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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 ...
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 ...
A sentence is said to be a logical consequence of a set of sentences, for a given language, if and only if, using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must be true if every sentence in the set is true.
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 proof or derivation is a finite sequence of well-formed formulas (which may be interpreted as sentences, or propositions) each of which is an axiom or follows from the preceding formulas in the sequence by a rule of inference. The last sentence in the sequence is a theorem of a formal system.
In most logical systems, one proves a statement of the form "P iff Q" by proving either "if P, then Q" and "if Q, then P", or "if P, then Q" and "if not-P, then not-Q". Proving these pairs of statements sometimes leads to a more natural proof, since there are not obvious conditions in which one would infer a biconditional directly.
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."
Financial statement, formal summary of the financial activities of a business, person, or other entity; Mathematical statement, a statement in logic and mathematics; Political statement, any act or nonverbal form of communication that is intended to influence a decision to be made for or by a group