The logic of Peirce algebras

Peirce algebras combine sets, relations and various operations linking the two in a unifying setting. This paper offers a modal perspective on Peirce algebras. Using modal logic a characterization of the full Peirce algebras is given, as well as a finite axiomatization of their equational theory that uses so-called unorthodox derivation rules. In addition, the expressive power of Peirce algebras is analyzed through their connection with first-order logic, and the fragment of first-order logic corresponding to Peirce algebras is described in terms of bisimulations.
Keywords Peirce algebras  modal logic  algebraic logic  relation algebras  logics of programs  knowledge representation
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DOI 10.1007/BF01049414
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References found in this work BETA
Derivation Rules as Anti-Axioms in Modal Logic.Yde Venema - 1993 - Journal of Symbolic Logic 58 (3):1003-1034.
Variable-Free Semantics for Anaphora.Michael Böttner - 1992 - Journal of Philosophical Logic 21 (4):375 - 390.
The Representation of Relational Algebras.Roger C. Lyndon - 1951 - Journal of Symbolic Logic 16 (4):279-280.

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A System of Dynamic Modal Rijke Maarten - 1998 - Journal of Philosophical Logic 27 (2):109-142.

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