Paraconsistent Semantics for Extended Fuzzy Logic Programs via Approximation Fixpoint Theory [Extended Version]
This work provides a unified semantic foundation for extended fuzzy logic programs, addressing a challenging problem for researchers in logic programming and knowledge representation.
The authors use approximation fixpoint theory to define semantics for fuzzy logic programs with both negation-as-failure and strong negation, showing that their framework generalizes several existing semantics and enables new ones.
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.