---
title: "Indefinite Reasoning with Definite Rules"
authors:
  - "L. Thorne McCarty"
  - "Ron van der Meyden"
doi: ""
url: "https://ijcai.org/proceedings/1991/131"
pdf: "https://ijcai.org/proceedings/1991/0131.pdf"
venue: "Proceedings of the Twelfth International Joint Conference on Artificial Intelligence"
year: 1991
pages: "890-895"
track: "Logic Programming"
keywords:
---

# Indefinite Reasoning with Definite Rules

L. Thorne McCarty, Ron van der Meyden

*Proceedings of the Twelfth International Joint Conference on Artificial Intelligence*, pages 890-895.

## Abstract

In this paper we present a novel explanation of the source of indefinite information in common sense reasoning: Indefinite information arises from reports about the world expressed in terms of concepts that have been defined using only definite rules. Adopting this point of view, we show that first-order logic is insufficiently expressive to handle important examples of common sense reasoning. As a remedy, we propose the use of circumscribed definite rules, and we then investigate the proof theory of this more expressive framework. We consider two approaches: First, prototypical proofs, a special type of proof by induction, which yields a sound proof theory. Second, we describe cases in which there exists a decision procedure for answering queries, a particularly significant result because it shows that it is possible to have decidable query processing in circumscribed theories that are not equivalent to any first order theory.