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A unified semantic framework for fully structural propositional sequent systems

A unified semantic framework for fully structural propositional sequent systems A Unified Semantic Framework for Fully Structural Propositional Sequent Systems ORI LAHAV and ARNON AVRON, Tel Aviv University We identify a large family of fully structural propositional sequent systems, which we call basic systems. We present a general uniform method for providing (potentially, nondeterministic) strongly sound and complete Kripke-style semantics, which is applicable for every system of this family. In addition, this method can also be applied when: (i) some formulas are not allowed to appear in derivations, (ii) some formulas are not allowed to serve as cut formulas, and (iii) some instances of the identity axiom are not allowed to be used. This naturally leads to new semantic characterizations of analyticity (global subformula property), cut admissibility and axiom expansion in basic systems. We provide a large variety of examples showing that many soundness and completeness theorems for different sequent systems, as well as analyticity, cut admissibility, and axiom expansion results, easily follow using the general method of this article. Categories and Subject Descriptors: F.4.1 [Mathematical Logic]: Proof Theory General Terms: Theory Additional Key Words and Phrases: Analyticity, axiom expansion, cut admissibility, Kripke semantics, logic, nondeterministic semantics, proof theory, semantic characterization, sequent calculi ACM Reference Format: Lahav, O. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

A unified semantic framework for fully structural propositional sequent systems

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References (34)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2013 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2528930
Publisher site
See Article on Publisher Site

Abstract

A Unified Semantic Framework for Fully Structural Propositional Sequent Systems ORI LAHAV and ARNON AVRON, Tel Aviv University We identify a large family of fully structural propositional sequent systems, which we call basic systems. We present a general uniform method for providing (potentially, nondeterministic) strongly sound and complete Kripke-style semantics, which is applicable for every system of this family. In addition, this method can also be applied when: (i) some formulas are not allowed to appear in derivations, (ii) some formulas are not allowed to serve as cut formulas, and (iii) some instances of the identity axiom are not allowed to be used. This naturally leads to new semantic characterizations of analyticity (global subformula property), cut admissibility and axiom expansion in basic systems. We provide a large variety of examples showing that many soundness and completeness theorems for different sequent systems, as well as analyticity, cut admissibility, and axiom expansion results, easily follow using the general method of this article. Categories and Subject Descriptors: F.4.1 [Mathematical Logic]: Proof Theory General Terms: Theory Additional Key Words and Phrases: Analyticity, axiom expansion, cut admissibility, Kripke semantics, logic, nondeterministic semantics, proof theory, semantic characterization, sequent calculi ACM Reference Format: Lahav, O.

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Nov 1, 2013

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