JOURNAL ARTICLE

Contact semilattices.

  • Published In: Logic Journal of the IGPL, 2024, v. 32, n. 5. P. 815 1 of 3

  • Database: Business Source Ultimate 2 of 3

  • Authored By: Lipparini, Paolo 3 of 3

Abstract

The article focuses on characterizing when a join semilattice equipped with a weak contact relation can be semilattice embedded into Boolean algebras or distributive lattices endowed with various forms of contact relations, such as overlap or additive contact. It establishes exact necessary and sufficient conditions—expressed as axioms (D1), (D2), and a weaker form (D2-)—that determine embeddability into Boolean algebras with overlap contact or weak contact, respectively. The work connects these algebraic structures to region-based spatial theories and logical applications, providing representation theorems that clarify the relationships between contact join-semilattices, contact distributive lattices, and contact Boolean algebras. Several examples illustrate distinctions between additive and non-additive contact relations, and the article concludes with open problems regarding axiomatizability and embeddings into modular lattices.

Additional Information

  • Source:Logic Journal of the IGPL. 2024/10, Vol. 32, Issue 5, p815
  • Document Type:Article
  • Subject Area:Science
  • Publication Date:2024
  • ISSN:1367-0751
  • DOI:10.1093/jigpal/jzad012
  • Accession Number:180267721
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