Concept
Many-valued logic
Overview
Many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., true and false) for any proposition. Classical two-valued logic may be extended to n-valued logic for n greater than 2. Those most popular in the literature are three-valued (e.g., Łukasiewicz's and Kleene's, which accept the values true, false, and unknown), four-valued, seven-valued, nine-valued, the finite-valued (finitely-many valued) with more than three values, and the infinite-valued (infinitely-many-valued), such as fuzzy logic and probability logic.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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The seventh sort are those who serve the public in expensive employments at their own charge: these are called the rich. The eighth are those who execute the different offices of the state, and without these it could not possibly subsist: it is therefore necessary that there should be some persons capable of governing and filling the places in the city; and this either for life or in rotation: the office of senator…
Aristotle, Politics
States what Many-valued logic is; the author is tied to Many-valued logic in the knowledge graph.
A man might, indeed, argue that 'much' was the contrary of 'little', and 'great' of 'small'. But these are not quantitative, but relative; things are not great or small absolutely, they are so called rather as the result of an act of comparison. For instance, a mountain is called small, a grain large, in virtue of the fact that the latter is greater than others of its kind, the former less. Thus there is a reference…
Aristotle, The Categories
States what Many-valued logic is; the author is tied to Many-valued logic in the knowledge graph.
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 Many-valued logic is.
Philosophers who discussed Many-valued logic
Related ideas
- Nuel Belnap
- Hans Reichenbach
- Negation
- Truth value
- Kurt Gödel
- Intuitionistic logic
- Law of excluded middle
- Logical conjunction
- Propositional logic
- Rational number
- Real number
- Logical biconditional
- Stephen Cole Kleene
- Semantics
- Jan Łukasiewicz
- Aristotle
- Term logic
- Emil Leon Post
- Graham Priest
- Tautology (logic)
- Logic
- Fuzzy logic
- Functional completeness
- Problem of future contingents
Opposing perspectives
Place in the tradition
Part of Outline of philosophy.
Narrower topics: