Admissible inference rules in the linear logic of knowledge and time $LTK_r$ with intransitive time relation

A. N. Luk'yanchuk^a, V. V. Rybakov<sup>ab

a</sup> Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russia
^b School of Computing, Mathematics and DT, Manchester Metropolitan University, John Dalton Building, Chester Street, Manchester, M1 5GD, UK

Abstract: We obtain a necessary condition and a sufficient condition for the admissibility of inference rules of the linear multi-modal logic of knowledge and time $LTK_r$ with reflexive and intransitive time relation. We also construct a special $n$-characterizing model for this logic.

Keywords: multi-modal logic, temporal logic, epistemic logic, $n$-characterizing model, admissibility of inference rules.

UDC: 510.665

Received: 02.09.2014

DOI: 10.17377/smzh.2015.56.309

 English version: Siberian Mathematical Journal, 2015, 56:3, 455–470

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