For a Peirce algebra P, lattices CongP of all heterogenous Peirce congruences and IdeP of all heterogenous Peirce ideals are presented. The notions of kernel of a Peirce congruence and the congruence induced by a Peirce ideal are introduced to describe an isomorphism between CongP and IdeP. This isomorphism leads us to conclude that the class of the Peirce algebras is ideal determined. Opposed ...

PEIRCE is a project aiming to build a state-of-the-art, industrial strength conceptual graphs workbench. PEIRCE is integrating the conceptual graphs development eeorts that are taking place around the world. There are already over 40 researchers from over 8 countries involved in the project. This paper describes the PEIRCE project and the structure for managing the distributed development of PE...

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 algebra...

Extended Abstract In this Note I prove a representation theorem for Peirce algebras introduced in Brink, Britz and Schmidt (1994b, 1994a). I show that the class of full Peirce algebras is characterised by the class of complete and atomic Peirce algebras in which the set of relational atoms is restricted by two conditions. One requires simplicity. The other requires that each relational element ...

In this paper, we introduce a general theory of corner rings in noncommutative rings that generalizes the classical notion of Peirce decompositions with respect to idempotents. Two basic types of corners are the Peirce corners eRe (e2 = e) and the unital corners (corners containing the identity of R). A general corner is both a unital corner of a Peirce corner, and a Peirce corner of a unital c...

Peirce algebras combine sets relations and various operations linking the two in a unifying setting This note o ers a modal perspective on Peirce algebras It uses modal logic to characterize the full Peirce algebras AMS Subject Classi cation B G G A CR Subject Classi cation F F I

We present a two-sorted algebra, called a Peirce algebra, of relations and sets interacting with each other. In a Peirce algebra, sets can combine with each other as in a Boolean algebra, relations can combine with each other as in a relation algebra, and in addition we have both a relationforming operator on sets (the Peirce product of Boolean modules) and a set-forming operator on relations (...

We present a two-sorted algebra, called a Peirce algebra, of relations and sets interacting with each other. In a Peirce algebra, sets can combine with each other as in a Boolean algebra, relations can combine with each other as in a relation algebra, and in addition we have both a relationforming operator on sets (the Peirce product of Boolean modules) and a set-forming operator on relations (...

Debates concerning the character, scope, and warrant of abductive inference have been active since Peirce first proposed that there was a third form of inference, distinct from induction and deduction. Abductive reasoning has been dubbed weak, incoherent, and even nonexistent. Part, at least, of the problem of articulating a clear sense of abductive inference is due to difficulty in interpretin...