On Testing Irreflexivity of Reduction Orderings for Combined Substitutions in Intuitionistic Matrix Proofs

P. Baumgartner, R. Hähnle & J. Posegga, eds., 4 Workshop on Theorem Proving with Analytic Tableaux and Related Methods (TABLEAUX’95) – Short Papers & Poster Sessions, Universität Koblenz, Mai 1995, pp. 55-60. Abstract. In this paper we present a syntactical criterion for checking irreflexivity of the reduction ordering imposed by so–called combined substitutions which are part of the Matrix characterisation for first–order intuitionistic logic as presented by L. Wallen. The solution presented here is the concept of variable domains that can be considered as an extension of the well–known occurs–check technique.