Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A Strong Completeness Theorem for the Gentzen systems associated with finite algebras

A Strong Completeness Theorem for the Gentzen systems associated with finite algebras In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the special case of the finite linear MV-algebras, the Strong Completeness Theorem was proved in [10], as a consequence of McNaughton's Theorem. The main tool to prove this result for arbitrary algebras is the deduction-detachment theorem for Gentzen systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Non-Classical Logics Taylor & Francis

A Strong Completeness Theorem for the Gentzen systems associated with finite algebras

Download PDF
28 pages

A Strong Completeness Theorem for the Gentzen systems associated with finite algebras

Abstract

In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the...
Loading next page...
 
/lp/taylor-francis/a-strong-completeness-theorem-for-the-gentzen-systems-associated-with-Vfje1Pek0L
Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1958-5780
eISSN
1166-3081
DOI
10.1080/11663081.1999.10510956
Publisher site
See Article on Publisher Site

Abstract

In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the special case of the finite linear MV-algebras, the Strong Completeness Theorem was proved in [10], as a consequence of McNaughton's Theorem. The main tool to prove this result for arbitrary algebras is the deduction-detachment theorem for Gentzen systems.

Journal

Journal of Applied Non-Classical Logics – Taylor & Francis

Published: Jan 1, 1999

Keywords: 03B50; 03F03; 03B22; Many-valued propositional logic; Gentzen system; sequent calculus; deduction theorem; completeness; cut elimination; finite algebra

There are no references for this article.