Each fuzzy set can be represented by a nested system of ordinary sets—its a-cuts. There is an extensive literature on fuzzy sets devoted to problems of the following kind: is it possible to reduce operations with fuzzy sets to operations with their a-cuts? Is it possible to reduce properties of fuzzy relations to properties of their a-cuts? More generally, can a fuzzy concept be represented by ...

We show by standard automated theorem proving methods and freely available automated theorem prover software that axiom (A2), stating that multiplicative conjunction implies its first member, is provable from other axioms in fuzzy logics BL and MTL without using axiom (A3), which is known to be provable from other axioms [1]. We also use freely available automated model generation software to s...

Abstract In 2021, Casares, Colcombet, and Fijalkow introduced the Alternating Cycle Decomposition (ACD) to study properties transformations of Muller automata. We present first practical implementation ACD in two different tools, Owl Spot, adapt it framework Emerson-Lei automata, i.e., $$\omega $$ ω -automata...