Computing with Logic as Operator Elimination: The ToyElim System

TL;DR

The ToyElim system is a prototype that performs operator elimination in propositional logic, enabling uniform computation of various knowledge representation tasks within a classical semantic framework.

Contribution

It introduces a system that eliminates second-order operators in propositional logic, unifying diverse knowledge representation and reasoning tasks.

Findings

Supports computation of abductive explanations

Handles models with logic programming semantics

Operates within a classical semantic framework

Abstract

A prototype system is described whose core functionality is, based on propositional logic, the elimination of second-order operators, such as Boolean quantifiers and operators for projection, forgetting and circumscription. This approach allows to express many representational and computational tasks in knowledge representation - for example computation of abductive explanations and models with respect to logic programming semantics - in a uniform operational system, backed by a uniform classical semantic framework.