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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.
Some frequentative verbs surviving in English, and their parent verbs are listed below. Additionally, some frequentative verbs are formed by reduplication of a monosyllable (e.g., coo-cooing, cf. Latin murmur). Frequentative nouns are often formed by combining two different vowel grades of the same word (as in teeter-totter, pitter-patter ...
are two different sentences that make the same statement. In either case, a statement is viewed as a truth bearer. Examples of sentences that are (or make) true statements: "Socrates is a man." "A triangle has three sides." "Madrid is the capital of Spain." Examples of sentences that are also statements, even though they aren't true:
Propositional logic deals with statements, which are defined as declarative sentences having truth value. [29] [1] Examples of statements might include: Wikipedia is a free online encyclopedia that anyone can edit. London is the capital of England. All Wikipedia editors speak at least three languages.
For example, Hamilton uses two symbols = and ≠ when he defines the notion of a valuation v of any well-formed formulas (wffs) A and B in his "formal statement calculus" L. A valuation v is a function from the wffs of his system L to the range (output) { T, F }, given that each variable p 1 , p 2 , p 3 in a wff is assigned an arbitrary truth ...
In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (x) that is not defined or specified (thus being a free variable), which leaves the statement undetermined. The sentence may contain several such ...
In this example, both sentences happen to have the common form () for some individual , in the first sentence the value of the variable x is "Socrates", and in the second sentence it is "Plato". Due to the ability to speak about non-logical individuals along with the original logical connectives, first-order logic includes propositional logic.
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P.