Abstract

Hybridization is a method invented by Arthur Prior for extending the expressive power of modal languages. Although developed in interesting ways by Robert Bull, and by the So a school (notably, George Gargov, Valentin Goranko, Solomon Passy and Tinko Tinchev), the method remains little known. In our view this has deprived temporal logic of a valuable tool. The aim of the paper is to explain why hybridization is useful in temporal logic. We make two major points, the rst technical, the second conceptual. First, we showthathybridization gives rise to well-behaved logics that exhibit an interesting synergy between modal and classical ideas. This synergy, obvious for hybrid languages with full rst-order expressive strength, is demonstrated for a weaker local language capable of de ning the Until operator � we provide a minimal axiomatization, and show that in a wide range of temporally interesting cases extended completeness results can be obtained automatically. Second, we argue that the idea of sorted atomic symbols which underpins the hybrid enterprise can be developed further. To illustrate this, we discuss the advantages and disadvantages of a simple hybrid language which can quantify over paths. 1

Citations