First-Order Definability of Transition Structures

Type of Publication: Journal article
Publication status: Published
URI (citable link): http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1ptg5sm10nfro6
Author: Rumberg, Antje; Zanardo, Alberto
Year of publication: 2019
Published in: Journal of Logic, Language and Information ; 28 (2019), 3. - pp. 459-488. - ISSN 0925-8531. - eISSN 1572-9583
DOI (citable link): https://dx.doi.org/10.1007/s10849-018-9276-4
Summary:
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 Lt 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 Lt-validity w.r.t. transition structures. As a consequence, for a certain fragment of Lt, validity w.r.t. transition structures turns out to be axiomatizable. The result is then extended to the entire language Lt by means of a quite natural ‘Henkin move’, i.e. by relaxing the notion of validity to bundled structures.
Subject (DDC): 100 Philosophy
Keywords: Branching time, Transition semantics, Index structures, First-order definability, Axiomatizability
Link to License: In Copyright
Refereed: Yes

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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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