Title On product fuzzy logic with truth-constants Publication Type Conference Paper Year of Publication 2005 Authors Cignoli R, Esteva F, Godo L, Noguera C Editor Liu GChen Yingm, Ying M Conference Name Proceedings of the Eleventh International Fuzzy Systems Association World Congress IFSA 2005 Publisher Tsinghua University Press, Springer Pagination 1244-1249 Abstract In this paper we present preliminary investigations on expansions of Product logic by adding into the language a countable set of truth constants and by adding the corresponding book-keeping axioms for the truth constants. In fact we consider here expansions with sets of truth constants defined by the natural and rational powers of an arbitrary real $a \in [0, 1]$, for which we prove weak standard completeness. Finite strong completeness results for these logics are studied, in particular when we restrict ourselves to formulas of the kind $\overline{r} \to \varphi$, where $\overline{r}$ is a truth constant denoting the truth degree $r$ and $\varphi$ is a formula without truth constants.