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For example, the connective "and" is truth-functional since a sentence like "Apples are fruits and carrots are vegetables" is true if, and only if, each of its sub-sentences "apples are fruits" and "carrots are vegetables" is true, and it is false otherwise. Some connectives of a natural language, such as English, are not truth-functional.
For example, after is a preposition in "he left after the fight" but a conjunction in "he left after they fought". In general, a conjunction is an invariant (non-inflecting) grammatical particle that stands between conjuncts. A conjunction may be placed at the beginning of a sentence, [1] but some superstition about the practice persists. [2]
One approach is to choose a minimal set, and define other connectives by some logical form, as in the example with the material conditional above. The following are the minimal functionally complete sets of operators in classical logic whose arities do not exceed 2:
Sometimes used for “relation”, also used for denoting various ad hoc relations (for example, for denoting “witnessing” in the context of Rosser's trick). The fish hook is also used as strict implication by C.I.Lewis p {\displaystyle p} ⥽ q ≡ ( p → q ) {\displaystyle q\equiv \Box (p\rightarrow q)} .
Pages in category "Logical connectives" The following 21 pages are in this category, out of 21 total. This list may not reflect recent changes. ...
Grammaticalization can involve content words, such as nouns and verbs, developing into new function words that express grammatical relationships among other words in a sentence. This may happen rather than speakers deriving such new function words from (for example) existing bound , inflectional constructions.
Example: Abdul is happy. Jeanne is a person. I am she. Subject + Verb (transitive) + Indirect Object + Direct Object Example: She made me a pie. This clause pattern is a derivative of S+V+O, transforming the object of a preposition into an indirect object of the verb, as the example sentence in transformational grammar is actually "She made a ...
The modern view is more complex, since a single judgement of Aristotle's system involves two or more logical connectives. For example, the sentence "All men are mortal" involves, in term logic, two non-logical terms "is a man" (here M) and "is mortal" (here D): the sentence is given by the judgement A(M,D).