Sequent Systems for Trilattice Logics

2011 ◽  
pp. 113-141
Author(s):  
Yaroslav Shramko ◽  
Heinrich Wansing
Keyword(s):  
Sequent Systems

scholarly journals One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity

2020 ◽  
Author(s):  
Paweł Płaczek
Keyword(s):  
Analogous Result ◽  
Cut Elimination ◽  
Sequent Systems ◽  
Natural Symmetry ◽  
Sequent System

Bilinear Logic of Lambek [10] amounts to Noncommutative MALL of Abrusci [1]. Lambek [10] proves the cut–elimination theorem for a onesided (in fact, left-sided) sequent system for this logic. Here we prove an analogous result for the nonassociative version of this logic. Like Lambek [10], we consider a left-sided system, but the result also holds for its right-sided version, by a natural symmetry. The treatment of nonassociative sequent systems involves some subtleties, not appearing in associative logics. We also prove the PTIME complexity of the multiplicative fragment of NBL.

scholarly journals Involutive Nonassociative Lambek Calculus: Sequent Systems and Complexity

2017 ◽  
Vol 46 (1/2) ◽  
Author(s):  
Wojciech Buszkowski
Keyword(s):  
Cut Elimination ◽  
Lambek Calculus ◽  
Double Negation ◽  
Sequent Systems ◽  
Sequent System

In [5] we study Nonassociative Lambek Calculus (NL) augmented with De Morgan negation, satisfying the double negation and contraposition laws. This logic, introduced by de Grooté and Lamarche [10], is called Classical Non-Associative Lambek Calculus (CNL). Here we study a weaker logic InNL, i.e. NL with two involutive negations. We present a one-sided sequent system for InNL, admitting cut elimination. We also prove that InNL is PTIME.

scholarly journals Correction to: Sequent Systems for Negative Modalities

2017 ◽  
Vol 13 (1) ◽  
pp. 135-135
Author(s):  
Ori Lahav ◽  
João Marcos ◽  
Yoni Zohar
Keyword(s):  
Sequent Systems

scholarly journals Analytic Non-Labelled Proof-Systems for Hybrid Logic: Overview and a couple of striking facts

2022 ◽  
Author(s):  
Torben Braüner
Keyword(s):  
Natural Deduction ◽  
Hybrid Logic ◽  
Proof Systems ◽  
Sequent Systems ◽  
Tableau Systems

This paper is about non-labelled proof-systems for hybrid logic, that is, proof-systems where arbitrary formulas can occur, not just satisfaction statements. We give an overview of such proof-systems, focusing on analytic systems: Natural deduction systems, Gentzen sequent systems and tableau systems. We point out major results and we discuss a couple of striking facts, in particular that non-labelled hybrid-logical natural deduction systems are analytic, but this is not proved in the usual way via step-by-step normalization of derivations.

SEQUENT SYSTEMS FOR CLASSICAL AND INTUITIONISTIC SUBSTRUCTURAL MODAL LOGICS

2003 ◽  
Author(s):  
OSAMU WATARI ◽  
TAKESHI UENO ◽  
KOJI NAKATOGAWA ◽  
MAYUKA F. KAWAGUCHI ◽  
MASAAKI MIYAKOSHI
Keyword(s):  
Modal Logics ◽  
Sequent Systems

ON NON-MONOTONOUS PROPERTIES OF SOME CLASSICAL AND NONCLASSICAL PROPOSITIONAL PROOF SYSTEMS

2020 ◽  
Vol 54 (3 (253)) ◽  
pp. 127-136
Author(s):  
Anahit A. Chubaryan ◽  
Arsen A. Hambardzumyan
Keyword(s):  
Cut Rule ◽  
Proof Systems ◽  
Nonclassical Logics ◽  
Frege Systems ◽  
Sequent Systems ◽  
Propositional Proof Systems ◽  
Propositional Proof

We investigate the relations between the proof lines of non-minimal tautologies and its minimal tautologies for the Frege systems, the sequent systems with cut rule and the systems of natural deductions of classical and nonclassical logics. We show that for these systems there are sequences of tautologies ψn, every one of which has unique minimal tautologies φn such that for each n the minimal proof lines of φn are an order more than the minimal proof lines of ψn.

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