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Term Rewriting that Preserves Models in KR-Logic

  • Kiyoshi Akama
  • Ekawit NantajeewarawatEmail author
  • Taketo Akama
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11431)

Abstract

In human proofs of mathematical problems, such as proofs in a group theory, term rewriting is usually used. When we consider Herbrand semantics for the first-order logic with constraints (\(\text {FOL}_\mathrm{c}\)), correct representation of evaluable terms cannot be obtained due to lack of representation power of the logic. In place of \(\text {FOL}_\mathrm{c}\) with Herbrand semantics, we use \(\text {KRL}_\mathrm{c}\) (KR-Logic with built-in constraints). We propose a class of term rewriting rules, and prove that they preserve the sets of all models in KR-Logic. Representation and computation by the rewriting rules in KR-Logic is well established in the space of \(\text {KRL}_\mathrm{c}\). This paper opens a new method of logical problem solving, with \(\text {KRL}_\mathrm{c}\) being the representation space and \(\text {ECLS}_\mathrm{N}\) being the computation space. This theory integrates logical inference and functional rewriting under the broader concept of equivalent transformation.

Keywords

Proof problem Query-answering problem Function variable Built-in equality KR-Logic Equivalent transformation Constructor Term rewriting rule Model preservation 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kiyoshi Akama
    • 1
  • Ekawit Nantajeewarawat
    • 2
    Email author
  • Taketo Akama
    • 3
  1. 1.Information Initiative CenterHokkaido UniversitySapporoJapan
  2. 2.Computer Science Program, Sirindhorn International Institute of TechnologyThammasat UniversityPathumthaniThailand
  3. 3.Modeleet LabsSapporoJapan

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