On the existence and unicity of stable models in normal residuated logic programs

Abstract

We introduce a sufficient condition which guarantees the existence of stable models for a normal residuated logic program interpreted on the truth-space [0, 1] ⁿ . Specifically, the continuity of the connectives involved in the program ensures the existence of stable models. Then, we study conditions which guarantee the uniqueness of stable models in the particular case of the product t-norm, its residuated implication and the standard negation.

Keywords:

• stable models
• residuated logic programming
• fuzzy logic programming
• existence of models
• uniqueness of models

2000 AMS Subject Classifications :

• 03B52
• 68N17

Acknowledgements

This work was partially supported by the Spanish Ministry of Science project TIN09-14562-C05-01 and Junta de Andalucía projects FQM-2049 and FQM-5233.

Notes

Note the overloaded use of the negation symbol, as a syntactic function in the formulas and as the algebraic negation in the truth-values.

The values are approximated to two digits precision.

If p does not appear in the head of any rule then .