Artificial intelligence and machine learning

Research Article

DOI 10.25209/2079-3316-2024-15-2-87-112

The use of distributed computing in domain modeling in universal syllogistics

Iurii Mikhailovich Smetanin

	Udmurt State University, Izhevsk, Russia
	gms1234gms@rambler.ru

Abstract. We consider the algorithmic aspects of calculations in the logical-semantic models of universal syllogistics $L_{S_{2}}$ . This non-classical propositional logic is based on an algebraic system containing a Boolean algebra of sets and two relations between sets: $\subset$ and $=$. Its closest analogue is Aristotle's syllogistics, the model of which is an algebraic system with a Boolean algebra of sets and one relation $\subset$. The disadvantage of syllogistics based on an algebraic system with a single relation $\subset$ is the ambiguity of the interpretation of their formulas and atomic judgments.

In this work, by a logical-semantic model of a subject area we understand the totality of the universal syllogistic formula $L_{S_{2}}$ and its semantic meaning, which is a finite set of non-negative integers. We propose an algorithm for computing semantic value of a conjunctive well-constructed formula $L_{S_{2}}$ , which has a high level of parallelism at the task level, at the data level, and at the level of algorithms realizing operations on constituent sets. Due to the peculiarities of union, intersection and complement operations over finite sets, all the processes of their computation and solution of subtasks occur at the bit level and, as a rule, are efficiently implemented in algorithmic languages. In the proposed algorithm, the transition to the bit level and back is realized by a set of software tools. (In Russian).

Keywords: Syllogistics, discrete Venn diagrams, logical-semantic models, frontal algorithm, distributed computing

MSC-2020

68T30; 03B45, 68W10

For citation: Iurii M. Smetanin. The use of distributed computing in domain modeling in universal syllogistics. Program Systems: Theory and Applications, 2024, 15:2, pp. 87–112. (In Russ.). https://psta.psiras.ru/2024/2_87-112.

Full text of article (PDF): https://psta.psiras.ru/read/psta2024_2_87-112.pdf.

The article was submitted 29.02.2024; approved after reviewing 09.04.2024; accepted for publication 17.04.2024; published online 17.05.2024.