Lindstrøm's Characterizability of Abstract Fuzzy Logic Systems for Convolutions

In 1969, Per Lindstrøm proved his famous theorem and established criteria for the first-order definability of formal theories for discrete structures. K. Barwise and S. Shelah extended Lindstrøm's characterizability program to the class of infinitary logic systems. This paper aims to give a frame for Lindstrøm's type characterizability of predicate logic systems interpreted semantically in models with convolutions. In particular, Hájek's Logic of Integrals and Convolutions is described and redefined as an abstract logic with a new type of Hájek's satisfiability. It is shown that this logic system constitutes a maximal logic in a class of logic systems for describing convolutions and satisfying compactness, elementary chain condition, and weak negation.