, Volume 4, Issue 1, pp 1–19 | Cite as

Peirce Grammar

  • Michael Böttner


Peirce grammar is a context-free grammar with a Peirce algebra as its semantics. A Peirce algebra is a two-sorted algebra that presupposes a Boolean algebra and a relation algebra. Since Peirce algebra has an equational theory many natural language inferences can be captured in terms of equational computation. The notions of a Peirce algebra and a Peirce grammar are applied to natural language. It is shown that the meaning of anaphoric pronouns, in particular possessive, relative, reciprocal, identity, and diversity pronouns can be constructed without use of variables or generalized quantifiers.

algebraic semantics anaphoric pronoun equational logic knowledge representation relation algebra relational grammar semantic grammar variable-free semantics 


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Michael Böttner
    • 1
  1. 1.Learning Research and Development CenterUniversity of PittsburghPittsburghUSA

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