Temporal logic with predicate abstraction

Abstract

A predicate linear temporal logic LTL_{λ,=} without quantifiers but with predicate abstraction mechanism and equality is considered. The models of LTL_{λ,=} can be naturally seen as the systems of pebbles (flexible constants) moving over the elements of some (possibly infinite) domain. This allows to use LTL_{λ,=} for the specification of dynamic systems using some resources, such as processes using memory locations, mobile agents occupying some sites, etc. On the other hand we show that LTL_{λ,=} is not recursively axiomatizable and, therefore, fully automated verification of LTL_{λ,=} specifications is not, in general, possible.