---
title: "A Functional Approach to Non-Monotonic Logic"
authors:
  - "Erik Sandewall"
doi: ""
url: "https://ijcai.org/proceedings/1985/18"
pdf: "https://ijcai.org/proceedings/1985/0018.pdf"
venue: "Proceedings of the Ninth International Joint Conference on Artificial Intelligence"
year: 1985
pages: "100-105"
track: "Automated Reasoning"
keywords:
---

# A Functional Approach to Non-Monotonic Logic

Erik Sandewall

*Proceedings of the Ninth International Joint Conference on Artificial Intelligence*, pages 100-105.

## Abstract

Axiom sets and their extensions are viewed as functions from the set of formulas in the language, to a set of four truth-values t, /, a for undefined, and A: for contradiction. Such functions form a lattice with 'contains less information' as the partial order ~. and 'combination of several sources of knowledge' as the l.u.b. operation U. We demonstrate the relevance of this approach by giving concise proofs for some previously known results about normal default rules. For non-monotonic rules in general (not only normal default rules) we define a stronger version of the minimality requirement on consistent fixpoints, and prove that it is sufficient for the existence of a derivation of the flXJloint.