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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 ...
In logic, the logical form of a statement is a precisely-specified semantic version of that statement in a formal system.Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system.
Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).
Rudolph Carnap defined the meaning of the adjective formal in 1934 as follows: "A theory, a rule, a definition, or the like is to be called formal when no reference is made in it either to the meaning of the symbols (for example, the words) or to the sense of the expressions (e.g. the sentences), but simply and solely to the kinds and order of the symbols from which the expressions are ...
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
A statement form can be shown to be a logical truth by either (a) showing that it is a tautology or (b) by means of a proof procedure. The corresponding conditional of a valid argument is a necessary truth (true in all possible worlds ) and so the conclusion necessarily follows from the premises, or follows of logical necessity.
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."
Semantics studies meaning in language, which is limited to the meaning of linguistic expressions. It concerns how signs are interpreted and what information they contain. An example is the meaning of words provided in dictionary definitions by giving synonymous expressions or paraphrases, like defining the meaning of the term ram as adult male sheep. [22]