---
title: "On Bimodal Nonmonotonic Logics and Their Unimodal and Nonmodal Equivalents"
authors:
  - "Alexander Bochman"
doi: ""
url: "https://ijcai.org/proceedings/1995/196"
pdf: "https://ijcai.org/proceedings/1995/0196.pdf"
venue: "Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence"
year: 1995
pages: "1518-1523"
track: "Non-monotonic Reasoning"
keywords:
---

# On Bimodal Nonmonotonic Logics and Their Unimodal and Nonmodal Equivalents

Alexander Bochman

*Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence*, pages 1518-1523.

## Abstract

We study a bimodal nonmonotonic logic MBNF suggested in [1ifschitz, 1994] as a generalization of a number of nonmonotonic formalisms . We show first that it is equivalent to a certain nonmodal system involving rules of a special kind . Next , it is shown that the latter admits a modal representation that uses only one modal operator, the ope rator of belief. Moreover, under this translation , the models of MBNF correspond to §-expansions of the associated modal nonmonotonic logic. Finally, we show that, as far as such models are concerned, MBNF is reducible to nonmodal default consequence relations from [Bochman, 1994]. These results have general consequences concerning relationship between different formalizations of nonmonotonic reasoning.