Varieties of pure first-order logics of partial quasiary predicates

Authors

DOI:

https://doi.org/10.17721/1812-5409.2024/2.13

Keywords:

logic, partial predicate, equality, logical consequence

Abstract

Classical predicate logic typically lies at the basis of various logical systems successfully used in computer science and programming. However, classical logic has fundamental limitations that complicate its application. Therefore, the task of developing new, program-oriented logics becomes important; this highlights the relevance of the proposed research. In this work we study new program-oriented logical formalisms – pure first-order composition-nominative logics of partial quasiary predicates, PCNL. Depending on the presence and type of special predicates-indicators, and equality predicates (weak or strong), the use of traditional or extended renomination, in this paper we specify a number of classes of PCNL. Special predicates-indicators determine the presence of components with the corresponding subject name in the input data, which is necessary to consider for the quantifier elimination in the logics of non-monotonic predicates. Two types of these predicates can be distinguished: total, which determine the presence or absence of a component with a given name, and partial, which only detect the presence of such a component. We propose partial predicates-indicators and the corresponding classes of PCNL. The basic compositions of these logics are described, and their properties are presented. The languages of the introduced classes of logics are specified, and a number of logical consequence relations for these languages are defined. The characteristics of these relations are investigated, and the relationships between them are provided.

Pages of the article in the issue: 80 - 88

Language of the article: English

References

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Published

2025-01-29

How to Cite

Shkilnyak, S. (2025). Varieties of pure first-order logics of partial quasiary predicates. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, 79(2), 80–88. https://doi.org/10.17721/1812-5409.2024/2.13

Issue

Section

Computer Science and Informatics