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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 allows the use of sentences that contain variables.
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier (" ∃x" or "∃(x)" or ...
Projection is relational algebra's counterpart of existential quantification in predicate logic. The attributes not included correspond to existentially quantified variables in the predicate whose extension the operand relation represents. The example below illustrates this point.
A predicate in the sense of predicate logic is a sequence of words with clearly defined spaces that becomes a propositional sentence if you insert a proper noun into each space. For example, the word sequence "_ x is a human" is a predicate because it gives rise to the declarative sentence "Peirce is a human" if you enter the proper name ...
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.
Predicate logic (2 C, 36 P) Pages in category "Basic concepts in set theory" ... Predicate (mathematical logic) Projection (set theory) R. Range of a function; S.
In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic.This formal system is distinguished from other systems such as propositional logic in that its formulas contain variables which can be quantified.
Kreisel's modified realizability applies to intuitionistic higher-order predicate logic and shows that the simply typed lambda term inductively extracted from the proof realizes the initial formula. In the case of propositional logic, it coincides with Howard's statement: the extracted lambda term is the proof itself (seen as an untyped lambda ...