Relational Representation Theorems for Extended Contact Algebras

Philippe Balbiani (1, 2) , Tatyana Ivanova (3)

1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
2 CNRS - Centre National de la Recherche Scientifique
3 BAS - Bulgarian Academy of Sciences

In topological spaces, the relation of extended contact is a ternary relation that holds between regular closed subsets A, B and D if the intersection of A and B is included in D. The algebraic counterpart of this mereotopological relation is the notion of extended contact algebra which is a Boolean algebra extended with a ternary relation. In this paper, we are interested in the relational representation theory for extended contact algebras. In this respect, we study the correspondences between point-free and point-based models of space in terms of extended contact. More precisely, we prove new representation theorems for extended contact algebras.

Mots clés: Regular closed subsets; Contact algebras; Extended contact algebras; Regular closed subsets; Topological representation; Relational representation

Domaines: Informatique [cs]; Logique en informatique [cs.LO]

Philippe Balbiani, Tatyana Ivanova. Relational Representation Theorems for Extended Contact Algebras. Studia Logica, 2020, 109, pp.701-723. ⟨10.1007/s11225-020-09923-0⟩. ⟨hal-03762140v2⟩