Proof Theory of Modal Logic pp 253-291

Part of the Applied Logic Series book series (APLS, volume 2) | Cite as

Translating Graded Modalities into Predicate Logics

  • H. J. Ohlbach
  • R. Schmidt
  • U. Hustadt

Abstract

From Minsky’s early frame systems, which were defined purely operationally, and Brachman’s kl-one knowledge representation system [4, 35] to the language AℒC of Schmidt-Schauß and Smolka’s [28] paper there has been a continuous trend in designing knowledge representation systems more and more according to logical principles with clear syntax and semantics and logical inferences as basic operations. AℒC in particular is a language with the usual logical connectives ⊓, ⊔, ⌝ and the additional constructs (all R C) and (some R C). For example, the following is an AℒC definition which defines a ‘concept’ proud-father as a father all of whose children are successful persons.

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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • H. J. Ohlbach
    • 1
  • R. Schmidt
    • 1
  • U. Hustadt
    • 1
  1. 1.Max Planck InstiuteSaarbrückenGermany

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