Graphical Conditions for the Existence, Unicity and Number of Regular Models
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915149722419200 |
|---|---|
| author | Trinh, Van-Giang Benhamou, Belaid Soliman, Sylvain Fages, François |
| author_facet | Trinh, Van-Giang Benhamou, Belaid Soliman, Sylvain Fages, François |
| contents | 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 well-founded 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09220 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graphical Conditions for the Existence, Unicity and Number of Regular Models Trinh, Van-Giang Benhamou, Belaid Soliman, Sylvain Fages, François Logic in Computer Science Artificial Intelligence Discrete Mathematics 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 well-founded 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. |
| title | Graphical Conditions for the Existence, Unicity and Number of Regular Models |
| topic | Logic in Computer Science Artificial Intelligence Discrete Mathematics |
| url | https://arxiv.org/abs/2502.09220 |