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Journal of Logic and Computation 2004 14(3):429-435; doi:10.1093/logcom/14.3.429
© 2004 by Oxford University Press
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Original Article

Rules and Refutation Rules for the Logic of Finite n-ary Trees

Tom Skura

Department of Logic, University of Wroclaw, Koszarowa 3, 51-149 Wroclaw, Poland. E-mail: tfskura{at}uni.wroc.pl

In this paper we give a new syntactic decision procedure for the logic of finite n-ary trees (axiomatized by Gabbay and de Jongh by means of semantic methods). In the decision procedure we use the simple concept of a rule both for proving valid formulas and for refuting invalid ones. Refutation rules with certain normal forms are introduced, and it is shown in a constructive way that every normal form is either provable or refutable.

Keywords: Intermediate logics, decidability, axiom systems, refutation rules, normal forms.

Received 24 March 2003.


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