ON NATURAL DEDUCTION IN FIRST-ORDER FIXPOINT LOGICS

Authors:
Andrzej Szalas
Affiliations:
(This research was supported in part by the KBN grant 3 P406 019 06) Institute of Informatics, University of Warsaw, 02-097 Warsaw, ul. Banacha 2, Poland, e-mail: szalas@mimuw.edu.pl
Venue:
Fundamenta Informaticae
Year:
1996

Citing 5
Cited 1

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Theoretical Computer Science - Special issue: Part B: Logic, semantics, and theory of programming
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Abstract

In the current paper we present a powerful technique of obtaining natural deduction proof systems for first-order fixpoint logics. The term fixpoint logics refers collectively to a class of logics consisting of modal logics with modalities definable at meta-level by fixpoint equations on formulas. The class was found very interesting as it contains most logics of programs with e.g. dynamic logic, temporal logic and the μ-calculus among them. In this paper we present a technique that allows us to derive automatically natural deduction systems for modal logics from fixpoint equations defining the modalities.