Abstract: We continue the research on quantitative comparison of two fuzzy logics: the Łukasiewicz logic and the Gödel-Dummett one. In 2020, we analytically computed the truth density and SAT density (with a specified precision) for both of these (3-valued) logics, restricted to a single-variable implication-negation language. A similar study was carried out for both of these logics restricted to an implicational language with two variables in 2022. There occurred that asymptotically they are very close. In the current paper we are expanding our investigation to 4-valued Łukasiewicz’s logic and Gödel-Dummett’s one, but in even simpler language consisting of implication and two literals. We prove that asymptotically around 50% of formulas in such a language are tautologies (in both cases of the Łukasiewicz logic and the Gödel-Dummett one).

Keywords: fuzzy logics, Łukasiewicz logic, Gödel-Dummett logic, asymptotic density, generating functions, analytic combinatorics

Pages: 620-630