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Preprints, Working Papers, ... Year : 2024

Logics for Contact and Measure

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≥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.
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Dates and versions

hal-04544145 , version 1 (12-04-2024)
hal-04544145 , version 2 (16-04-2024)

Identifiers

  • HAL Id : hal-04544145 , version 1

Cite

Philippe Balbiani, Quentin Gougeon, Tinko Tinchev. Logics for Contact and Measure. 2024. ⟨hal-04544145v1⟩
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