Communication Dans Un Congrès Année : 2025

Graphical conditions for the existence, unicity and number of regular models

Résumé

The regular models of a normal logic program are a particular type of partial (i.e. 3-valued) models which correspond to stable partial models with minimal undefinedness. In this paper, we explore graphical conditions on the dependency graph of a finite ground normal logic program to analyze the existence, unicity and number of regular models for the program. We show three main results: 1) a necessary condition for the existence of non-trivial (i.e. non-2-valued) regular models, 2) a sufficient condition for the unicity of regular models, and 3) two upper bounds for the number of regular models based on positive feedback vertex sets. The first two conditions generalize the finite cases of the two existing results obtained by You and Yuan (1994) for normal logic programs with wellfounded stratification. The third result is also new to the best of our knowledge. Key to our proofs is a connection that we establish between finite ground normal logic programs and Boolean network theory.

Fichier principal
Vignette du fichier
paper.pdf (187.2 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-04708861 , version 1 (22-11-2024)

Licence

Identifiants

Citer

Van-Giang Trinh, Belaid Benhamou, Sylvain Soliman, François Fages. Graphical conditions for the existence, unicity and number of regular models. ICLP 2024 - 40th International Conference on Logic Programming, Oct 2024, Dallas, United States. pp.175-187, ⟨10.4204/EPTCS.416.16⟩. ⟨hal-04708861⟩
493 Consultations
238 Téléchargements

Altmetric

Partager

  • More