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Sequents for non-wellfounded mereology

100%
Maffezioli P.
Logic and Logical Philosophy
|
2016
|
vol. 25
|
issue 3 Mereology and Beyond (II)
351-369
EN
The paper explores the proof theory of non-wellfounded mereology with binary fusions and provides a cut-free sequent calculus equivalent to the standard axiomatic system.
2

Hypersequent Calculi for S5: The Methods of Cut Elimination

100%
Bednarska K., Indrzejczak A.
Logic and Logical Philosophy
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2015
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vol. 24
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issue 3
277–311
EN
S5 is one of the most important modal logic with nice syntactic, semantic and algebraic properties. In spite of that, a successful (i.e. cut-free) formalization of S5 on the ground of standard sequent calculus (SC) was problematic and led to the invention of numerous nonstandard, generalized forms of SC. One of the most interesting framework which was very often used for this aim is that of hypersequent calculi (HC). The paper is a survey of HC for S5 proposed by Pottinger, Avron, Restall, Poggiolesi, Lahav and Kurokawa. We are particularly interested in examining different methods which were used for proving the eliminability/admissibility of cut in these systems and present our own variant of a system which admits relatively simple proof of cut elimination.
3
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Automated Proof-searching for Strong Kleene Logic and its Binary Extensions via Correspondence Analysis

75%
Petrukhin Y., Shangin V.
Logic and Logical Philosophy
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2019
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vol. 28
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issue 2
223–257
EN
Using the method of correspondence analysis, Tamminga obtains sound and complete natural deduction systems for all the unary and binary truth-functional extensions of Kleene’s strong three-valued logic K3 . In this paper, we extend Tamminga’s result by presenting an original finite, sound and complete proof-searching technique for all the truth-functional binary extensions of K3.
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