First-Order Definability of Transition Structures

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RUMBERG, Antje, Alberto ZANARDO, 2019. First-Order Definability of Transition Structures. In: Journal of Logic, Language and Information. 28(3), pp. 459-488. ISSN 0925-8531. eISSN 1572-9583. Available under: doi: 10.1007/s10849-018-9276-4

@article{Rumberg2019-09First-47045, title={First-Order Definability of Transition Structures}, year={2019}, doi={10.1007/s10849-018-9276-4}, number={3}, volume={28}, issn={0925-8531}, journal={Journal of Logic, Language and Information}, pages={459--488}, author={Rumberg, Antje and Zanardo, Alberto} }

Rumberg, Antje terms-of-use 2019-09-26T13:47:43Z eng First-Order Definability of Transition Structures 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<sub>t</sub> 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<sub>t</sub>-validity w.r.t. transition structures. As a consequence, for a certain fragment of L<sub>t</sub>, validity w.r.t. transition structures turns out to be axiomatizable. The result is then extended to the entire language L<sub>t</sub> by means of a quite natural ‘Henkin move’, i.e. by relaxing the notion of validity to bundled structures. Zanardo, Alberto 2019-09-26T13:47:43Z Rumberg, Antje 2019-09 Zanardo, Alberto

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