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A logic translation is a translation of a text into a logical system. For example, translating the sentence "all skyscrapers are tall" as (() ()) is a logic translation that expresses an English language sentence in the logical system known as 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 allows the use of sentences that contain variables.
The modal depth of a formula also becomes apparent in the translation to first-order logic. When the modal depth of a formula is k, then the first-order logic formula contains a 'chain' of k transitions from the starting world . The worlds are 'chained' in the sense that these worlds are visited by going from accessible to accessible world.
A definite clause grammar (DCG) is a way of expressing grammar, either for natural or formal languages, in a logic programming language such as Prolog.It is closely related to the concept of attribute grammars / affix grammars.
A predicate that takes a single argument, used to express properties of objects or entities within a domain of discourse. [195] monadic predicate logic First-order logic with predicates that only take one argument, allowing for the expression of properties of individuals. monadic relation See unary relation. monism See logical monism. monomorphism
The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways of presenting an interpretation. In these contexts an interpretation is a function that provides the extension of symbols and strings of symbols of an object language.
Montague's thesis was that natural languages (like English) and formal languages (like programming languages) can be treated in the same way: . There is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians; indeed, I consider it possible to comprehend the syntax and semantics of both kinds of language within a single natural and ...
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 .
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