research-article

Inferential equivalence, normal forms, and isomorphisms of knowledge bases in institutions of conditional logics

Author:

Christoph BeierleAuthors Info & Claims

SAC '19: Proceedings of the 34th ACM/SIGAPP Symposium on Applied Computing

Pages 1131 - 1138

https://doi.org/10.1145/3297280.3297391

Published: 08 April 2019 Publication History

Abstract

Conditionals of the form "If A, then usually B" play an important role in formal approaches to knowledge representation and reasoning. Sets of such conditionals, called a knowledge base, may represent the explicitly given knowledge of an intelligent agent. For many operations involving kowledge bases, it is advantageous to have a compact and standardized form for them. In this paper, we show how to obtain a unique minimal normal form for every conditional knowledge base. The normal form is independent of a specific notion of semantic models and their particular notion of satisfaction between models and conditionals. This abstraction is achieved by employing Goguen and Burstall's framework of institutions and introducing the general notion of an institution of conditional logic. It covers previously proposed formalizations of conditional logics as institutions with specific semantics, like total preorders on worlds, possibility distributions, ranking functions, or big-stepped probabilities. The concepts of model equivalence and elementwise equivalence of knowledge bases are generalized first to arbitrary institutions of conditional logic and then further by taking also isomorphisms into account. We introduce the notion of inferential equivalence of knowledge bases for two different nonmonotonic inference relations induced by a knowledge base. For inferential equivalences with respect to these nonmonotonic inference relations, we prove how they are preserved under normalization and isomorphisms.

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Cited By

Beierle CHaldimann J(2022)Normal forms of conditional knowledge bases respecting system P-entailments and signature renamingsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-021-09745-390:2-3(149-179)Online publication date: 1-Mar-2022
https://dl.acm.org/doi/10.1007/s10472-021-09745-3
Beierle CHaldimann J(2020)Normal Forms of Conditional Knowledge Bases Respecting Entailments and RenamingsFoundations of Information and Knowledge Systems10.1007/978-3-030-39951-1_2(22-41)Online publication date: 17-Feb-2020
https://dl.acm.org/doi/10.1007/978-3-030-39951-1_2
Beierle CKutsch S(2019)On the Antecedent Normal Form of Conditional Knowledge BasesSymbolic and Quantitative Approaches to Reasoning with Uncertainty10.1007/978-3-030-29765-7_15(175-186)Online publication date: 18-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-29765-7_15
Show More Cited By

Index Terms

Inferential equivalence, normal forms, and isomorphisms of knowledge bases in institutions of conditional logics
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
      1. Nonmonotonic, default reasoning and belief revision
      2. Reasoning about belief and knowledge

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cover image ACM Conferences

SAC '19: Proceedings of the 34th ACM/SIGAPP Symposium on Applied Computing

April 2019

2682 pages

ISBN:9781450359337

DOI:10.1145/3297280

Conference Chairs:
Chih-Cheng Hung
Kennesaw State University, Marietta, Georgia
,
George A. Papadopoulos
University of Cyprus, Nicosia, Cyprus

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SIGAPP: ACM Special Interest Group on Applied Computing

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Published: 08 April 2019

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SAC '19: The 34th ACM/SIGAPP Symposium on Applied Computing

April 8 - 12, 2019

Limassol, Cyprus

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Cited By

Beierle CHaldimann J(2022)Normal forms of conditional knowledge bases respecting system P-entailments and signature renamingsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-021-09745-390:2-3(149-179)Online publication date: 1-Mar-2022
https://dl.acm.org/doi/10.1007/s10472-021-09745-3
Beierle CHaldimann J(2020)Normal Forms of Conditional Knowledge Bases Respecting Entailments and RenamingsFoundations of Information and Knowledge Systems10.1007/978-3-030-39951-1_2(22-41)Online publication date: 17-Feb-2020
https://dl.acm.org/doi/10.1007/978-3-030-39951-1_2
Beierle CKutsch S(2019)On the Antecedent Normal Form of Conditional Knowledge BasesSymbolic and Quantitative Approaches to Reasoning with Uncertainty10.1007/978-3-030-29765-7_15(175-186)Online publication date: 18-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-29765-7_15
Beierle CKutsch S(2019)Systematic Generation of Conditional Knowledge Bases up to Renaming and EquivalenceLogics in Artificial Intelligence10.1007/978-3-030-19570-0_18(279-286)Online publication date: 6-May-2019
https://doi.org/10.1007/978-3-030-19570-0_18

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