Complete Axiomatisations of Properties of Finite Sets
Thomas Ågotnes, Michał Walicki · Logic Journal of IGPL · 2008
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.