First-Order Definability of Transition Structures

Antje Rumberg, Alberto Zanardo
2018 Journal of Logic, Language and Information  
The transition semantics presented in Rumberg (J Log Lang Inf 25(1):77-108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language L t are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves L t -validity w.r.t. transition structures. As a
more » ... consequence, for a certain fragment of L t , validity w.r.t. transition structures turns out to be axiomatizable. The result is then extended to the entire language L t by means of a quite natural 'Henkin move', i.e. by relaxing the notion of validity to bundled structures.
doi:10.1007/s10849-018-9276-4 fatcat:wocsnw7dnrc6dadmdz3xzpym2q