Admissibility of Logical Inference Rules

ISBN: 9780444895059 出版年：1997 页码：622 Rybakov, V V North Holland_RM

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.