Bases of admissible rules of the logics S4 and Int

DOI10.1007/BF01978706zbMath0598.03014MaRDI QIDQ1079559

Vladimir Vladimirovich Rybakov

Publication date: 1985

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/187304

zbMATH Keywords

modal logicfinite basisadmissible rulesintuitionistic propositional calculusinfinite basis

Mathematics Subject Classification ID

Modal logic (including the logic of norms) (03B45) Other nonclassical logic (03B60) Decidability of theories and sets of sentences (03B25) Other algebras related to logic (03G25) Metamathematics of constructive systems (03F50) Intermediate logics (03B55)

Related Items (20)

Criteria for admissibility of inference rules. Modal and intermediate logics with the branching property ⋮ Jankov Formulas and Axiomatization Techniques for Intermediate Logics ⋮ Admissible bases via stable canonical rules ⋮ Admissible and derivable rules in intuitionistic logic ⋮ Unnamed Item ⋮ Rules admissible in transitive temporal logic \(\mathrm{T}_{\mathrm{S}4}\), sufficient condition ⋮ KD is nullary ⋮ Admissibility in positive logics ⋮ Globally admissible inference rules ⋮ Admissible inference rules of modal WCP-logics ⋮ An explicit basis for \textit{WCP}-globally admissible inference rules ⋮ An explicit basis for admissible inference rules in table modal logics of width 2 ⋮ Table admissible inference rules ⋮ Problems of substitution and admissibility in the modal system Grz and in intuitionistic propositional calculus ⋮ Branching time logics \(\mathcal {BTL}^{\text{U,S}}_{\text{N},\text{N}^{-1}}(\mathcal {Z})_{\alpha }\) with operations \textit{Until} and \textit{Since} based on bundles of integer numbers, logical consecutions, deciding algorithms ⋮ Solvability of logical equations in the modal system Grz and intuitionistic logic ⋮ Admissible inference rules in the linear logic of knowledge and time \(\mathrm{LTK}_r\) with intransitive time relation ⋮ Deductive systems with multiple-conclusion rules and the disjunction property ⋮ Logical consecutions in discrete linear temporal logic ⋮ DECIDABILITY OF ADMISSIBILITY: ON A PROBLEM BY FRIEDMAN AND ITS SOLUTION BY RYBAKOV

Cites Work

• Unnamed Item
• Decidability of the admissibility problem in layer-finite logics
• Completeness of calculii for axiomatically defined classes of algebras
• One hundred and two problems in mathematical logic
• ON ADMISSIBLE RULES OF INTUITIONISTIC PROPOSITIONAL LOGIC
• Modal Logics Between S 4 and S 5

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