Fuzzy description logics with general t-norms and datatypes

Fuzzy description logics (DLs) are a family of logics which allow the representation of (and the reasoning within) structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, current fuzzy DLs still present several limitations. In this work we face two problems: the common restriction to Zadeh and Łukasiewicz fuzzy logics and the inability to deal with datatypes different from fuzzy sets. In particular, we propose a semantics based on the use of a general left-continuous t-norm and an involutive negation (specially focused on Product logic) and, furthermore, we show how to handle functional concrete roles relating individuals of the domain and strings, real or integer numbers.