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Programmers can use assertions to help specify programs and to reason about program correctness. For example, a precondition—an assertion placed at the beginning of a section of code—determines the set of states under which the programmer expects the code to execute.
In general, a judgment may be any inductively definable assertion in the metatheory. Judgments are used in formalizing deduction systems: a logical axiom expresses a judgment, premises of a rule of inference are formed as a sequence of judgments, and their conclusion is a judgment as well (thus, hypotheses and conclusions of proofs are judgments).
The fifth and sixth examples are meaningful declarative sentences, but are not statements but rather matters of opinion or taste. Whether or not the sentence "Pegasus exists." is a statement is a subject of debate among philosophers. Bertrand Russell held that it is a (false) statement. [citation needed] Strawson held it is not a statement at all.
Logical assertion, a statement that asserts that a certain premise is true; Proof by assertion, an informal fallacy in which a proposition is repeatedly restated; Time of assertion, in linguistics a secondary temporal reference in establishing tense; Assertive, a speech act that commits a speaker to the truth of the expressed proposition
These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [11] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...
Negative assertions may function as positives in sarcastic contexts. For example, in response to being informed that smoking can increase the possibility of developing lung cancer, someone could respond with the question, "Who knew?" The question functions as an assertion that the truth of the statement should have been utterly obvious.
In computer software testing, a test assertion is an expression which encapsulates some testable logic specified about a target under test. The expression is formally presented as an assertion, along with some form of identifier, to help testers and engineers ensure that tests of the target relate properly and clearly to the corresponding specified statements about the target.
For example, oxygen is necessary for fire. But one cannot assume that everywhere there is oxygen, there is fire. A condition X is sufficient for Y if X, by itself, is enough to bring about Y. For example, riding the bus is a sufficient mode of transportation to get to work.