Indexed Flows in Temporal x Modal Logic with Functional Semantics
Abstract
Two classical semantical approaches to studying logics which combine time and modality are the T /spl times/ W-frames and Kamp-frames (Thomason (1984)). In this paper we study a new kind of frame that extends the one introduced in Burrieza et al. (2002). The motivation is twofold: theoretical, i.e., representing properties of the basic theory of functions (definability); and practical, their use in computational applications (considering time-flows as memory of computers connected in a net, each computer with its own clock). Specifically, we present a temporal /spl times/ modal (labelled) logic, whose semantics are given by ind-functional frames in which accessibility functions are used in order to interconnect time-flows. This way, we can: (i) specify to what time-flow we want to go; (ii) carry out different comparisons among worlds with different time measures; and (iii) define properties of certain kinds of functions (in particular, of total, injective, surjective, constant, increasing and decreasing functions), without the need to resort to second-order theories. In addition, we define a minimal axiomatic system and give the completeness theorem (Henkin-style).
Citation
Please, cite this work as:
[BGM02] A. Burrieza, I. P. de Guzmán, and E. Mu~noz-Velasco. “Indexed Flows in Temporal x Modal Logic with Functional Semantics”. In: 9th International Symposium on Temporal Representation and Reasoning, TIME-2002, Manchester, UK, July 7-9, 2002. IEEE Computer Society, 2002, pp. 146-153. DOI: 10.1109/TIME.2002.1027488. URL: https://doi.org/10.1109/TIME.2002.1027488.
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Papers citing this work
The following is a non-exhaustive list of papers that cite this work:
[1] G. Aguilera, A. Burrieza, P. Cordero, et al. “MAT Logic: A Temporal×Modal Logic with Non-deterministic Operators to Deal with Interactive Systems in Communication Technologies”. In: Advances in Artificial Intelligence - IBERAMIA-SBIA 2006. Springer Berlin Heidelberg, 2006, p. 602–611. ISBN: 9783540454649. DOI: 10.1007/11874850_64. URL: http://dx.doi.org/10.1007/11874850_64.
[2] A. Burrieza, I. P. De Guzmán, and E. Muñoz-Velasco. “Generalization of some properties of relations in the context of functional temporal×modal logic”. In: International Journal of Computer Mathematics 85.3–4 (Apr. 2008), p. 371–383. ISSN: 1029-0265. DOI: 10.1080/00207160701210141. URL: http://dx.doi.org/10.1080/00207160701210141.
[3] A. Burrieza, I. Fortes, and I. P. de Guzmán. “Completeness of a functional system for surjective functions”. In: Mathematical Logic Quarterly 63.6 (Dec. 2017), p. 574–597. ISSN: 1521-3870. DOI: 10.1002/malq.201600011. URL: http://dx.doi.org/10.1002/malq.201600011.
[4] A. Burrieza, I. P. de Guzmán, and E. Muñoz-Velasco. “Functional systems in the context of temporal×modal logics with indexed flows”. In: International Journal of Computer Mathematics 86.10–11 (Nov. 2009), p. 1696–1706. ISSN: 1029-0265. DOI: 10.1080/00207160902795619. URL: http://dx.doi.org/10.1080/00207160902795619.
[5] A. Burrieza, I. P. de Guzmán, and E. Muñoz‐Velasco. “Analyzing completeness of axiomatic functional systems for temporal × modal logics”. In: Mathematical Logic Quarterly 56.1 (Jan. 2010), p. 89–102. ISSN: 1521-3870. DOI: 10.1002/malq.200810038. URL: http://dx.doi.org/10.1002/malq.200810038.