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For example, that the box is on the table can be represented by (,), where is a function and not a predicate. In first-order logic, converting predicates to functions is called reification; for this reason, fluents represented by functions are said to be reified. When using reified fluents, a separate predicate is necessary to tell when a ...
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.
For a first-order predicate calculus, Gödel's completeness theorem states that the theorems (provable statements) are exactly the semantically valid well-formed formulas, so the valid formulas are computably enumerable: given unbounded resources, any valid formula can eventually be proven.
The Advisor Taker, on the other hand, proposed the use of the predicate calculus to represent common sense reasoning. Many of the early approaches to knowledge represention in Artificial Intelligence (AI) used graph representations and semantic networks, similar to knowledge graphs today.
The propositional calculus [a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [4] [1] or sometimes zeroth-order logic. [b] [6] [7] [8] Sometimes, it is called first-order propositional logic [9] to contrast it with System F, but it should not be confused with ...
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.
Logic has developed artificial languages, for example sentential calculus and predicate calculus, partly with the purpose of revealing the underlying logic of natural-language statements, the surface grammar of which may conceal the underlying logical structure. In these artificial languages an atomic sentence is a string of symbols which can ...
Montague grammar is an approach to natural language semantics, named after American logician Richard Montague.The Montague grammar is based on mathematical logic, especially higher-order predicate logic and lambda calculus, and makes use of the notions of intensional logic, via Kripke models.