Extending Classical Logic with Inductive Definitions

TL;DR

This paper introduces an extension of classical logic that incorporates inductive definitions with positive and negative induction, exploring its properties, relationships to other logics, and applications in knowledge representation.

Contribution

It presents a novel logical framework integrating inductive definitions, expanding classical logic's capabilities for non-monotonic reasoning and knowledge representation.

Findings

Defines a generalized inductive logic with positive and negative induction

Analyzes properties and relationships to existing non-monotonic logics

Provides a typology of definitional knowledge for applications

Abstract

The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of non-monotonic reasoning, logic programming and deductive databases, and to show its application for knowledge representation by giving a typology of definitional knowledge.