The calculus of binary relations was introduced by De Morgan in 1860, and was subsequently greatly developed by Peirce and Schröder. Half a century later Tarski, Jónsson, Lyndon, and Monk further developed the calculus from the perspective of modern model theory.

According to Peirce a great part of mathematical thinking consists in observing or imagining the outcomes and regularities of manipulations of all sorts of diagrams. This tenet is explicated and substantiated by expounding the notion of diagram and by analyzing several specific cases from different parts of mathematics.

The notion of a relational grammar is extended to ternary relations and illustrated by a fragment of English. Some of Peirce's terms for ternary relations are shown to be incorrect and corrected. Binary relations have been studied extensively by Peirce and Schrr oder in the nineteenth century, and in this century by Tarski and his students. No comparable attention has been paid to ternary relat...

We propose to reconsider abductive reasonning in the context of empirical reasonning, and to investigate its deep relations with constraint-based reasonning, a currently very success-full approach used in the problem-solving community. Abduction has been proposed in the rst years of this century by the logician and philosopher C. S. Peirce as a new inference mechanism for logical system along i...

Peirce introduced an ingenious classification of signs and a theory of reasoning. Though he maintained that reasoning presupposes signs, to our best knowledge, he did not define a link between his two theories. In this paper we make a first attempt to reveal the possibility for such a relation, in the framework of a cognitively based model of