The Algebras of Atomic Formulas Generated by Mappings with an Invariant Set
Keywords:
formula, a mapping with an invariant set , operation , monoidAbstract
Background and Objectives : Atomic formulas, mathematical expressions used in a theory of classical logic, are combined from terms and relation symbols.
Methodology : Based on a mapping with an invariant set on a finite set (1,...,n) for a positive integer n. Atomic formulas generated by such mapping and some concrete examples are presented. By applying a superposition operation Rn, we show that the algebra of atomic formulas generated by a mapping with an invariant set satisfying some axioms is formed.
Main Results : The monoid of full hypersubstitutions for algebraic systems of some types defined on the set of atomic formulas generated by a mapping with an invariant set is proved. Two algebras of such formulas with respect to a superposition Rn and a binary operation or which are tools to study a theory of hyperidentities are constructed.
Conclusions : Atomic formulas generated by mappings with an invariant set are given. Algebras of these formulas satisfty the superassociative law.
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