Logics for Contact and Measure

Philippe Balbiani (1, 2) , Quentin Gougeon (3, 2) , Tinko Tinchev (4)

1 CNRS - Centre National de la Recherche Scientifique
2 IRIT-LILaC - Logique, Interaction, Langue et Calcul
3 UT3 - Université Toulouse III - Paul Sabatier
4 Софийски университет = Sofia University

We enrich contact algebras with a new binary relation that compares the size of regions, and provide axiom systems for various logics of contact and measure. Our contribution is three-fold: (1) we characterize the relations on a Boolean algebra that derive from a measure, thereby improving an old result of Kraft, Pratt and Seidenberg; (2) for all n≥1, we axiomatize the logic of regular closed sets of R^n with null boundary; (3) considering a broad class of equational theories that contains all logics of contact, we prove that they all have unary or finitary unification, and that unification and admissibility are decidable.

Keywords: Contact algebras; Measure; Logic; Real line; Unification; Admissibility

Domains: Computer Science [cs]

Philippe Balbiani, Quentin Gougeon, Tinko Tinchev. Logics for Contact and Measure. 2024. ⟨hal-04544145v2⟩