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Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory.
The typical example is in propositional logic, wherein a compound statement is constructed using individual statements connected by logical connectives; if the truth value of the compound statement is entirely determined by the truth value(s) of the constituent statement(s), the compound statement is called a truth function, and any logical ...
In some logical calculi (notably, in classical logic), certain essentially different compound statements are logically equivalent. A less trivial example of a redundancy is the classical equivalence between ¬ p ∨ q {\displaystyle \neg p\vee q} and p → q {\displaystyle p\to q} .
If a compound is built up from n distinct sentence letters, its truth table will have 2 n rows, since there are two ways of assigning T or F to the first letter, and for each of these there will be two ways of assigning T or F to the second, and for each of these there will be two ways of assigning T or F to the third, and so on, giving 2.2.2 ...
The predicate calculus goes a step further than the propositional calculus to an "analysis of the inner structure of propositions" [4] It breaks a simple sentence down into two parts (i) its subject (the object (singular or plural) of discourse) and (ii) a predicate (a verb or possibly verb-clause that asserts a quality or attribute of the object(s)).
Two meaningful declarative sentences express the same proposition, if and only if they mean the same thing. [citation needed] which defines proposition in terms of synonymity. For example, "Snow is white" (in English) and "Schnee ist weiß" (in German) are different sentences, but they say the same thing, so they express the same proposition.
The classic instance of an exocentric construction is the sentence (in a phrase structure grammar). [5] The traditional binary division [6] of the sentence (S) into a subject noun phrase (NP) and a predicate verb phrase (VP) was exocentric: Hannibal destroyed Rome. - Sentence (S) Since the whole is unlike either of its parts, it is exocentric.
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