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The fundamental difference between modern formal logic and traditional, or Aristotelian logic, lies in their differing analysis of the logical form of the sentences they treat: On the traditional view, the form of the sentence consists of (1) a subject (e.g., "man") plus a sign of quantity ("all" or "some" or "no"); (2) the copula , which is of ...
In the latter case, a (declarative) sentence is just one way of expressing an underlying statement. A statement is what a sentence means, it is the notion or idea that a sentence expresses, i.e., what it represents. For example, it could be said that "2 + 2 = 4" and "two plus two equals four" are two different sentences expressing the same ...
A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive apparatus (also called a deductive system). The deductive apparatus may consist of a set of transformation rules (also called inference rules) or a set of axioms, or have both. A formal system is used to derive one ...
Interjections are another word class, but these are not described here as they do not form part of the clause and sentence structure of the language. [2] Linguists generally accept nine English word classes: nouns, verbs, adjectives, adverbs, pronouns, prepositions, conjunctions, determiners, and exclamations.
A word over an alphabet can be any finite sequence (i.e., string) of letters. The set of all words over an alphabet Σ is usually denoted by Σ * (using the Kleene star). The length of a word is the number of letters it is composed of. For any alphabet, there is only one word of length 0, the empty word, which is often denoted by e, ε, λ or ...
Syntax refers to the linguistic structure above the word level (for example, how sentences are formed) – though without taking into account intonation, which is the domain of phonology. Morphology, by contrast, refers to the structure at and below the word level (for example, how compound words are formed), but above the level of individual ...
Translation of an English sentence to first-order logic. Logic translation is the process of representing a text in the formal language of a logical system.If the original text is formulated in ordinary language then the term natural language formalization is often used.
A formal grammar describes which strings from an alphabet of a formal language are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language.
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