Record in the Commens Bibliography. Retrieved from http://www.commens.org/bibliography/journal_article/maarten-de-rijke-1995-logic-peirce-algebras, 28.03.2024.
Title:
The Logic of Peirce Algebras
Journal:
Journal of Logic, Language and Information
Keywords:
Peirce algebras, Modal logic, Algebraic logic, Relation algebras, Logics of programs, Knowledge representation
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.