Concept
Finite-valued logic
Overview
In logic, a finite-valued logic (also finitely many-valued logic) is a propositional calculus in which truth values are discrete. Traditionally, in Aristotle's logic, the bivalent logic, also known as binary logic was the norm, as the law of the excluded middle precluded more than two possible values (i.e., "true" and "false") for any proposition. Modern three-valued logic (ternary logic) allows for an additional possible truth value (i.e. "undecided").
The term finitely many-valued logic is typically used to describe many-valued logic having three or more, but not infinite, truth values. The term finite-valued logic encompasses both finitely many-valued logic and bivalent logic. Fuzzy logics, which allow for degrees of values between "true" and "false", are typically not considered forms of finite-valued logic. However, finite-valued logic can be applied in Boolean-valued modeling, description logics, and defuzzification of fuzzy logic. A finite-valued logic is decidable (sure to determine outcomes of the logic when it is applied to propositions) if and only if it has a computational semantics.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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And so the extreme characters push away, so to speak, towards each other the man in the mean state; the brave man is called a rash man by the coward, and a coward by the rash man, and in the other cases accordingly. And there being this mutual opposition, the contrariety between the extremes is greater than between either and the mean, because they are further from one another than from the mean, just as the greater…
Aristotle, The Nicomachean ethics of Aristotle
States what Finite-valued logic is; the author is tied to Finite-valued logic in the knowledge graph.
Quantities have no contraries. In the case of definite quantities this is obvious; thus, there is nothing that is the contrary of 'two cubits long' or of 'three cubits long', or of a surface, or of any such quantities. 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…
Aristotle, The Categories
States what Finite-valued logic is; the author is tied to Finite-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 Finite-valued logic is.
Related ideas
- Formal language
- Nuel Belnap
- Truth value
- Kurt Gödel
- Law of excluded middle
- Propositional logic
- Mathematics
- Neuron
- Natural language
- Linguistics
- Sorites paradox
- Probability theory
- Principle of bivalence
- Three-valued logic
- Truth table
- Set theory
- Stephen Cole Kleene
- Jan Łukasiewicz
- Age of Enlightenment
- Aristotle
- Emil Leon Post
- Brain
- Many-valued logic
- George Boole
Place in the tradition
Part of Intuitionistic logic.