Complete Axiomatisations of Properties of Finite Sets

T. Agotnes, M. Walicki
2008 Logic Journal of the IGPL  
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. Vol. 16 No. 3,
doi:10.1093/jigpal/jzn008 fatcat:4zmkp5bgincatjoyqvbvxvuguy