Handbook of Trivalent Logics

A handbook on trivalent logics and their applications in a systematic and accessible way, for beginners to advanced readers.

Trivalent logics, also known as three-valued logics, are systems of logic that incorporate a third truth value besides the values True and False. They made their first appearance around 1910 in the works of the Polish logician Jan Łukasiewicz and the American polymath Charles Sanders Peirce.

This handbook, edited by Paul Égré and Lorenzo Rossi, is the first of its kind to present trivalent logics in a systematic and accessible way. It is organized in four parts—the first two, intended for a wide readership, explore philosophical foundations with applications, and the latter two, intended for more advanced readers, discuss proof systems and relations of trivalent logics to other logics, including modal logics, fuzzy logics, probability logics, and quantum logics.

Trivalent logics have a surprisingly wide range of applications in various domains of interest to philosophy, linguistics, cognitive psychology, and computer science. While these applications concern different phenomena—truth, vagueness, conditional reasoning, presupposition, belief representation—the addition of a third truth value beside True and False is significant for solving problems that would otherwise lead to difficulties and paradoxes in a standard bivalent framework.