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  1. Neighborhood Semantics for Modal Logic.Eric Pacuit - 2017 - Cham, Switzerland: Springer.
    This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic. In addition, the book discusses a broad range of topics, including standard modal logic results ; bisimulations for neighborhood models and other model-theoretic (...)
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  • Implicit and Explicit Stances in Logic.Johan van Benthem - 2019 - Journal of Philosophical Logic 48 (3):571-601.
    We identify a pervasive contrast between implicit and explicit stances in logical analysis and system design. Implicit systems change received meanings of logical constants and sometimes also the notion of consequence, while explicit systems conservatively extend classical systems with new vocabulary. We illustrate the contrast for intuitionistic and epistemic logic, then take it further to information dynamics, default reasoning, and other areas, to show its wide scope. This gives a working understanding of the contrast, though we stop short of a (...)
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  • Intellectual Modesty in Socratic Wisdom: Problems of Epistemic Logic and an Intuitionist Solution.Guido Löhrer - 2022 - History of Philosophy & Logical Analysis 25 (2):282-308.
    According to Plato’s Apology of Socrates, a humanly wise person is distinguished by her ability to correctly assess the epistemic status and value of her beliefs. She knows when she has knowledge or has mere belief or is ignorant. She makes no unjustified knowledge claims and considers her knowledge to be limited in scope and value. This means: A humanly wise person is intellectually modest. However, when interpreted classically, Socratic wisdom cannot be modest. For in classical epistemic logic, modelling second-order (...)
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  • Implicit and Explicit Stances in Logic.Johan Benthem - 2019 - Journal of Philosophical Logic 48 (3):571-601.
    We identify a pervasive contrast between implicit and explicit stances in logical analysis and system design. Implicit systems change received meanings of logical constants and sometimes also the notion of consequence, while explicit systems conservatively extend classical systems with new vocabulary. We illustrate the contrast for intuitionistic and epistemic logic, then take it further to information dynamics, default reasoning, and other areas, to show its wide scope. This gives a working understanding of the contrast, though we stop short of a (...)
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  • Technology and Mathematics.Sven Ove Hansson - 2020 - Philosophy and Technology 33 (1):117-139.
    In spite of their practical importance, the connections between technology and mathematics have not received much scholarly attention. This article begins by outlining how the technology–mathematics relationship has developed, from the use of simple aide-mémoires for counting and arithmetic, via the use of mathematics in weaving, building and other trades, and the introduction of calculus to solve technological problems, to the modern use of computers to solve both technological and mathematical problems. Three important philosophical issues emerge from this historical résumé: (...)
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  • Curry–Howard–Lambek Correspondence for Intuitionistic Belief.Cosimo Perini Brogi - 2021 - Studia Logica 109 (6):1441-1461.
    This paper introduces a natural deduction calculus for intuitionistic logic of belief \ which is easily turned into a modal \-calculus giving a computational semantics for deductions in \. By using that interpretation, it is also proved that \ has good proof-theoretic properties. The correspondence between deductions and typed terms is then extended to a categorical semantics for identity of proofs in \ showing the general structure of such a modality for belief in an intuitionistic framework.
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  • A First-Order Expansion of Artemov and Protopopescu’s Intuitionistic Epistemic Logic.Youan Su & Katsuhiko Sano - 2023 - Studia Logica 111 (4):615-652.
    Intuitionistic epistemic logic by Artemov and Protopopescu (Rev Symb Log 9:266–298, 2016) accepts the axiom “if A, then A is known” (written $$A \supset K A$$ ) in terms of the Brouwer–Heyting–Kolmogorov interpretation. There are two variants of intuitionistic epistemic logic: one with the axiom “ $$KA \supset \lnot \lnot A$$ ” and one without it. The former is called $$\textbf{IEL}$$, and the latter is called $$\textbf{IEL}^{-}$$. The aim of this paper is to study first-order expansions (with equality and function (...)
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  • Reasoning about proof and knowledge.Steffen Lewitzka - 2019 - Annals of Pure and Applied Logic 170 (2):218-250.
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  • Admissible rules for six intuitionistic modal logics.Iris van der Giessen - 2023 - Annals of Pure and Applied Logic 174 (4):103233.
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  • Reflections on Orlov.Graham Priest - 2021 - History and Philosophy of Logic 42 (2):118-128.
    In 1928 Ivan Orlov published a remarkable paper which contains the first formulation of a relevant logic. The paper remained largely unknown to English-speakers until this discovery of relevant log...
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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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