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Proofnets for S5: sequents and circuits for modal logic

In C. Dimitracopoulos, L. Newelski & D. Normann (eds.), Logic Colloquium 2005. Cambridge: Cambridge University Press. pp. 151-172 (2007)

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  1. Simple Decision Procedure for S5 in Standard Cut-Free Sequent Calculus.Andrzej Indrzejczak - 2016 - Bulletin of the Section of Logic 45 (2).
    In the paper a decision procedure for S5 is presented which uses a cut-free sequent calculus with additional rules allowing a reduction to normal modal forms. It utilizes the fact that in S5 every formula is equivalent to some 1-degree formula, i.e. a modally-flat formula with modal functors having only boolean formulas in its scope. In contrast to many sequent calculi for S5 the presented system does not introduce any extra devices. Thus it is a standard version of SC but (...)
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  • On a Multilattice Analogue of a Hypersequent S5 Calculus.Oleg Grigoriev & Yaroslav Petrukhin - forthcoming - Logic and Logical Philosophy:1.
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  • Anti-Realist Classical Logic and Realist Mathematics.Greg Restall - unknown
    I sketch an application of a semantically anti-realist understanding of the classical sequent calculus to the topic of mathematics. The result is a semantically anti-realist defence of a kind of mathematical realism. In the paper, I begin the development of the view and compare it to orthodox positions in the philosophy of mathematics.
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  • Natural Deduction Calculi and Sequent Calculi for Counterfactual Logics.Francesca Poggiolesi - 2016 - Studia Logica 104 (5):1003-1036.
    In this paper we present labelled sequent calculi and labelled natural deduction calculi for the counterfactual logics CK + {ID, MP}. As for the sequent calculi we prove, in a semantic manner, that the cut-rule is admissible. As for the natural deduction calculi we prove, in a purely syntactic way, the normalization theorem. Finally, we demonstrate that both calculi are sound and complete with respect to Nute semantics [12] and that the natural deduction calculi can be effectively transformed into the (...)
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  • A Cut-Free Sequent System for Two-Dimensional Modal Logic, and Why It Matters.Greg Restall - 2012 - Annals of Pure and Applied Logic 163 (11):1611-1623.
    The two-dimensional modal logic of Davies and Humberstone [3] is an important aid to our understanding the relationship between actuality, necessity and a priori knowability. I show how a cut-free hypersequent calculus for 2D modal logic not only captures the logic precisely, but may be used to address issues in the epistemology and metaphysics of our modal concepts. I will explain how the use of our concepts motivates the inference rules of the sequent calculus, and then show that the completeness (...)
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  • Hypersequent Calculi for S5: The Methods of Cut Elimination.Kaja Bednarska & Andrzej Indrzejczak - 2015 - Logic and Logical Philosophy 24 (3):277–311.
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  • Grafting Hypersequents Onto Nested Sequents.Roman Kuznets & Björn Lellmann - 2016 - Logic Journal of the IGPL 24 (3):375-423.
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  • Comparing Modal Sequent Systems.Greg Restall - unknown
    This is an exploratory and expository paper, comparing display logic formulations of normal modal logics with labelled sequent systems. We provide a translation from display sequents into labelled sequents. The comparison between different systems gives us a different way to understand the difference between display systems and other sequent calculi as a difference between local and global views of consequence. The mapping between display and labelled systems also gives us a way to understand labelled systems as properly structural and not (...)
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  • 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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  • Truth Values.Greg Restall - unknown
    I present an account of truth values for classical logic, intuitionistic logic, and the modal logic s5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.
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  • Second-Order Modal Logic.Andrew Parisi - 2017 - Dissertation, University of Connecticut
    This dissertation develops an inferentialist theory of meaning. It takes as a starting point that the sense of a sentence is determined by the rules governing its use. In particular, there are two features of the use of a sentence that jointly determine its sense, the conditions under which it is coherent to assert that sentence and the conditions under which it is coherent to deny that sentence. From this starting point the dissertation develops a theory of quantification as marking (...)
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  • Question.Greg Restall - 2006 - In Vincent F. Hendricks & John Symons (eds.), Masses of Formal Philosophy. Automatic Press/VIP.
    I suppose the natural way to interpret this question is something like “why do formal methods rather than anything else in philosophy” but in my case I’d rather answer the related question “why, given that you’re interested in formal methods, apply them in philosophy rather than elsewhere?” I started off my academic life as an undergraduate student in mathematics, because I was good at mathematics and studying it more seemed like a good idea at the time. I enjoyed mathematics a (...)
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