Rules admissible in transitive temporal logic [formula omitted], sufficient condition

Abstract

The paper 1 1 Supported by Engineering and Physical Sciences Research Council (EPSRC), U.K., grant EP/F014406/1. develops a technique for computation inference rules admissible in temporal logic T S 4 . The problem whether there exists an algorithm recognizing inference rules admissible in T S 4 is a long-standing open problem. The logic T S 4 has neither the extension property nor the co-cover property which previously were central instruments for construction decision algorithms for admissibility in modal logics (e.g. reflexive and transitive modal logic S 4 ). Our paper uses a linear-compression property, a zigzag-ray property and a zigzag stretching property which hold for T S 4 . The main result of the paper is a sufficient condition for admissibility inference rules in T S 4 . It is shown that all rules which are valid in special finite models (with an effective upper bound on size) must be admissible in T S 4 .