MK-fuzzy Automata and MSO Logics

We introduce MK-fuzzy automata over a bimonoid K which is related to the fuzzification of the McCarthy-Kleene logic. Our automata are inspired by, and intend to contribute to, practical applications being in development in a project on runtime network monitoring based on predicate logic. We investigate closure properties of the class of recognizable MK-fuzzy languages accepted by MK-fuzzy automata as well as of deterministically recognizable MK-fuzzy languages accepted by their deterministic counterparts. Moreover, we establish a Nivat-like result for recognizable MK-fuzzy languages. We introduce an MK-fuzzy MSO logic and show the expressive equivalence of a fragment of this logic with MK-fuzzy automata, i.e., a B"uchi type theorem.

💡 Research Summary

The paper introduces a novel class of weighted automata, called MK‑fuzzy automata, built over a bimonoid K that captures a fuzzy version of McCarthy‑Kleene (MK) logic. The bimonoid K consists of 4‑tuples (t, f, u, e) of real numbers in