Bounded Sequent Calculi for Non-classical Logics via Hypersequents

2019 ◽  
pp. 94-110 ◽  
Author(s):  
Agata Ciabattoni ◽  
Timo Lang ◽  
Revantha Ramanayake
Keyword(s):  
Sequent Calculi

Sequent Calculi for Global Modal Consequence Relations

Studia Logica ◽  
2018 ◽  
Vol 107 (4) ◽  
pp. 613-637
Author(s):  
Minghui Ma ◽  
Jinsheng Chen
Keyword(s):  
Consequence Relations ◽  
Sequent Calculi

scholarly journals First order abduction via tableau and sequent calculi

1993 ◽  
Vol 1 (1) ◽  
pp. 99-117 ◽  
Author(s):  
MARTA CIALDEA MAYER ◽  
FIORA PIRRI
Keyword(s):  
Sequent Calculi ◽  
First Order

Sequent-Calculi for Metainferential Logics

Studia Logica ◽  
2021 ◽  
Author(s):  
Bruno Da Ré ◽  
Federico Pailos
Keyword(s):  
Sequent Calculi

Sequent Calculi for Intuitionistic Gödel–Löb Logic

2021 ◽  
Vol 62 (2) ◽  
Author(s):  
Iris van der Giessen ◽  
Rosalie Iemhoff
Keyword(s):  
Sequent Calculi

scholarly journals The Method of Socratic Proofs Meets Correspondence Analysis

2019 ◽  
Vol 48 (2) ◽  
pp. 99-116
Author(s):  
Dorota Leszczyńska-Jasion ◽  
Yaroslav Petrukhin ◽  
Vasilyi Shangin
Keyword(s):  
Correspondence Analysis ◽  
Boolean Functions ◽  
Propositional Logic ◽  
Sequent Calculus ◽  
Sequent Calculi ◽  
Classical Propositional Logic ◽  
Logic Of Questions ◽  
Proof Systems

The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence analysis resulting in invertible rules can constitute a new foundation for the method of Socratic proofs. Correspondence analysis is Kooi and Tamminga's technique for designing proof systems. In this paper it is used to consider sequent calculi with non-branching (the only exception being the rule of cut), invertible rules for the negation fragment of classical propositional logic and its extensions by binary Boolean functions.

scholarly journals Empirical Negation, Co-negation and the Contraposition Rule II: Proof-Theoretical Investigations

2020 ◽  
Author(s):  
Satoru Niki
Keyword(s):  
Sequent Calculi ◽  
Theoretical Investigations

We continue the investigation of the first paper where we studied logics with various negations including  empirical negation and co-negation. We established how such logics can be treated uniformly with R. Sylvan's CCω as the basis. In this paper we use this result to obtain cut-free labelled sequent calculi for the logics.

From the subformula property to cut-admissibility in propositional sequent calculi

2018 ◽  
Vol 28 (6) ◽  
pp. 1341-1366 ◽  
Author(s):  
Ori Lahav ◽  
Yoni Zohar
Keyword(s):  
Sequent Calculi ◽  
Subformula Property

UNIFORM INTERPOLATION IN SUBSTRUCTURAL LOGICS

2014 ◽  
Vol 7 (3) ◽  
pp. 455-483 ◽  
Author(s):  
MAJID ALIZADEH ◽  
FARZANEH DERAKHSHAN ◽  
HIROAKIRA ONO
Keyword(s):  
Propositional Logic ◽  
Predicate Logic ◽  
Interpolation Property ◽  
Substructural Logics ◽  
Substructural Logic ◽  
Sequent Calculi ◽  
Structural Rule ◽  
Modal Propositional Logic ◽  
Uniform Interpolation ◽  
Classical Predicate

AbstractUniform interpolation property of a given logic is a stronger form of Craig’s interpolation property where both pre-interpolant and post-interpolant always exist uniformly for any provable implication in the logic. It is known that there exist logics, e.g., modal propositional logic S4, which have Craig’s interpolation property but do not have uniform interpolation property. The situation is even worse for predicate logics, as classical predicate logic does not have uniform interpolation property as pointed out by L. Henkin.In this paper, uniform interpolation property of basic substructural logics is studied by applying the proof-theoretic method introduced by A. Pitts (Pitts, 1992). It is shown that uniform interpolation property holds even for their predicate extensions, as long as they can be formalized by sequent calculi without contraction rules. For instance, uniform interpolation property of full Lambek predicate calculus, i.e., the substructural logic without any structural rule, and of both linear and affine predicate logics without exponentials are proved.

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