Complete Axiomatisations of Properties of Finite Sets

Logic Journal of the IGPL 16 (3):293-313 (2008)
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Abstract

We study a logic whose formulae are interpreted as properties of a finite set over some universe. The language is propositional, with two unary operators inclusion and extension, both taking a finite set as argument. We present a basic Hilbert-style axiomatisation, and study its completeness. The main results are syntactic and semantic characterisations of complete extensions of the logic

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