TitleOn product fuzzy logic with truth-constants
Publication TypeConference Paper
Year of Publication2005
AuthorsCignoli R, Esteva F, Godo L, Noguera C
EditorLiu GChen Yingm, Ying M
Conference NameProceedings of the Eleventh International Fuzzy Systems Association World Congress IFSA 2005
PublisherTsinghua University Press, Springer

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.