Results 251 to 260 of about 5,524 (273)

Sequent Calculi for Modal Logics

2020
In this chapter we focus on standard and generalised sequent calculi for some modal logics. In general, the application of SC apparatus to non-classical logics showed several limitations of the Gentzen’s approach. In sections 4.2 - 4.4 we describe extensions of LK and G3 to modal logics. In particular, we provide proofs of cut elimination/admissibility
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Sequent Calculi for Normal Modal Propositional Logics

Journal of Logic and Computation, 1994
This is a streamlined exposition of \textit{N. Belnap}'s display logic DL [J. Philos. Logic 11, 375-417 (1982; Zbl 0509.03008)]. DL can be seen as an encoding of a formalization introduced by \textit{S. Kripke} [Z. Math. Logik Grundlagen Math. 9, 67-96 (1963; Zbl 0118.013)] where finite systems of sequents \(S; \sigma_ 1 S_ 1; \sigma_ 2 S_ 2;\dots ...
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Proof Search in Nested Sequent Calculi

2015
We propose a notion of focusing for nested sequent calculi for modal logics which brings down the complexity of proof search to that of the corresponding sequent calculi. The resulting systems are amenable to specifications in linear logic. Examples include modal logic $$\mathsf {K}$$, a simply dependent bimodal logic and the standard non-normal modal ...
Lellmann, Björn, Pimentel, Elaine
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Metainferential Sequent Calculi

2023
Federico Pailos, Bruno Da Ré
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MODULAR SEQUENT CALCULI FOR INTERPRETABILITY LOGICS

The Review of Symbolic Logic
AbstractAn original family of labelled sequent calculi $\mathsf {G3IL}^{\star }$ for classical interpretability logics is presented, modularly designed on the basis of Verbrugge semantics (a.k.a. generalised Veltman semantics) for those logics.
Perini Brogi C., Negri S., Olivetti N.
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Sequent Calculi for Normal Update Logics

2019
Normal update logic is the temporalization of normal conditional logic. Sequent calculi for the least normal update logic \(\mathbf {UCK}\) by Andreas Herzig (1998) and some of its extensions are developed. The subformula property of these sequent calculi is shown by Takano’s semantic method.
Katsuhiko Sano, Minghui Ma
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Interpolation Method for Multicomponent Sequent Calculi

2015
The proof-theoretic method of proving the Craig interpolation property was recently extended from sequents to nested sequents and hypersequents. There the notations were formalism-specific, obscuring the underlying common idea, which is presented here in a general form applicable also to other similar formalisms, e.g., prefixed tableaus.
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Falsification-Aware Semantics and Sequent Calculi for Classical Logic

Journal of Philosophical Logic, 2021
Norihiro Kamide
exaly  

Modal Logic and Ordinary Sequent Calculi

2010
The first part of the chapter is dedicated to a brief summary of the main notions and results of what is usually called normal modal logic. In the second part of the chapter we present the ordinary sequent calculi that have been developed for modal logic.
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Cut-free sequent calculi for some tense logics

Studia Logica, 1994
Ryo Kashima
exaly