Existentially Quantified Systems of Equations as an Implicit Representation of Answers in Logic Programming

TL;DR

This paper introduces a novel formalization of logic programming using existentially quantified systems of equations to represent answers, simplifying substitution issues and enabling parallel computation models.

Contribution

It presents an alternative logic programming formalization with existential quantification, facilitating parallelism and avoiding substitution problems common in standard approaches.

Findings

Answers are represented by existentially quantified systems of equations.

The approach simplifies handling of variable substitutions.

It provides a foundation for concurrent logic programming and parallel answer composition.

Abstract

In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer will be played by existentially quantified systems of equations. This allows us to avoid problems when we deal with substitutions. In particular, we need no ''global'' variable separated conditions when new variables are introduced by input clauses. Moreover, this formalization can be regarded as a basis for the theory of concurrent logic languages, since it also includes a wide spectrum of parallel computational methods. Moreover, the parallel composition of answers can be defined directly -- as a consistent conjunction of answers.