripke resource models (...)
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  30. Semantic Information and the Complexity of Deduction.Salman Panahy - 2023 - Erkenntnis 88 (4):1-22.
    In the chapter “Information and Content” of their Impossible Worlds, Berto and Jago provide us with a semantic account of information in deductive reasoning such that we have an explanation for why some, but not all, logical deductions are informative. The framework Berto and Jago choose to make sense of the above-mentioned idea is a semantic interpretation of Sequent Calculus rules of inference for classical logic. I shall argue that although Berto and Jago’s idea and framework are hopeful, (...)
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  31. Sets, Logic, Computation: An Open Introduction to Metalogic.Richard Zach - 2021 - Open Logic Project.
    An introductory textbook on metalogic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. The audience is undergraduate students with some background in formal logic.
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  32. Natural Deduction for the Sheffer Stroke and Peirce’s Arrow (and any Other Truth-Functional Connective).Richard Zach - 2015 - Journal of Philosophical Logic 45 (2):183-197.
    Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...)
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  33. Topics in the Proof Theory of Non-classical Logics. Philosophy and Applications.Fabio De Martin Polo - 2023 - Dissertation, Ruhr-Universität Bochum
    Chapter 1 constitutes an introduction to Gentzen calculi from two perspectives, logical and philosophical. It introduces the notion of generalisations of Gentzen sequent calculus and the discussion on properties that characterize good inferential systems. Among the variety of Gentzen-style sequent calculi, I divide them in two groups: syntactic and semantic generalisations. In the context of such a discussion, the inferentialist philosophy of the meaning of logical constants is introduced, and some potential objections – mainly concerning the choice (...)
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  34. Subatomic Inferences: An Inferentialist Semantics for Atomics, Predicates, and Names.Kai Tanter - 2021 - Review of Symbolic Logic:1-28.
    Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom’s notion of material inference and Greg Restall’s (...)
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  35. Completeness of a first-order temporal logic with time-gaps.Matthias Baaz, Alexander Leitsch & Richard Zach - 1996 - Theoretical Computer Science 160 (1-2):241-270.
    The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.
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  36. Minimally Nonstandard K3 and FDE.Rea Golan & Ulf Hlobil - 2022 - Australasian Journal of Logic 19 (5):182-213.
    Graham Priest has formulated the minimally inconsistent logic of paradox (MiLP), which is paraconsistent like Priest’s logic of paradox (LP), while staying closer to classical logic. We present logics that stand to (the propositional fragments of) strong Kleene logic (K3) and the logic of first-degree entailment (FDE) as MiLP stands to LP. That is, our logics share the paracomplete and the paraconsistent-cum-paracomplete nature of K3 and FDE, respectively, while keeping these features to a minimum in order to stay closer to (...)
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  37. Against Harmony.Ian Rumfitt - 1995 - In B. Hale & Crispin Wright (eds.), Blackwell Companion to the Philosophy of Language. Blackwell.
    Many prominent writers on the philosophy of logic, including Michael Dummett, Dag Prawitz, Neil Tennant, have held that the introduction and elimination rules of a logical connective must be ‘in harmony ’ if the connective is to possess a sense. This Harmony Thesis has been used to justify the choice of logic: in particular, supposed violations of it by the classical rules for negation have been the basis for arguments for switching from classical to intuitionistic logic. The Thesis has also (...)
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  38. From Display to Labelled Proofs for Tense Logics.Agata Ciabattoni, Tim Lyon & Revantha Ramanayake - 2013 - In Sergei Artemov & Anil Nerode (eds.), Logical Foundations of Computer Science (Lecture Notes in Computer Science 7734). Springer. pp. 120 - 139.
    We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt.
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  39. Some investigations on mbC and mCi.Marcelo E. Coniglio & Tarcísio G. Rodrígues - 2014 - In Cezar A. Mortari (ed.), Tópicos de lógicas não clássicas. NEL/UFSC. pp. 11-70.
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  40. The Display Problem Revisited.Tyke Nunez - 2010 - In Michal Peliš Vit Punčochàr (ed.), The Logica Yearbook. College Publications. pp. 143-156.
    In this essay I give a complete join semi-lattice of possible display-equivalence schemes for Display Logic, using the standard connectives, and leaving fixed only the schemes governing the star. In addition to proving the completeness of this list, I offer a discussion of the basic properties of these schemes.
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  41. The Metaphysical Commitments of Logic.Thomas Brouwer - 2013 - Dissertation, University of Leeds
    This thesis is about the metaphysics of logic. I argue against a view I refer to as ‘logical realism’. This is the view that the logical constants represent a particular kind of metaphysical structure, which I dub ‘logico-metaphysical structure’. I argue instead for a more metaphysically lightweight view of logic which I dub ‘logical expressivism’. -/- In the first part of this thesis (Chapters I and II) I argue against a number of arguments that Theodore Sider has given for logical (...)
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  42. Labeled calculi and finite-valued logics.Matthias Baaz, Christian G. Fermüller, Gernot Salzer & Richard Zach - 1998 - Studia Logica 61 (1):7-33.
    A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is (...)
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  43. Display to Labeled Proofs and Back Again for Tense Logics.Agata Ciabattoni, Tim Lyon, Revantha Ramanayake & Alwen Tiu - 2021 - ACM Transactions on Computational Logic 22 (3):1-31.
    We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special (...)
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  44. VALIDITY: A Learning Game Approach to Mathematical Logic.Steven James Bartlett - 1973 - Hartford, CT: Lebon Press. Edited by E. J. Lemmon.
    The first learning game to be developed to help students to develop and hone skills in constructing proofs in both the propositional and first-order predicate calculi. It comprises an autotelic (self-motivating) learning approach to assist students in developing skills and strategies of proof in the propositional and predicate calculus. The text of VALIDITY consists of a general introduction that describes earlier studies made of autotelic learning games, paying particular attention to work done at the Law School of Yale University, (...)
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  45. The (Greatest) Fragment of Classical Logic that Respects the Variable-Sharing Principle (in the FMLA-FMLA Framework).Damian E. Szmuc - 2021 - Bulletin of the Section of Logic 50 (4):421-453.
    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 (...)
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  46. On Deriving Nested Calculi for Intuitionistic Logics from Semantic Systems.Tim Lyon - 2013 - In Sergei Artemov & Anil Nerode (eds.), Logical Foundations of Computer Science (Lecture Notes in Computer Science 7734). Springer. pp. 177-194.
    This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its (...)
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  47. Refining Labelled Systems for Modal and Constructive Logics with Applications.Tim Lyon - 2021 - Dissertation, Technischen Universität Wien
    This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly incorporates (...)
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  48.  22
    Calculus of Qualia 1: Zombies, Spectrum Inversion, Knowledge Argument, Hard Problems and Understanding their Solutions.Paul Merriam & M. A. Z. Habeeb - manuscript
    A Calculus of Qualia (CQ) was proposed (on PhilPapers). The key idea is that, for example, blackness is radically different than █. The former term, “blackness” refers to or is about a quale, whereas the latter term, “█” instantiates a quale in the reader's mind and is non-referential, *it does not even refer to itself*. The meaning and behavior of these terms is radically different. In this paper in this series of papers, we give a discussion zombies, spectrum inversion, (...)
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  49.  45
    Calculus of Qualia 6: Materialism, Dualism, Idealism, and 14 others.P. Merriam & M. A. Z. Habeeb - manuscript
    General Introduction: In [1] a Calculus of Qualia (CQ) was proposed. The key idea is that, for example, blackness is radically different than █. The former term, “blackness” refers to or is about a quale, whereas the latter term, “█” instantiates a quale in the reader’s mind and is non-referential; it does not even refer to itself. The meaning and behavior of these terms is radically different. All of philosophy, from Plato through Descartes through Chalmers, including hieroglyphics and emojis, (...)
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  50. Proofnets for S5: sequents and circuits for modal logic.Greg Restall - 2007 - In C. Dimitracopoulos, L. Newelski & D. Normann (eds.), Logic Colloquium 2005: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Athens, Greece, July 28-August 3, 2005. Cambridge: Cambridge University Press. pp. 151-172.
    In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic, or multiple-conclusion calculi for classical logic). -/- The sequent derivations and proofnets are both simple extensions of sequents and proofnets for classical propositional logic, in which the new machinery—to take account of the modal vocabulary—is directly motivated (...)
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