@conference {3775, title = {Decidability of a Description Logic over infinite-valued Product Logic}, booktitle = {12th Conference on Principles of Knowledge Representation and Reasoning, KR 2010}, year = {2010}, month = {10/05/2010}, pages = {203-213}, publisher = {AAAI Press}, organization = {AAAI Press}, address = {Toronto (Canada)}, 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.}, author = {Marco Cerami and Francesc Esteva and F{\`e}lix Bou}, editor = {Fangzhen Lin, Ulrike Sattler and Miroslaw Truszczynski} }