Minimal knowledge problem: A new approach
type: Item
instance of: scholarly article
title: Minimal knowledge problem: A new approach
zbMATH Open document ID: 0820.68115
DOI: 10.1016/0004-3702(94)90013-2
author: Grigori Schwarz
author: Mirosław Truszczyński
published in: Artificial Intelligence
publication date: 1994-07-04T00:00:00Z
review text: The paper introduces a new logic of minimal knowledge, which falls into the general scheme of Shoham's preference semantics. It is argued that this logic overcomes some of the limitations of earlier formalisms, and can be viewed as a generalization of default and autoepistemic logics. It is also shown that the logic of minimal knowledge is a special case of McDermott and Doyle's nonmonotonic modal logic, which makes it possible to use standard modal logic techniques in proving the results introduced in the paper. The main result is a new specification of the general minimal knowledge paradigm, represented by means of a class of knowledge- belief models. Given a class of such models of a theory \(I\) describing initial assumptions, it is possible to specify a subclass by defining the notion of maximality, which is different from the notion used by \textit{J. Halpern} and \textit{Y. Moses} [Logics and models of concurrent systems, Proc. NATO Adv. Study Inst., La Colle-su-Loup/France 1984, NATO ASI Sér., Sér. F 13, 459-476 (1985; Zbl 0581.68067)]. The approach presented in the paper yields two minimal knowledge-belief logics: one bimodal, and one with a single modality. This allows to vary domains, and thus to model the situation when the agent is not aware of all of the objects existing in the world. The obtained formalisms are nonmonotonic because they model a nonmonotonic reasoning. The relationship between the proposed logics and other nonmonotonic formalisms is also considered.
Mathematics Subject Classification ID: 68T27
zbMATH DE Number: 599999
zbMATH Keywords: nonmonotonic modal logic
zbMATH Keywords: maximality
reviewed by: Neli Zlatareva
MaRDI profile type: Publication
full work available at URL: 0004-3702(94)90013-2
OpenAlex ID: W2018314350
cites work: Q3983043
cites work: Q3703315
cites work: Knowledge and common knowledge in a distributed environment
cites work: Q3026978
cites work: On the relation between default and autoepistemic logic
cites work: Q4180316
cites work: All I know: A study in autoepistemic logic
cites work: Q4012230
cites work: Modal nonmonotonic logics
cites work: Modal logic for default reasoning
cites work: Nonmonotonic Logic II
cites work: Non-monotonic logic. I
cites work: Semantical considerations on nonmonotonic logic
cites work: A logic for default reasoning
cites work: Q4068699
cites work: Nonmonotonic default modal logics
cites work: Q4012232
cites work: Q5202996
cites work: Q4287517
Recommended article: Q4215601
Recommended article: Possible world semantics and autoepistemic reasoning
Recommended article: Reasoning about minimal knowledge in nonmonotonic modal logics
Recommended article: Q5711865
Recommended article: Multi-modal nonmonotonic logics of minimal knowledge
Recommended article: Minimal belief and negation as failure
Recommended article: Q4518910
Recommended article: A logic of knowledge and justified assumption
Recommended article: Q4282588
Recommended article: Relating only knowing to minimal belief and negation as failure
description: scientific article; zbMATH DE number 599999