Switch to: References

Add citations

You must login to add citations.
  1. Strong Connexivity.Andreas Kapsner - 2012 - Thought: A Journal of Philosophy 1 (2):141-145.
    Connexive logics aim to capture important logical intuitions, intuitions that can be traced back to antiquity. However, the requirements that are imposed on connexive logic are actually not enough to do justice to these intuitions, as I will argue. I will suggest how these demands should be strengthened.
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • Dialogues as a dynamic framework for logic.Helge Rückert - unknown
    Dialogical logic is a game-theoretical approach to logic. Logic is studied with the help of certain games, which can be thought of as idealized argumentations. Two players, the Proponent, who puts forward the initial thesis and tries to defend it, and the Opponent, who tries to attack the Proponent’s thesis, alternately utter argumentative moves according to certain rules. For a long time the dialogical approach had been worked out only for classical and intuitionistic logic. The seven papers of this dissertation (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • The subjunctive conditional as relevant implication.John Bacon - 1971 - Philosophia 1 (1-2):61-80.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Fusion, fission, and Ackermann’s truth constant in relevant logics: A proof-theoretic investigation.Fabio De Martin Polo - 2024 - In Andrew Tedder, Shawn Standefer & Igor Sedlar (eds.), New Directions in Relevant Logic. Springer.
    The aim of this paper is to provide a proof-theoretic characterization of relevant logics including fusion and fission connectives, as well as Ackermann’s truth constant. We achieve this by employing the well-established methodology of labelled sequent calculi. After having introduced several systems, we will conduct a detailed proof-theoretic analysis, show a cut-admissibility theorem, and establish soundness and completeness. The paper ends with a discussion that contextualizes our current work within the broader landscape of the proof theory of relevant logics.
    Download  
     
    Export citation  
     
    Bookmark  
  • Connexive Negation.Luis Estrada-González & Ricardo Arturo Nicolás-Francisco - 2023 - Studia Logica 112 (1):511-539.
    Seen from the point of view of evaluation conditions, a usual way to obtain a connexive logic is to take a well-known negation, for example, Boolean negation or de Morgan negation, and then assign special properties to the conditional to validate Aristotle’s and Boethius’ Theses. Nonetheless, another theoretical possibility is to have the extensional or the material conditional and then assign special properties to the negation to validate the theses. In this paper we examine that possibility, not sufficiently explored in (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Connexivity in the Logic of Reasons.Andrea Iacona - 2023 - Studia Logica 112 (1):325-342.
    This paper discusses some key connexive principles construed as principles about reasons, that is, as principles that express logical properties of sentences of the form ‘p is a reason for q’. Its main goal is to show how the theory of reasons outlined by Crupi and Iacona, which is based on their evidential account of conditionals, yields a formal treatment of such sentences that validates a restricted version of the principles discussed, overcoming some limitations that affect most extant accounts of (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Classical Logic Is Connexive.Camillo Fiore - 2024 - Australasian Journal of Logic (2):91-99.
    Connexive logics are based on two ideas: that no statement entails or is entailed by its own negation (this is Aristotle’s thesis) and that no statement entails both something and the negation of this very thing (this is Boethius' thesis). Usually, connexive logics are contra-classical. In this note, I introduce a reading of the connexive theses that makes them compatible with classical logic. According to this reading, the theses in question do not talk about validity alone; rather, they talk in (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Rewriting the History of Connexive Logic.Wolfgang Lenzen - 2022 - Journal of Philosophical Logic 51 (3):525-553.
    The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  • An Easy Road to Multi-contra-classicality.Luis Estrada-González - 2023 - Erkenntnis 88 (6):2591-2608.
    A contra-classical logic is a logic that, over the same language as that of classical logic, validates arguments that are not classically valid. In this paper I investigate whether there is a single, non-trivial logic that exhibits many features of already known contra-classical logics. I show that Mortensen’s three-valued connexive logic _M3V_ is one such logic and, furthermore, that following the example in building _M3V_, that is, putting a suitable conditional on top of the \(\{\sim, \wedge, \vee \}\) -fragment of (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • The Evidential Conditional.Vincenzo Crupi & Andrea Iacona - 2022 - Erkenntnis 87 (6):2897-2921.
    This paper outlines an account of conditionals, the evidential account, which rests on the idea that a conditional is true just in case its antecedent supports its consequent. As we will show, the evidential account exhibits some distinctive logical features that deserve careful consideration. On the one hand, it departs from the material reading of ‘if then’ exactly in the way we would like it to depart from that reading. On the other, it significantly differs from the non-material accounts which (...)
    Download  
     
    Export citation  
     
    Bookmark   32 citations  
  • Strictness and connexivity.Andrea Iacona - 2021 - Inquiry: An Interdisciplinary Journal of Philosophy 64 (10):1024-1037.
    .This paper discusses Aristotle’s thesis and Boethius’ thesis, the most distinctive theorems of connexive logic. Its aim is to show that, although there is something plausible in Aristotle’s thesis and Boethius’ thesis, the intuitions that may be invoked to motivate them are consistent with any account of indicative conditionals that validates a suitably restricted version of them. In particular, these intuitions are consistent with the view that indicative conditionals are adequately formalized as strict conditionals.
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • Logics of Nonsense and Parry Systems.Thomas Macaulay Ferguson - 2015 - Journal of Philosophical Logic 44 (1):65-80.
    We examine the relationship between the logics of nonsense of Bochvar and Halldén and the containment logics in the neighborhood of William Parry’s A I. We detail two strategies for manufacturing containment logics from nonsense logics—taking either connexive and paraconsistent fragments of such systems—and show how systems determined by these techniques have appeared as Frederick Johnson’s R C and Carlos Oller’s A L. In particular, we prove that Johnson’s system is precisely the intersection of Bochvar’s B 3 and Graham Priest’s (...)
    Download  
     
    Export citation  
     
    Bookmark   33 citations  
  • Cause and counterfactual.Herbert A. Simon & Nicholas Rescher - 1966 - Philosophy of Science 33 (4):323-340.
    It is shown how a causal ordering can be defined in a complete structure, and how it is equivalent to identifying the mechanisms of a system. Several techniques are shown that may be useful in actually accomplishing such identification. Finally, it is shown how this explication of causal ordering can be used to analyse causal counterfactual conditionals. First the counterfactual proposition at issue is articulated through the device of a belief-contravening supposition. Then the causal ordering is used to provide modal (...)
    Download  
     
    Export citation  
     
    Bookmark   25 citations  
  • Aristotle's thesis in consistent and inconsistent logics.Chris Mortensen - 1984 - Studia Logica 43 (1-2):107 - 116.
    A typical theorem of conaexive logics is Aristotle''s Thesis(A), (AA).A cannot be added to classical logic without producing a trivial (Post-inconsistent) logic, so connexive logics typically give up one or more of the classical properties of conjunction, e.g.(A & B)A, and are thereby able to achieve not only nontriviality, but also (negation) consistency. To date, semantical modellings forA have been unintuitive. One task of this paper is to give a more intuitive modelling forA in consistent logics. In addition, while inconsistent (...)
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  • Fragility and Strength.Teodor-Tiberiu Călinoiu & Daniele Bruno Garancini - forthcoming - Analysis.
    It is customarily assumed that paracomplete and paraconsistent solutions to liar paradoxes require a logical system weaker than classical logic. That is, if a logic is not fragile to liar paradoxes, it must be logically weaker than classical logic. Defenders of classical logic argue that the losses of weakening it outweigh the gains. Advocates of paracomplete and paraconsistent solutions disagree. We articulate the notion of fragility with respect to the liar paradox and show that it can be disentangled from logical (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Axioms for a Logic of Consequential Counterfactuals.Claudio E. A. Pizzi - 2023 - Logic Journal of the IGPL 31 (5):907-925.
    The basis of the paper is a logic of analytical consequential implication, CI.0, which is known to be equivalent to the well-known modal system KT thanks to the definition A → B = df A ⥽ B ∧ Ξ (Α, Β), Ξ (Α, Β) being a symbol for what is called here Equimodality Property: (□A ≡ □B) ∧ (◊A ≡ ◊B). Extending CI.0 (=KT) with axioms and rules for the so-called circumstantial operator symbolized by *, one obtains a system CI.0*Eq (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • (1 other version)Connexive logics. An overview and current trends.Hitoshi Omori & Heinrich Wansing - forthcoming - Logic and Logical Philosophy:1.
    In this introduction, we offer an overview of main systems developed in the growing literature on connexive logic, and also point to a few topics that seem to be collecting attention of many of those interested in connexive logic. We will also make clear the context to which the papers in this special issue belong and contribute.
    Download  
     
    Export citation  
     
    Bookmark   39 citations  
  • (1 other version)Connexive logic.Heinrich Wansing - 2008 - Stanford Encyclopedia of Philosophy.
    Download  
     
    Export citation  
     
    Bookmark   50 citations  
  • Negation as cancellation, and connexive logic.Graham Priest - 1999 - Topoi 18 (2):141-148.
    Of the various accounts of negation that have been offered by logicians in the history of Western logic, that of negation as cancellation is a very distinctive one, quite different from the explosive accounts of modern "classical" and intuitionist logics, and from the accounts offered in standard relevant and paraconsistent logics. Despite its ancient origin, however, a precise understanding of the notion is still wanting. The first half of this paper offers one. Both conceptually and historically, the account of negation (...)
    Download  
     
    Export citation  
     
    Bookmark   50 citations  
  • On Beall’s New Interpretation of $$WK_{3}$$ W K 3.Nissim Francez - 2019 - Journal of Logic, Language and Information 28 (1):1-7.
    I argue that a recent philosophical interpretation by Jc Beall of the middle value of Weak Kleene logic as ‘being off-topic’ is untenable. My main claim is that “being off-topic” is a relation, not a property, and as such cannot serve as an interpretation of a truth-value.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Two Kinds of Consequential Implication.Claudio E. A. Pizzi - 2018 - Studia Logica 106 (3):453-480.
    The first section of the paper establishes the minimal properties of so-called consequential implication and shows that they are satisfied by at least two different operators of decreasing strength and \). Only the former has been analyzed in recent literature, so the paper focuses essentially on the latter. Both operators may be axiomatized in systems which are shown to be translatable into standard systems of normal modal logic. The central result of the paper is that the minimal consequential system for (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Kripke Completeness of Bi-intuitionistic Multilattice Logic and its Connexive Variant.Norihiro Kamide, Yaroslav Shramko & Heinrich Wansing - 2017 - Studia Logica 105 (6):1193-1219.
    In this paper, bi-intuitionistic multilattice logic, which is a combination of multilattice logic and the bi-intuitionistic logic also known as Heyting–Brouwer logic, is introduced as a Gentzen-type sequent calculus. A Kripke semantics is developed for this logic, and the completeness theorem with respect to this semantics is proved via theorems for embedding this logic into bi-intuitionistic logic. The logic proposed is an extension of first-degree entailment logic and can be regarded as a bi-intuitionistic variant of the original classical multilattice logic (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Aristotle's Thesis between paraconsistency and modalization.Claudio Pizzi - 2005 - Journal of Applied Logic 3 (1):119-131.
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Modal and Intuitionistic Variants of Extended Belnap–Dunn Logic with Classical Negation.Norihiro Kamide - 2021 - Journal of Logic, Language and Information 30 (3):491-531.
    In this study, we introduce Gentzen-type sequent calculi BDm and BDi for a modal extension and an intuitionistic modification, respectively, of De and Omori’s extended Belnap–Dunn logic BD+ with classical negation. We prove theorems for syntactically and semantically embedding BDm and BDi into Gentzen-type sequent calculi S4 and LJ for normal modal logic and intuitionistic logic, respectively. The cut-elimination, decidability, and completeness theorems for BDm and BDi are obtained using these embedding theorems. Moreover, we prove the Glivenko theorem for embedding (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Contra-classical logics.Lloyd Humberstone - 2000 - Australasian Journal of Philosophy 78 (4):438 – 474.
    Only propositional logics are at issue here. Such a logic is contra-classical in a superficial sense if it is not a sublogic of classical logic, and in a deeper sense, if there is no way of translating its connectives, the result of which translation gives a sublogic of classical logic. After some motivating examples, we investigate the incidence of contra-classicality (in the deeper sense) in various logical frameworks. In Sections 3 and 4 we will encounter, originally as an example of (...)
    Download  
     
    Export citation  
     
    Bookmark   40 citations  
  • Kapsner Complementation: An Algebraic Take on Kapsner Strong Logics.Andrew Tedder - 2023 - Studia Logica 111 (2):321-352.
    Kapsner strong logics, originally studied in the context of connexive logics, are those in which all formulas of the form \(A\rightarrow \lnot A\) or \(\lnot A\rightarrow A\) are unsatisfiable, and in any model at most one of \(A\rightarrow B, A\rightarrow \lnot B\) is satisfied. In this paper, such logics are studied algebraically by means of algebraic structures in which negation is modeled by an operator \(\lnot \) s.t. any element _a_ is incomparable with \(\lnot a\). A range of properties which (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Completeness and Cut-Elimination for First-Order Ideal Paraconsistent Four-Valued Logic.Norihiro Kamide & Yoni Zohar - 2020 - Studia Logica 108 (3):549-571.
    In this study, we prove the completeness and cut-elimination theorems for a first-order extension F4CC of Arieli, Avron, and Zamansky’s ideal paraconsistent four-valued logic known as 4CC. These theorems are proved using Schütte’s method, which can simultaneously prove completeness and cut-elimination.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Gentzen-Type Sequent Calculi for Extended Belnap–Dunn Logics with Classical Negation: A General Framework.Norihiro Kamide - 2019 - Logica Universalis 13 (1):37-63.
    Gentzen-type sequent calculi GBD+, GBDe, GBD1, and GBD2 are respectively introduced for De and Omori’s axiomatic extensions BD+, BDe, BD1, and BD2 of Belnap–Dunn logic by adding classical negation. These calculi are constructed based on a small modification of the original characteristic axiom scheme for negated implication. Theorems for syntactically and semantically embedding these calculi into a Gentzen-type sequent calculus LK for classical logic are proved. The cut-elimination, decidability, and completeness theorems for these calculi are obtained using these embedding theorems. (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Dialogical connexive logic.Shahid Rahman & Helge Rückert - 2001 - Synthese 127 (1-2):105-139.
    Many of the discussions about conditionals can best be put as follows:can those conditionals that involve an entailment relation be formulatedwithin a formal system? The reasons for the failure of the classical approachto entailment have usually been that they ignore the meaning connectionbetween antecedent and consequent in a valid entailment. One of the firsttheories in the history of logic about meaning connection resulted from thestoic discussions on tightening the relation between the If- and the Then-parts of conditionals, which in this (...)
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • A Reinterpretation of Beall’s ‘Off-Topic’ Semantics.Jeremiah Joven B. Joaquin - 2022 - Journal of Logic, Language and Information 31 (3):409-421.
    Jc Beall’s off-topic interpretation of Weak Kleene logic offers a logic of ‘true-and-topic’ preservation. However, Nissim Francez has recently argued that being ‘off-topic’ is a relational and not an _absolute_ semantic property; as such, it fails to satisfy the conditions of truth-functionality. For Francez, this means that it ‘cannot serve as an interpretation of a truth-value’. In this paper, I propose a two-layered _re_interpretation of Beall’s off-topic semantics. This two-layered framework has two crucial features: a sentential topic-tagging device and a (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • An Analysis of Poly-connexivity.Luis Estrada-González - 2022 - Studia Logica 110 (4):925-947.
    Francez has suggested that connexivity can be predicated of connectives other than the conditional, in particular conjunction and disjunction. Since connexivity is not any connection between antecedents and consequents—there might be other connections among them, such as relevance—, my question here is whether Francez’s conjunction and disjunction can properly be called ‘connexive’. I analyze three ways in which those connectives may somehow inherit connexivity from the conditional by standing in certain relations to it. I will show that Francez’s connectives fail (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Modal extension of ideal paraconsistent four-valued logic and its subsystem.Norihiro Kamide & Yoni Zohar - 2020 - Annals of Pure and Applied Logic 171 (10):102830.
    This study aims to introduce a modal extension M4CC of Arieli, Avron, and Zamansky's ideal paraconsistent four-valued logic 4CC as a Gentzen-type sequent calculus and prove the Kripke-completeness and cut-elimination theorems for M4CC. The logic M4CC is also shown to be decidable and embeddable into the normal modal logic S4. Furthermore, a subsystem of M4CC, which has some characteristic properties that do not hold for M4CC, is introduced and the Kripke-completeness and cut-elimination theorems for this subsystem are proved. This subsystem (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Angell and McCall Meet Wansing.Hitoshi Omori & Andreas Kapsner - 2024 - Studia Logica 112 (1):141-165.
    In this paper, we introduce a new logic, which we call AM3. It is a connexive logic that has several interesting properties, among them being strongly connexive and validating the Converse Boethius Thesis. These two properties are rather characteristic of the difference between, on the one hand, Angell and McCall’s CC1 and, on the other, Wansing’s C. We will show that in other aspects, as well, AM3 combines what are, arguably, the strengths of both CC1 and C. It also allows (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Connexive Logic, Connexivity, and Connexivism: Remarks on Terminology.Heinrich Wansing & Hitoshi Omori - 2023 - Studia Logica 112 (1):1-35.
    Over the past ten years, the community researching connexive logics is rapidly growing and a number of papers have been published. However, when it comes to the terminology used in connexive logic, it seems to be not without problems. In this introduction, we aim at making a contribution towards both unifying and reducing the terminology. We hope that this can help making it easier to survey and access the field from outside the community of connexive logicians. Along the way, we (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Intuitionistic Logic is a Connexive Logic.Davide Fazio, Antonio Ledda & Francesco Paoli - 2023 - Studia Logica 112 (1):95-139.
    We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic ($$\textrm{CHL}$$ CHL ), hereby introduced as an example of a strongly connexive logic with an intuitive semantics. We use the reverse algebraisation paradigm: $$\textrm{CHL}$$ CHL is presented as the assertional logic of a point regular variety (whose structure theory is examined in detail) that turns out to be term equivalent to the variety of Heyting algebras. We provide Hilbert-style and Gentzen-style proof systems for $$\textrm{CHL}$$ CHL ; moreover, we (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Embedding Friendly First-Order Paradefinite and Connexive Logics.Norihiro Kamide - 2022 - Journal of Philosophical Logic 51 (5):1055-1102.
    First-order intuitionistic and classical Nelson–Wansing and Arieli–Avron–Zamansky logics, which are regarded as paradefinite and connexive logics, are investigated based on Gentzen-style sequent calculi. The cut-elimination and completeness theorems for these logics are proved uniformly via theorems for embedding these logics into first-order intuitionistic and classical logics. The modified Craig interpolation theorems for these logics are also proved via the same embedding theorems. Furthermore, a theorem for embedding first-order classical Arieli–Avron–Zamansky logic into first-order intuitionistic Arieli–Avron–Zamansky logic is proved using a modified (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Off-Topic: A New Interpretation of Weak-Kleene Logic.Jc Beall - 2016 - Australasian Journal of Logic 13 (6).
    This paper offers a new and very simple alternative to Bochvar's well known nonsense -- or meaninglessness -- interpretation of Weak Kleene logic. To help orient discussion I begin by reviewing the familiar Strong Kleene logic and its standard interpretation; I then review Weak Kleene logic and the standard interpretation. While I note a common worry about the Bochvar interpretation my aim is only to give an alternative -- and I think very elegant -- interpretation, not necessarily a replacement.
    Download  
     
    Export citation  
     
    Bookmark   34 citations  
  • Semantics for connexive logics. I.Richard Routley - 1978 - Studia Logica 37 (4):393 - 412.
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  • Boolean Connexive Logic and Content Relationship.Mateusz Klonowski & Luis Estrada-González - 2023 - Studia Logica 112 (1):207-248.
    We present here some Boolean connexive logics (BCLs) that are intended to be connexive counterparts of selected Epstein’s content relationship logics (CRLs). The main motivation for analyzing such logics is to explain the notion of connexivity by means of the notion of content relationship. The article consists of two parts. In the first one, we focus on the syntactic analysis by means of axiomatic systems. The starting point for our syntactic considerations will be the smallest BCL and the smallest CRL. (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Stalnakerian Connexive Logics.Xuefeng Wen - 2023 - Studia Logica 112 (1):365-403.
    Motivated by supplying a new strategy for connexive logic and a better semantics for conditionals so that negating a conditional amounts to negating its consequent under the condition, we propose a new semantics for connexive conditional logic, by combining Kleene’s three-valued logic and a slight modification of Stalnaker’s semantics for conditionals. In the new semantics, selection functions for selecting closest worlds for evaluating conditionals can be undefined. Truth and falsity conditions for conditionals are then supplemented with a precondition that the (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • An Extended Paradefinite Logic Combining Conflation, Paraconsistent Negation, Classical Negation, and Classical Implication: How to Construct Nice Gentzen-type Sequent Calculi.Norihiro Kamide - 2022 - Logica Universalis 16 (3):389-417.
    In this study, an extended paradefinite logic with classical negation (EPLC), which has the connectives of conflation, paraconsistent negation, classical negation, and classical implication, is introduced as a Gentzen-type sequent calculus. The logic EPLC is regarded as a modification of Arieli, Avron, and Zamansky’s ideal four-valued paradefinite logic (4CC) and as an extension of De and Omori’s extended Belnap–Dunn logic with classical negation (BD+) and Avron’s self-extensional four-valued paradefinite logic (SE4). The completeness, cut-elimination, and decidability theorems for EPLC are proved (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Kripke-Completeness and Cut-elimination Theorems for Intuitionistic Paradefinite Logics With and Without Quasi-Explosion.Norihiro Kamide - 2020 - Journal of Philosophical Logic 49 (6):1185-1212.
    Two intuitionistic paradefinite logics N4C and N4C+ are introduced as Gentzen-type sequent calculi. These logics are regarded as a combination of Nelson’s paraconsistent four-valued logic N4 and Wansing’s basic constructive connexive logic C. The proposed logics are also regarded as intuitionistic variants of Arieli, Avron, and Zamansky’s ideal paraconistent four-valued logic 4CC. The logic N4C has no quasi-explosion axiom that represents a relationship between conflation and paraconsistent negation, but the logic N4C+ has this axiom. The Kripke-completeness and cut-elimination theorems for (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Natural deduction systems for Nelson's paraconsistent logic and its neighbors.Norihiro Kamide - 2005 - Journal of Applied Non-Classical Logics 15 (4):405-435.
    Firstly, a natural deduction system in standard style is introduced for Nelson's para-consistent logic N4, and a normalization theorem is shown for this system. Secondly, a natural deduction system in sequent calculus style is introduced for N4, and a normalization theorem is shown for this system. Thirdly, a comparison between various natural deduction systems for N4 is given. Fourthly, a strong normalization theorem is shown for a natural deduction system for a sublogic of N4. Fifthly, a strong normalization theorem is (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Connexive logic.Michael Astroh - 1999 - Nordic Journal of Philosophical Logic 4:31-72.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Boethius' thesis and conditional logic.Claudio Pizzi - 1977 - Journal of Philosophical Logic 6 (1):283 - 302.
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • Frontiers of Conditional Logic.Yale Weiss - 2019 - Dissertation, The Graduate Center, City University of New York
    Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the exotic (e.g. conditional (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Hugh maccoll: eine bibliographische erschließung seiner hauptwerke und notizen zu ihrer rezeptionsgeschichte.Shahid Rahman - 1997 - History and Philosophy of Logic 18 (3):165-183.
    The work of Hugh MacColl (1837–1909) suffered the same fate after his death as before it:despite being vaguely alluded to and in part even commended, on the whole it has remained an unknown quantity. Even worse, those of his ideas which have played a decisive role in the history of logic have been credited to his successors; this is especially the case with the definition of strict implication and the first formal development of formal modal logic. This paper takes an (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Two Objections to System CC1 of Connexive Implication.John Woods - 1968 - Dialogue 7 (3):473-475.
    Download  
     
    Export citation  
     
    Bookmark   3 citations