A. N. Luk'yanchuk, V. V. Rimatskiĭ, “An axiomatization for the linear logic of knowledge and time <nobr>$LTK_r$</nobr> with intransitive time relation”, Sibirsk. Mat. Zh., 2013, Volume 54, Number 6,Pages <nobr>1304

This article is cited in 3 papers

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

A. N. Luk'yanchuk^a, V. V. Rimatskiĭ^b

^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.

UDC: 510.643

Received: 25.03.2013