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 Sibirsk. Mat. Zh., 2013, Volume 54, Number 6, Pages 1304–1314 (Mi smj2497)

An axiomatization for the linear logic of knowledge and time $LTK_r$ with intransitive time relation

A. N. Luk'yanchuka, V. V. Rimatskiĭb

a Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russia
b Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russia

Abstract: We study the problem of the axiomatization of the linear multimodal logic of knowledge and time $LTK_r$ with reflexive intransitive time relation. The logic is defined semantically as the set of formulas true on frames of a special kind. The $LTK_r$-frames are linear chains of clusters connected by a reflexive intransitive relation $R_T$ which simulates time. Elements inside a cluster are connected by several equivalence relations imitating the knowledge of different agents. The main result of the article is the proof of the fact that the finite set of formulas proposed by the authors is an axiomatization of the logic $LTK_r$ with reflexive intransitive time relation.

Keywords: multimodal logic, linear temporal logic, epistemic logic, axiomatization, $n$-canonical model.

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English version:
Siberian Mathematical Journal, 2013, 54:6, 1037–1045

Bibliographic databases:

UDC: 510.643

Citation: A. N. Luk'yanchuk, V. V. Rimatskiǐ, “An axiomatization for the linear logic of knowledge and time $LTK_r$ with intransitive time relation”, Sibirsk. Mat. Zh., 54:6 (2013), 1304–1314; Siberian Math. J., 54:6 (2013), 1037–1045

Citation in format AMSBIB
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This publication is cited in the following articles:
1. V. F. Yun, “On the linear logic of knowledge and time with intransitive time relation”, Siberian Math. J., 56:3 (2015), 565–568
2. V. F. Yun, “On linear logic of knowledge and time”, Larisa Maksimova on Implication, Interpolation, and Definability, Outstanding Contributions to Logic, 15, ed. S. Odintsov, Springer, 2018, 339–349
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