Y. Venema, L. Santocanale, Completeness for flat modal fixpoint logics,

Luigi Santocanale (1, 2) , Yde Venema (3)

1 Université de Provence - Aix-Marseille 1
2 LIF - Laboratoire d'informatique Fondamentale de Marseille
3 ILLC - Institute for Logic, Language and Computation

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 connectives #γ, γ in Γ. Each term #γ is meant to be interpreted as the 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.

Domaines: Logique en informatique [cs.LO]; Logique [math.LO]

Luigi Santocanale, Yde Venema. Y. Venema, L. Santocanale, Completeness for flat modal fixpoint logics,. 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, Oct 2007, Yerevan, Armenia. pp.499--513, ⟨10.1007/978-3-540-75560-9_36⟩. ⟨hal-01290705⟩