Reasoning in Infinitely Valued G-IALCQ
This work addresses a specific challenge in formal knowledge representation for AI, providing a decidable reasoning method for a logic that handles vague knowledge, but it is incremental as it builds on existing techniques.
The paper tackles the problem of reasoning in fuzzy description logics with infinitely valued Gödel semantics, extending previous decidability results to include qualified number restrictions. The result is a novel approach that combines crispification and automata-based methods, overcoming their individual drawbacks.
Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable in the presence of a negation constructor and general concept inclusion axioms. One exception to this negative result are FDLs whose semantics is based on the infinitely valued Gödel t-norm (G). In this paper, we extend previous decidability results for G-IALC to deal also with qualified number restrictions. Our novel approach is based on a combination of the known crispification technique for finitely valued FDLs and the automata-based procedure originally developed for reasoning in G-IALC. The proposed approach combines the advantages of these two methods, while removing their respective drawbacks.