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
Pagination1244-1249
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.