Weighted first-order logics over semirings - Mandrali Eleni (Acta cybernetica, 2015)
We consider a first-order logic, a linear temporal logic, star-free expressions and counter-free Büchi automata, with weights, over idempotent, zerodivisor free and totally commutative complete semirings. We show the expressive equivalence (of fragments) of these concepts, generalizing in the quantitative setup, the corresponding folklore result of formal language theory.