Paraconsistent Semantics for Extended Fuzzy Logic Programs via Approximation Fixpoint Theory

Pascal KettmannPascal Kettmann, Hannes StraßHannes Straß, Jesse HeyninckJesse Heyninck, Jeroen SpaansJeroen Spaans

Pascal Kettmann, Hannes Straß, Jesse Heyninck, Jeroen Spaans
Paraconsistent Semantics for Extended Fuzzy Logic Programs via Approximation Fixpoint Theory
The 10th International Joint Conference on Rules and Reasoning, to appear

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Bibtex

KurzfassungAbstract
In logic programming, negation can be interpreted in various ways. Probably best known is the concept of “negation as failure”, where “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.
Projekt:Project: SECAI
Forschungsgruppe:Research Group: Computational LogicComputational Logic

@inproceedings{KSHS2026,
  author    = {Pascal Kettmann and Hannes Stra{\ss} and Jesse Heyninck and
               Jeroen Spaans},
  title     = {Paraconsistent Semantics for Extended Fuzzy Logic Programs via
               Approximation Fixpoint Theory},
  booktitle = {The 10th International Joint Conference on Rules and Reasoning},
  year      = {2026}
}