This article is cited in 20 papers

On the Positive Fragment of the Polymodal Provability Logic $\mathbf{GLP}$

E. V. Dashkov

M. V. Lomonosov Moscow State University

Abstract: The fragment of the polymodal provability logic $\mathbf{GLP}$ in the language with connectives $\top$, $\wedge$, and $\langle n\rangle$ for all $n\in\omega$ is considered. For this fragment, a deductive system it constructed, a Kripke semantics is proposed, and a polynomial bound for the complexity of a decision procedure is obtained.

Keywords: modal logic, graded provability logic $\mathbf{GLP}$, equational calculus, deductive system, Kripke semantics, complexity of a decision procedure.

UDC: 510

Received: 24.04.2011
Revised: 17.07.2011

DOI: 10.4213/mzm9138

 English version: Mathematical Notes, 2012, 91:3, 318–333

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