Complete Axiomatisations of Properties of Finite Sets

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.

• Type: Journal
• Year: 2008
• Where: IGPL
• Authors: Thomas Ågotnes, Michal Walicki
• Keywords: Basic Hilbert-style Axiomatisation, IGPL 2008, Semantic Characterisations, Unary Operators Inclusion