Algebraic and logical methods in computer science and artificial intelligence

Partial algebras of formulas under generalized superpositions

T. Kumduang^a, K. Wattanatripop<sup>b

a</sup> Rajamangala University of Technology Rattanakosin, Nakhon Pathom, Thailand
^b Rajamangala University of Technology Lanna, Chiang Mai, Thailand

Abstract: Formulas which are tools for describing algebraic systems are formal expressions arising from terms, relation symbols, and logical connectives. Under composition of the generalized superposition operation, the set of all terms forms a unitary superassociative algebra. This paper deals with construction of the partial generalized superposition on the set of all terms and formulas satisfying the superassociativity as a weak identity. Partial binary operations induced by such partial generalized superpositions are given and the fact that these operations are weak associative are proved.

Keywords: partial algebra, formula, term, superassociativity, partial semigroup, weak identity, superposition, operation, embeddability, weak monomorphism.

UDC: 512.577

MSC: 08A02, 08A05, 08A70, 20N02, 20N15

Received: 05.01.2025
Revised: 28.03.2025
Accepted: 06.06.2025

Language: English

DOI: 10.26516/1997-7670.2025.54.160