On fuzzyfied public announcement operators in G\"odel-Dummett logic
Nicholas Pischke · arXiv (Cornell University) · 2017
In this paper, we consider the expansion of basic modal Godel logic with the notions of public announcements. Additionally, the public announcement operators are itself fuzzyfied, allowing statements about relations between the truth-value of a formula and rational constant values as well as various combinations of these. Following from this, the problems of the classic style of axiomatization of this new logic are discussed and we investigate the usual reduction-style axioms where we present a work-around for various problems using the Baaz-$\Delta$ and respective constants value formulas as extensions for basic Godel logic. For this we show, that this logic is itself more expressive than our newly introduced one. Finally, we consider the expansion of the fuzzy public announcement logic itself with the notions of the $\Delta$-operator and rational constants, which resolves the before presented problems and from which we can provide the usual proof of completeness by reduction.