---
title: "Curb Your Theory! A Circumspective Approach for Inclusive Interpretation of Disjunctive Information"
authors:
  - "Thomas Eiter"
  - "Georg Gottlob"
  - "Yuri Gurevich"
doi: ""
url: "https://ijcai.org/proceedings/1993/89"
pdf: "https://ijcai.org/proceedings/1993/0089.pdf"
venue: "Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence"
year: 1993
pages: "634-638"
track: "Knowledge Representation"
keywords:
---

# Curb Your Theory! A Circumspective Approach for Inclusive Interpretation of Disjunctive Information

Thomas Eiter, Georg Gottlob, Yuri Gurevich

*Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence*, pages 634-638.

## Abstract

We introduce curbing, a new nonmonotonic technique of commonsense reasoning that is based on model minimality but unlike circumscription treats disjunction inclusively. A finitely axiomatized first-order theory T is transformed to a formula Curb(T) whose set of models is defined as the smallest collection of models which contains all minimal models ofT and which is closed und er formation of minimal upper bounds with respect to inclusion. We first give an intuitive definition of Curb in third-order logic and th en show how Curb can be equivalently expressed in second-order logic. We study the complexity of inferencing from a curbed propositional theory and present a PSPACE algorithm for this problem. Finally, we address different possibilities to approximate the curb of a theory.