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Three-valued logic

Three-valued logic
The original uploader was Magnus Manske at English Wikipedia. Later versions were uploaded by Optimager at en.wikipedia. · Public domain · source

Overview

A three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false, and some third value. This is contrasted with the more commonly known bivalent logics (such as classical sentential or Boolean logic) which provide only for true and false.

Emil Leon Post is credited with first introducing additional logical truth degrees in his 1921 theory of elementary propositions. The conceptual form and basic ideas of three-valued logic were initially published by Jan Łukasiewicz and Clarence Irving Lewis. These were then re-formulated by Grigore Constantin Moisil in an axiomatic algebraic form, and also extended to n-valued logics in 1945.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

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  1. The copula is the sign denoting that there is an affirmation or denial; and thereby enabling the hearer or reader to distinguish a proposition from any other kind of discourse. Thus, in the proposition, The earth is round, the Predicate is the word _round_, which denotes the quality affirmed, or (as the phrase is) predicated: _the earth_, words denoting the object which that quality is affirmed of, compose the…

    John Stuart Mill, A System of Logic

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  2. The first includes all the sciences which are concerned with inanimate nature and which can be treated mathematically, more or less--mathematics, astronomy, mechanics, physics and chemistry. If one like to use big words to express simple things, it may be said that certain results of these sciences are eternal truths, final truths of last instance, whence they are called the exact sciences. But all the results are…

    Friedrich Engels, Landmarks of Scientific Socialism

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  3. Hence, in the conclusion of a syllogism we restrict a predicate to a certain object, after having thought it in the major in its whole extent under a certain condition. This complete quantity of the extent in relation to such a condition is called universality (universalitas). To this corresponds totality (universitas) of conditions in the synthesis of intuitions. The transcendental conception of reason is therefore…

    Immanuel Kant, The Critique of Pure Reason

    States what Three-valued logic is.

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Philosophers who discussed Three-valued logic

Related ideas

Opposing perspectives

Place in the tradition

Part of Non-classical logic.

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