The relation of semiadjacency of $\cap$-semigroups of transformations

TL;DR

This paper investigates two relations on a $ ext{cap}$-semigroup of partial functions, focusing on domain inclusion and semiadjacency, and characterizes these relations using axiomatic systems in predicate calculus.

Contribution

It provides an axiomatic characterization of semiadjacency and domain inclusion relations in $ ext{cap}$-semigroups of partial functions.

Findings

Characterization of domain inclusion relation.

Axiomatic description of semiadjacency.

Formal system conditions for these relations.

Abstract

We consider two relations on a $\cap$-semigroup of partial functions of a given set: the inclusion of domains and the semiadjacencity (i.e., the inclusion of the image of the first function into the domain of the second), which characterized with an abstract point of view using the elementary system of axioms, i.e., system conditions, recorded in the language narrow predicate calculus with equality.