Revisiting completeness for the Kn modal logics: a new proof

Logic Journal of the IGPL 8 (1):101-105 (2000)
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Abstract

Apostoli and Brown have shown that the class of formulae valid with respect to the class of -ary relational frames is completely axiomatized by Kn: an n-place aggregative system which adjoins [RM], [RN], and a complete axiomatization of propositional logic, with [Kn]:□α1 ∧...∧□αn+1 → □2/ is the disjunction of all pairwise conjunctions αi∧αj )).Their proof exploits the chromatic indices of n-uncolourable hypergraphs, or n-traces. Here, we use the notion of the χ-product of a family of sets to formulate an alternative definition of an n-trace, which in turn enables a new and simpler completeness proof

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References found in this work

Inference and necessity.P. K. Schotch & R. E. Jennings - 1980 - Journal of Philosophical Logic 9 (3):327-340.
Some remarks on (weakly) weak modal logics.R. E. Jennings & P. K. Schotch - 1981 - Notre Dame Journal of Formal Logic 22 (4):309-314.

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