RETRACTED AND REPLACED: 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 $n \geq 1$, 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.
Authors
- Tinko Tinchev (ORCID: https://orcid.org/0000-0002-0545-0364)
- Philippe Balbiani (ORCID: https://orcid.org/0000-0002-3569-9160)
- Quentin Gougeon (ORCID: https://orcid.org/0000-0002-3886-1143)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université Toulouse III - Paul Sabatier (FR)
- Institut National Polytechnique de Toulouse (FR)
- Université Toulouse-I-Capitole (FR)
- Institut de Recherche en Informatique de Toulouse (FR)
- Université Toulouse - Jean Jaurès (FR)
- Institut Polytechnique de Bordeaux (FR)
- Sofia University "St. Kliment Ohridski" (BG)
Publication Details
- Journal
- Journal of Logic and Computation
- Published
- 2024-09-05
- DOI
- https://doi.org/10.1093/logcom/exae065
- Primary Topic
- Logic, Reasoning, and Knowledge
- Type
- article
- Field-Weighted Citation Impact
- 0.00