---
title: "Constrained and Rational Default Logics"
authors:
  - "Artur Mikitiuk"
  - "Miroslaw Truszczynski"
doi: ""
url: "https://ijcai.org/proceedings/1995/195"
pdf: "https://ijcai.org/proceedings/1995/0195.pdf"
venue: "Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence"
year: 1995
pages: "1509-1516"
track: "Non-monotonic Reasoning"
keywords:
---

# Constrained and Rational Default Logics

Artur Mikitiuk, Miroslaw Truszczynski

*Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence*, pages 1509-1516.

## Abstract

In this paper we consider constrained and rational default logics. We provide two characterizations of constrained extensions. One of them is used to derive complexity results for decision problems involving constrained extensions. In particular, we show that the problem of membership of a formula in at least one (in all) constrained extension(s) of a default theory is :Ef -complete (IIf -complete). We establish the relationship between constrained and rational default logics. We prove that rational extensions determine constrained extensions and that for seminormal default theories there is a one-to-one correspondence between these objects. We also show that the definition of a constrained extension can be extended to cover the case of default theories which may contain justification-free defaults.