Abstract:

This paper proves that validity and satisfiability of
assertions in the Fuzzy Description Logic based on infinite-valued
Product Logic with universal and existential quantifiers (which are
non-interdefinable) is decidable when we only consider quasi-witnessed
interpretations. We prove that this restriction is neither necessary for the validity
problem (i.e., the validity of assertions in the Fuzzy Description Logic
based on infinite-valued Product Logic is decidable) nor for the
positive satisfiability problem, because quasi-witnessed interpretations
are particularly adequate for the infinite-valued Product Logic.
We give an algorithm that reduces the problem of validity (and
satisfiability) of assertions in our Fuzzy Description Logic (restricted to
quasi-witnessed interpretations) to a semantic consequence problem, with
finite number of hypothesis, on infinite-valued propositional Product
Logic.

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