Journal of Logic, Language and Information 4 (3):227-250 (1995)
Abstract |
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.
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Keywords | Peirce algebras modal logic algebraic logic relation algebras logics of programs knowledge representation |
Categories | (categorize this paper) |
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.
Sahlqvist's Theorem for Boolean Algebras with Operators with an Application to Cylindric Algebras.Maarten de Rijke & Yde Venema - 1995 - Studia Logica 54 (1):61-78.
Sahlqvist's Theorem for Boolean Algebras with Operators with an Application to Cylindric Algebras.Maarten De Rijke & Yde Venema - 1995 - Studia Logica 54 (1):61 - 78.
Elimination of Quantifiers in the Semantics of Natural Language by Use of Extended Relation Algebras.Patrick Suppes - 1976 - Revue Internationale de Philosophie 30 (3/4=117/118):243-259.
View all 7 references / Add more references
Citations of this work BETA
A System of Dynamic Modal Logic.Maarten de Rijke - 1998 - Journal of Philosophical Logic 27 (2):109-142.
Peirce’s Contributions to Possible-Worlds Semantics.Ahti-Veikko Pietarinen - 2006 - Studia Logica 82 (3):345 - 369.
Peirce’s Contributions to Possible-Worlds Semantics.Ahti-Veikko Pietarinen - 2006 - Studia Logica 82 (3):345-369.
The Modal Multilogic of Geometry.Philippe Balbiani - 1998 - Journal of Applied Non-Classical Logics 8 (3):259-281.
Zooming in, Zooming Out.Patrick Blackburn & Maarten de Rijke - 1997 - Journal of Logic, Language and Information 6 (1):5-31.
View all 6 citations / Add more citations
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