Normal forms of conditional knowledge bases respecting system P-entailments and signature renamings View Full Text


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Article Info

DATE

2021-08-17

AUTHORS

Christoph Beierle, Jonas Haldimann

ABSTRACT

Conditionals are defeasible rules of the form If A then usually B, and they play a central role in many approaches to nonmonotonic reasoning. Normal forms of conditional knowledge bases consisting of a set of such conditionals are useful to create, process, and compare the knowledge represented by them. In this article, we propose several new normal forms for conditional knowledge bases. Compared to the previously introduced antecedent normal form, the reduced antecedent normal form (RANF) represents conditional knowledge with significantly fewer conditionals by taking nonmonotonic entailments licenced by system P into account. The renaming normal form(ρNF) addresses equivalences among conditional knowledge bases induced by renamings of the underlying signature. Combining the concept of renaming normal form with other normal forms yields the renaming antecedent normal form (ρ ANF) and the renaming reduced antecedent normal form (ρ RANF). For all newly introduced normal forms, we show their key properties regarding, existence, uniqueness, model equivalence, and inferential equivalence, and we develop algorithms transforming every conditional knowledge base into an equivalent knowledge base being in the respective normal form. For the most succinct normal form, the ρ RANF, we present an algorithm KBρra systematically generating knowledge bases over a given signature in ρ RANF. We show that the generated knowledge bases are consistent, pairwise not antecedentwise equivalent, and pairwise not equivalent under signature renaming. Furthermore, the algorithm is complete in the sense that, when taking signature renamings and model equivalence into account, every consistent knowledge base is generated. Observing that normalizing the set of all knowledge bases over a signature Σ to ρ RANF yields exactly the same result as KBρra (Σ), highlights the interrelationship between normal form transformations on the one hand and systematically generating knowledge bases in normal form on the other hand. More... »

PAGES

1-31

References to SciGraph publications

  • 2019-05-06. Systematic Generation of Conditional Knowledge Bases up to Renaming and Equivalence in LOGICS IN ARTIFICIAL INTELLIGENCE
  • 2019-09-04. On the Antecedent Normal Form of Conditional Knowledge Bases in SYMBOLIC AND QUANTITATIVE APPROACHES TO REASONING WITH UNCERTAINTY
  • 1975. The Logic of Conditionals, An Application of Probability to Deductive Logic in NONE
  • 2017-06-15. A Transformation System for Unique Minimal Normal Forms of Conditional Knowledge Bases in SYMBOLIC AND QUANTITATIVE APPROACHES TO REASONING WITH UNCERTAINTY
  • 2019-06-01. A KLM Perspective on Defeasible Reasoning for Description Logics in DESCRIPTION LOGIC, THEORY COMBINATION, AND ALL THAT
  • 2004-01. A Thorough Axiomatization of a Principle of Conditional Preservation in Belief Revision in ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
  • 2017-06-04. On Transformations and Normal Forms of Conditional Knowledge Bases in ADVANCES IN ARTIFICIAL INTELLIGENCE: FROM THEORY TO PRACTICE
  • 2016-11-01. A Practical Comparison of Qualitative Inferences with Preferred Ranking Models in KI - KÜNSTLICHE INTELLIGENZ
  • 2020-01-03. Normal Forms of Conditional Knowledge Bases Respecting Entailments and Renamings in FOUNDATIONS OF INFORMATION AND KNOWLEDGE SYSTEMS
  • 2001-09-13. Conditionals in Nonmonotonic Reasoning and Belief Revision, Considering Conditionals as Agents in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10472-021-09745-3

    DOI

    http://dx.doi.org/10.1007/s10472-021-09745-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1140468467


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