Extending Prolog for Quantified Boolean Horn Formulas

TL;DR

This paper extends Prolog to handle quantified Boolean Horn formulas, enabling it to solve more complex logical problems with arbitrary quantifiers, and introduces a new declarative programming approach for such formulas.

Contribution

It introduces an extension of Prolog for quantified Boolean Horn formulas, overcoming previous limitations and supporting first-order predicate Horn logic with arbitrary quantifiers.

Findings

Extended Prolog supports arbitrary quantified Boolean Horn formulas.

Proposed implementation efficiently handles first-order predicate Horn logic.

Introduced a declarative programming paradigm for quantified Boolean Horn formulas.

Abstract

Prolog is a well known declarative programming language based on propositional Horn formulas. It is useful in various areas, including artificial intelligence, automated theorem proving, mathematical logic and so on. An active research area for many years is to extend Prolog to larger classes of logic. Some important extensions of it includes the constraint logic programming, and the object oriented logic programming. However, it cannot solve problems having arbitrary quantified Horn formulas. To be precise, the facts, rules and queries in Prolog are not allowed to have arbitrary quantified variables. The paper overcomes this major limitations of Prolog by extending it for the quantified Boolean Horn formulas. We achieved this by extending the SLD-resolution proof system for quantified Boolean Horn formulas, followed by proposing an efficient model for implementation. The paper shows that the proposed implementation also supports the first-order predicate Horn logic with arbitrary quantified variables. The paper also introduces for the first time, a declarative programming for the quantified Boolean Horn formulas.