Abstract
Abstract 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 $n \geq 1$, we axiomatize the logic of regular closed sets of ${\mathbb{R}}^{n}$ with null boundary; (3) considering a broad class of equational theories that contains all logics of contact, we prove that they all have unitary or finitary unification, and that unification and admissibility are decidable.
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