B. R. Fedorishin, “An explicit basis for the admissible inference rules in the Gödel–Löb logic <nobr>$GL$</nobr>”, Sibirsk. Mat. Zh., 2007, Volume 48, Number 2,Pages <nobr>423

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An explicit basis for the admissible inference rules in the Gödel–Löb logic $GL$

B. R. Fedorishin

Krasnoyarsk State Technical University

Abstract: We describe an explicit basis for the admissible inference rules in the Gödel–Löb logic. The basis consists of a sequence of inference rules in infinitely many variables. Inference rules in the reduced form play an important role in this study. Alongside a basis for the admissible rules we obtain a basis for the quasi-identities of the countable rank free algebra in the Gödel–Löb logic.

Keywords: modal logic, inference rule, admissible rule, frame, basis.

UDC: 510.643

Received: 18.07.2003