Completeness for flat modal fixpoint logics

Authors:
Luigi Santocanale;Yde Venema
Affiliations:
Laboratoire d'Informatique Fondamentale de Marseille, Université de Provence;Institute for Logic, Language and Computation, Universiteit van Amsterdam
Venue:
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Year:
2007

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Abstract

Given a set Γ of modal formulas of the form γ(x, p), where x occurs positively in γ, the language L #(Γ) is obtained by adding to the language of polymodal logic K connectives #γ, γ ∈ Γ. Each term #γ is meant to be interpreted as the parametrized least fixed point of the functional interpretation of the term γ(x). Given such a Γ, we construct an axiom system K #(Γ) which is sound and complete w.r.t. the concrete interpretation of the language L #(Γ) on Kripke frames. If Γ is finite, then K #(Γ) is a finite set of axioms and inference rules.