Search results
Results From The WOW.Com Content Network
More formally, proposition B is a corollary of proposition A, if B can be readily deduced from A or is self-evident from its proof. In many cases, a corollary corresponds to a special case of a larger theorem, [4] which makes the theorem easier to use and apply, [5] even though its importance is generally considered to be secondary to that of ...
A proposition is a statement that makes a claim about what is the case. In this regard, propositions act as truth-bearers: they are either true or false. [18] [19] [3] For example, the sentence "The water is boiling." expresses a proposition since it can be true or false. The sentences "Is the water boiling?"
Each proposition (statement that is a thought of the kind expressible by a declarative sentence) [5] of a syllogism is a categorical sentence which has a subject and a predicate connected by a verb. The usual way of connecting the subject and predicate of a categorical sentence as Aristotle does in On Interpretation is by using a linking verb e ...
Propositional logic, as currently studied in universities, is a specification of a standard of logical consequence in which only the meanings of propositional connectives are considered in evaluating the conditions for the truth of a sentence, or whether a sentence logically follows from some other sentence or group of sentences.
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.
a proposition. Which is the assertion that is made by (i.e., the meaning of) a true or false declarative sentence. [1] [2] 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.
There is a simple randomized algorithm due to Schöning (1999) that runs in time (4/3) n where n is the number of variables in the 3-SAT proposition, and succeeds with high probability to correctly decide 3-SAT. [12]
corollary A proposition that follows directly from another proposition or theorem with little or no additional proof. correspondence theory of truth The philosophical doctrine that the truth or falsity of a statement is determined by how it relates to the world and whether it accurately describes (corresponds with) that world. counterexample 1.