Paraconsistent Semantics for Extended Fuzzy Logic Programs via Approximation Fixpoint Theory [Extended Version]
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917524444020736 |
|---|---|
| author | Kettmann, Pascal Strass, Hannes Heyninck, Jesse Spaans, Jeroen |
| author_facet | Kettmann, Pascal Strass, Hannes Heyninck, Jesse Spaans, Jeroen |
| contents | In logic programming, negation can be interpreted in various ways. Probably best known is the concept of "negation as failure", where "$\mathit{not}\, p$" is true if we have no evidence for $p$. On the other hand, strong negation requires that we have evidence for $p$ being false. Defining semantics for logic programs containing both kinds of negation is a challenging task, and this becomes even more challenging when combining this with other extensions of logic programming, e.g. fuzziness. In this work, we use the framework of approximating fixpoint theory to formulate well-behaved semantics for fuzzy logic programs containing both "by-failure" and strong negation. We show that this framework generalizes several existing semantics as well as giving rise to a host of new semantics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05286 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Paraconsistent Semantics for Extended Fuzzy Logic Programs via Approximation Fixpoint Theory [Extended Version] Kettmann, Pascal Strass, Hannes Heyninck, Jesse Spaans, Jeroen Logic in Computer Science In logic programming, negation can be interpreted in various ways. Probably best known is the concept of "negation as failure", where "$\mathit{not}\, p$" is true if we have no evidence for $p$. On the other hand, strong negation requires that we have evidence for $p$ being false. Defining semantics for logic programs containing both kinds of negation is a challenging task, and this becomes even more challenging when combining this with other extensions of logic programming, e.g. fuzziness. In this work, we use the framework of approximating fixpoint theory to formulate well-behaved semantics for fuzzy logic programs containing both "by-failure" and strong negation. We show that this framework generalizes several existing semantics as well as giving rise to a host of new semantics. |
| title | Paraconsistent Semantics for Extended Fuzzy Logic Programs via Approximation Fixpoint Theory [Extended Version] |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2605.05286 |