Hierarchies of modal and temporal logics with reference pointers

Abstract
We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions.
Keywords Modal and temporal logics  reference pointers  expressiveness  axiomatization  completeness
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    Citations of this work BETA
    M. J. Cresswell (2010). Temporal Reference in Linear Tense Logic. Journal of Philosophical Logic 39 (2):173 - 200.
    Martin Lange (2009). Model Checking for Hybrid Logic. Journal of Logic, Language and Information 18 (4):465-491.
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