LOGICAL AND PHILOSOPHICAL FOUNDATIONS FOR THE DEVELOPMENT OF CONCEPTUAL THINKING IN STUDENTS

As a person matures, he or she develops the ability to compare, see logical connections between objects and phenomena, and then generalize what they see. This generalization entails the formation, assimilation, transfer, generalization, and concretization of concepts—both those already existing in society and those created within one's own experience. Subsequently, a person is able to recognize and identify objects and phenomena, previously seen or unfamiliar, classify them into a particular conceptual category, and apply a generalized approach to solving new creative problems. This is conceptual thinking in action. In light of modern requirements for school graduates, this paper examines the shortcomings of classical logic used to model cause-and-effect relationships between phenomena in the surrounding world. It also proposes a replacement in the form of universal syllogistic, which allows for the development of the foundations of logical thinking at a higher level using computer-assisted logical-semantic modeling of fragments of the surrounding world. Logical skills and their role in conceptual thinking are considered. An applied syllogistic system has been developed to formalize the concept of implication as a model of cause-and-effect relationships for phenomena in the surrounding world. We consider the algorithmic aspects of computations in logicalsemantic models of the universal syllogistic $L_{S_{2}}$. This non-classical propositional logic is built on the basis of an algebraic system containing the Boolean algebra of sets and two relations between sets $\subset$, $=$. Its closest analogue is Aristotle's syllogistics, whose mathematical model is an algebraic system with a non-degenerate Boolean algebra of sets and a single $\subseteq$ relation. A one-to-one correspondence is established between the formulas of Boolean logic algebra and the formulas of $L_{S_{2}}$. This eliminates the main drawback of previously known syllogistics, which is the ambiguity of interpreting their conjunctive formulas and atomic judgments in Venn diagrams. The proposed syllogistics allows one to develop the logical components of conceptual thinking (necessity, sufficiency, necessity and sufficiency) at a higher level by solving logical problems of increased complexity. According to psychologist I.P. Kaloshina, logical components are related to methodological knowledge, without which it is impossible to develop methods for solving creative problems—a skill so essential in the era of the digital transformation of our lives. A software tool for modeling logical problem statements and identifying logical consequences has been used in undergraduate and graduate courses in applied mathematics, systems analysis, and decision-making models and methods for the past eight years.