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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 form of an argument can be shown by the use of symbols. For each argument form, there is a corresponding statement form, called a corresponding conditional, and an argument form is valid if and only if its corresponding conditional is a logical truth. A statement form which is logically true is also said to be a valid statement form.
a sentential form is a member of () that can be derived in a finite number of steps from the start symbol ; that is, a sentential form is a member of {()}. A sentential form that contains no nonterminal symbols (i.e. is a member of Σ ∗ {\displaystyle \Sigma ^{*}} ) is called a sentence .
An incomplete sentence, or sentence fragment, is a set of words that does not form a complete sentence, either because it does not express a complete thought or because it lacks some grammatical element, such as a subject or a verb. [6] [7] A dependent clause without an independent clause is an example of an incomplete sentence.
A complete theory is a theory that contains every sentence or its negation. The complete theory of all sentences satisfied by a structure is also called the theory of that structure . It's a consequence of Gödel's completeness theorem (not to be confused with his incompleteness theorems ) that a theory has a model if and only if it is ...
In language, a clause is a constituent or phrase that comprises a semantic predicand (expressed or not) and a semantic predicate. [1] A typical clause consists of a subject and a syntactic predicate, [2] the latter typically a verb phrase composed of a verb with or without any objects and other modifiers.
The word what can be used to form a free relative clause – one that has no antecedent and that serves as a complete noun phrase in itself, as in I like what he likes. The words whatever and whichever can be used similarly, in the role of either pronouns ( whatever he likes ) or determiners ( whatever book he likes ).
A major sentence is a regular sentence; it has a subject and a predicate, e.g. "I have a ball." In this sentence, one can change the persons, e.g. "We have a ball." However, a minor sentence is an irregular type of sentence that does not contain a main clause, e.g. "Mary!", "Precisely so.", "Next Tuesday evening after it gets dark."