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  2. Sentence (mathematical logic) - Wikipedia

    en.wikipedia.org/wiki/Sentence_(mathematical_logic)

    In mathematical logic, a sentence (or closed formula) [1] of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition , something that must be true or false.

  3. Law of excluded middle - Wikipedia

    en.wikipedia.org/wiki/Law_of_excluded_middle

    He then proposes that "there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate" (Book IV, CH 7, p. 531). In the context of Aristotle's traditional logic, this is a remarkably precise statement of the law of excluded middle, P ∨ ~P.

  4. Predicate (mathematical logic) - Wikipedia

    en.wikipedia.org/wiki/Predicate_(mathematical_logic)

    A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates. [1] In a sense, these are nullary (i.e. 0-arity) predicates.

  5. First-order logic - Wikipedia

    en.wikipedia.org/wiki/First-order_logic

    First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and

  6. Predicate (grammar) - Wikipedia

    en.wikipedia.org/wiki/Predicate_(grammar)

    [a] The predicate must contain a verb, and the verb requires or permits other elements to complete the predicate, or else precludes them from doing so. These elements are objects (direct, indirect, prepositional), predicatives, and adjuncts: She dances. — Verb-only predicate. Ben reads the book. — Verb-plus-direct-object predicate.

  7. Control (linguistics) - Wikipedia

    en.wikipedia.org/wiki/Control_(linguistics)

    Control predicates semantically select their arguments, as stated above. Raising predicates, in contrast, do not semantically select (at least) one of their dependents. The contrast is evident with the so-called raising-to-object verbs (=ECM-verbs) such as believe, expect, want, and prove. Compare the following a- and b-sentences: a.

  8. Truth predicate - Wikipedia

    en.wikipedia.org/wiki/Truth_predicate

    A language is called fully interpreted if meanings are attached to its sentences so that they all are either true or false. A fully interpreted language L which does not have a truth predicate can be extended to a fully interpreted language Ľ that contains a truth predicate T , i.e., the sentence A ↔ T (⌈ A ⌉) is true for every sentence ...

  9. Logic translation - Wikipedia

    en.wikipedia.org/wiki/Logic_translation

    This function maps sentences of the first system to sentences of the second system while obeying the entailment relations between the original sentences. This means that if a sentence entails another sentence in the first logic, then the translation of the first sentence should entail the translation of the second sentence in the second logic.

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