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  1. A basic system of paraconsistent Nelsonian logic of conditionals.Grigory K. Olkhovikov - 2024 - Journal of Logic, Language and Information 33 (4):299-337.
    We define a Kripke semantics for a conditional logic based on the propositional logic $$\textsf{N4}$$ N 4, the paraconsistent variant of Nelson’s logic of strong negation; we axiomatize the minimal system induced by this semantics. The resulting logic, which we call $$\textsf{N4CK}$$ N 4 CK, shows strong connections both with the basic intuitionistic logic of conditionals $$\textsf{IntCK}$$ IntCK introduced earlier in (Olkhovikov, 2023) and with the $$\textsf{N4}$$ N 4 -based modal logic $$\textsf{FSK}^d$$ FSK d introduced in (Odintsov and Wansing, 2004) (...)
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  • Against Hypothetical Syllogism.Lee Walters - 2014 - Journal of Philosophical Logic 43 (5):979-997.
    The debate over Hypothetical Syllogism is locked in stalemate. Although putative natural language counterexamples to Hypothetical Syllogism abound, many philosophers defend Hypothetical Syllogism, arguing that the alleged counterexamples involve an illicit shift in context. The proper lesson to draw from the putative counterexamples, they argue, is that natural language conditionals are context-sensitive conditionals which obey Hypothetical Syllogism. In order to make progress on the issue, I consider and improve upon Morreau’s proof of the invalidity of Hypothetical Syllogism. The improved proof (...)
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  • Conditionals, Context, and Transitivity.E. J. Lowe - 1990 - Analysis 50 (2):80 - 87.
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  • Strict conditionals: A negative result.Jan Heylen & Leon Horsten - 2006 - Philosophical Quarterly 56 (225):536–549.
    Jonathan Lowe has argued that a particular variation on C.I. Lewis' notion of strict implication avoids the paradoxes of strict implication. We show that Lowe's notion of implication does not achieve this aim, and offer a general argument to demonstrate that no other variation on Lewis' notion of constantly strict implication describes the logical behaviour of natural-language conditionals in a satisfactory way.
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  • Strict conditionals.Jan Heylen & Leon Horsten - 2022 - Croatian Journal of Philosophy 22 (64):123-131.
    Both Lowe and Tsai have presented their own versions of the theory that both indicative and subjunctive conditionals are strict conditionals. We critically discuss both versions and we find each version wanting.
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  • Counterfactuals and modality.Gabriel Greenberg - 2021 - Linguistics and Philosophy 44 (6):1255-1280.
    This essay calls attention to a set of linguistic interactions between counterfactual conditionals, on one hand, and possibility modals like could have and might have, on the other. These data present a challenge to the popular variably strict semantics for counterfactual conditionals. Instead, they support a version of the strict conditional semantics in which counterfactuals and possibility modals share a unified quantificational domain. I’ll argue that pragmatic explanations of this evidence are not available to the variable analysis. And putative counterexamples (...)
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  • (1 other version)Counterfactual Logic and the Necessity of Mathematics.Samuel Elgin - manuscript
    This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne (2018), who seek to establish that mathematics is committed to its own necessity. I claim that their argument fails to establish this result for two reasons. First, their assumptions force our hand on a controversial debate within counterfactual logic. In particular, they license counterfactual strengthening— the inference from ‘If A (...)
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  • Basic Intuitionistic Conditional Logic.Yale Weiss - 2019 - Journal of Philosophical Logic 48 (3):447-469.
    Conditional logics have traditionally been intended to formalize various intuitively correct modes of reasoning involving conditional expressions in natural language. Although conditional logics have by now been thoroughly studied in a classical context, they have yet to be systematically examined in an intuitionistic context, despite compelling philosophical and technical reasons to do so. This paper addresses this gap by thoroughly examining the basic intuitionistic conditional logic ICK, the intuitionistic counterpart of Chellas’ important classical system CK. I give ICK both worlds (...)
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  • 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 (...)
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  • Super-Strict Implications.Guido Gherardi & Eugenio Orlandelli - 2021 - Bulletin of the Section of Logic 50 (1):1-34.
    This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are (...)
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  • 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 (...)
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  • (1 other version)Counterfactual Logic and the Necessity of Mathematics.Samuel Z. Elgin - 2020 - Journal of Philosophical Logic 50 (1):97-115.
    This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne, who seek to establish that mathematics is committed to its own necessity. I demonstrate that their assumptions collapse the counterfactual conditional into the material conditional. This collapse entails the success of counterfactual strengthening, which is controversial within counterfactual logic, and which has counterexamples within pure and applied mathematics. I close (...)
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  • Lowe's Argument Against the Psychoneural Token Identity Thesis.Katarzyna Paprzycka - 2014 - Pacific Philosophical Quarterly 95 (3):372-396.
    E. J. Lowe argues that the mental event token cannot be identical to the complex neural event token for they have different counterfactual properties. If the mental event had not occurred, the behavior would not have ensued, while if the neural event had not occurred, the behavior would have ensued albeit slightly differently. Lowe's argument for the neural counterfactual relies on standard possible world semantics, whose evaluation of such counterfactuals is problematic. His argument for the mental counterfactual relies on a (...)
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  • Counterfactuals as modal conditionals, and their probability.Giuliano Rosella, Tommaso Flaminio & Stefano Bonzio - 2023 - Artificial Intelligence 323 (C):103970.
    In this paper we propose a semantic analysis of Lewis' counterfactuals. By exploiting the structural properties of the recently introduced boolean algebras of conditionals, we show that counterfactuals can be expressed as formal combinations of a conditional object and a normal necessity modal operator. Specifically, we introduce a class of algebras that serve as modal expansions of boolean algebras of conditionals, together with their dual relational structures. Moreover, we show that Lewis' semantics based on sphere models can be reconstructed in (...)
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  • Connexive Extensions of Regular Conditional Logic.Yale Weiss - 2019 - Logic and Logical Philosophy 28 (3):611-627.
    The object of this paper is to examine half and full connexive extensions of the basic regular conditional logic CR. Extensions of this system are of interest because it is among the strongest well-known systems of conditional logic that can be augmented with connexive theses without inconsistency resulting. These connexive extensions are characterized axiomatically and their relations to one another are examined proof-theoretically. Subsequently, algebraic semantics are given and soundness, completeness, and decidability are proved for each system. The semantics is (...)
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  • An Intuitionistically Complete System of Basic Intuitionistic Conditional Logic.Grigory Olkhovikov - 2024 - Journal of Philosophical Logic 53 (5).
    We introduce a basic intuitionistic conditional logic \(\textsf{IntCK}\) that we show to be complete both relative to a special type of Kripke models and relative to a standard translation into first-order intuitionistic logic. We show that \(\textsf{IntCK}\) stands in a very natural relation to other similar logics, like the basic classical conditional logic \(\textsf{CK}\) and the basic intuitionistic modal logic \(\textsf{IK}\). As for the basic intuitionistic conditional logic \(\textsf{ICK}\) proposed in Weiss (_Journal of Philosophical Logic_, _48_, 447–469, 2019 ), \(\textsf{IntCK}\) (...)
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  • Mumford and Anjum on causal necessitarianism and antecedent strengthening.E. J. Lowe - 2012 - Analysis 72 (4):731-735.
    Stephen Mumford and Rani Lill Anjum have recently attacked causal necessitarianism – the doctrine that causes necessitate their effects – on the grounds that causation does not survive what they describe as the test of antecedent strengthening. This article shows that there are credible conditional logics which do not sanction this test, thereby providing an escape route for proponents of causal necessitarianism from Mumford and Anjum's argument.
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  • Another dubious counter-example to conditional transitivity.E. J. Lowe - 2010 - Analysis 70 (2):286-289.
    (No abstract is available for this citation).
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