Admissibility of Logical Inference Rules - 1st Edition - ISBN: 9780444895059, 9780080525990

Admissibility of Logical Inference Rules, Volume 136

1st Edition

Authors: V.V. Rybakov
Hardcover ISBN: 9780444895059
eBook ISBN: 9780080525990
Imprint: North Holland
Published Date: 14th March 1997
Page Count: 616
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Table of Contents

Preface and acknowledgments. Introduction. Syntaxes and Semantics. Syntax of formal logic systems. First-order semantics and universal algebra. Algebraic semantics for propositional logics. Admissible rules in algebraic logics. Logical consequence relations. Algebraizable consequence relations. Admissibility for consequence relations. Lattices of logical consequences. Semantics for Non-Standard Logics. Algebraic semantics for intuitionistic logic. Algebraic semantics, modal and tense logics. Kripke semantics for modal and temporal logic. Kripke semantics for intuitionistic logic. Stone's theory and Kripke semantics. The finite model property. Relation of intuitionistic and modal logics. Advanced tools for the finite model property. Kripke incomplete logics. Advanced tools for Kripke completeness.Criteria for Admissibility. Reduced forms. T–translation of inference rules. Semantic criteria for admissibility. Some technical lemmas. Criteria for determining admissibility. Elementary theories of free algebras. Scheme–logics of first–order theories. Some counterexamples. Admissibility through reduced forms. Bases for Inference Rules. Initial auxiliary results. The absence of finite bases. Bases for some strong logics. Bases for valid rules of tabular logics. Tabular logics without independent bases. Structural Completeness. General properties, descriptions. Quasi–characteristic inference rules. Some preliminary technical results. Hereditary structural completeness. Structurally complete fragments. Related Questions. Rules with meta–variables. The preservation of admissible for S4 rules. The preservation of admissibility for H. Non-compact modal logics. Decidable Kripke non–compact logics. Non–compact superintuitionistic logics. Index. Bibliography.


Description

Preface and acknowledgments. Introduction. Syntaxes and Semantics. Syntax of formal logic systems. First-order semantics and universal algebra. Algebraic semantics for propositional logics. Admissible rules in algebraic logics. Logical consequence relations. Algebraizable consequence relations. Admissibility for consequence relations. Lattices of logical consequences. Semantics for Non-Standard Logics. Algebraic semantics for intuitionistic logic. Algebraic semantics, modal and tense logics. Kripke semantics for modal and temporal logic. Kripke semantics for intuitionistic logic. Stone's theory and Kripke semantics. The finite model property. Relation of intuitionistic and modal logics. Advanced tools for the finite model property. Kripke incomplete logics. Advanced tools for Kripke completeness.Criteria for Admissibility. Reduced forms. T–translation of inference rules. Semantic criteria for admissibility. Some technical lemmas. Criteria for determining admissibility. Elementary theories of free algebras. Scheme–logics of first–order theories. Some counterexamples. Admissibility through reduced forms. Bases for Inference Rules. Initial auxiliary results. The absence of finite bases. Bases for some strong logics. Bases for valid rules of tabular logics. Tabular logics without independent bases. Structural Completeness. General properties, descriptions. Quasi–characteristic inference rules. Some preliminary technical results. Hereditary structural completeness. Structurally complete fragments. Related Questions. Rules with meta–variables. The preservation of admissible for S4 rules. The preservation of admissibility for H. Non-compact modal logics. Decidable Kripke non–compact logics. Non–compact superintuitionistic logics. Index. Bibliography.


Details

No. of pages:
616
Language:
English
Copyright:
© North Holland 1997
Published:
Imprint:
North Holland
eBook ISBN:
9780080525990
Hardcover ISBN:
9780444895059

About the Authors

V.V. Rybakov Author

Affiliations and Expertise

Krasnoyarsk University, Mathematics Department, Krasnoyarsk, Russia