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Communication is one of the most notable processes in a multi-agent system. For this reason, considerable attention is paid to it—from abstract levels presenting theoretical models describing the basic principles to an implementation level with many details. However, most of these models build on a kind of unchanging basis, which characterizes communication between agents of a multi-agent system as a mutual exchange of messages expressed in a specific language or formal logic system, most often first-order predicate logic. Since most logical systems specialize in a particular area of natural language, the choice of a logical system reduces the communication potential of a multi-agent system. Therefore, we decide to choose the transparent intensional logic, a highly expressive methodology of logical analysis of natural language based on the symmetry between the syntax of expressions and their semantics, which minimizes these limitations and brings a new perspective on the issue of formalization of communication in multi-agent systems. By choosing transparent intensional logic as the central logical apparatus of our solution and postulating the general criterion for the synthesis of the concept of a message, the framework idea of our solution, which is based on hypotheses formulated in the analysis of Singh's formal theory of communication, we have reached the synthesis of the so-called TIL-Message Formalization System. This system, unlike others based on traditionally used formalisms, simplifies the communication process itself by reducing the level of semantic interpretation of messages formalized by it, and in addition to formalism itself, this system also provides an abstract description of the background of the course of communication, proved by its application on specific examples, by standing out from the order of other formalisms providing only a kind of syntactic standard. [ABSTRACT FROM AUTHOR]

We present a categorical formalization of a variant of first-order logic. Unlike other texts on this topic, the goal of this paper is to give a very transparent and self-contained account without requiring more background than basic logic and set theory. Our focus is to show how the semantics of first-order formulas can be derived from their usual deduction rules. For understanding the core ideas, it is not necessary to investigate the internal term structure of atomic formulas, thus we abstract atomic formulas to (syntactically opaque) relations; in this sense, our variant of first-order logic is "relational". While the derived semantics is based on categorical principles (even the duality that arises from a symmetry between two ways of looking at something where there is no reason to choose one over the other), it is nevertheless "constructive" in that it describes explicit computations of the truth values of formulas. We demonstrate this by modeling the categorical semantics in the RISCAL (RISC Algorithm Language) system which allows us to validate the core propositions by automatically checking them in finite models. [ABSTRACT FROM AUTHOR]