In formal logic (such as sequent calculus or natural deduction) a hypothesis or premise is the antecedent of a sequent (or part of one):
A general judgement asserts the proof of a proposition (or, more generally, the term of some type) assuming the given hypothesis, which itself may or may not have a (known) proof.
In the practice of mathematics (or beyond), hypotheses that that are expected to have a proof, even if currently unknown, are known as conjectures.
For example, the “standard conjectures” in algebraic geometry serve as hypotheses in a wealth of theorems which are all proven (only) “assuming the standard conjectures” (cf. e.g. arXiv:9804123).
mathematical statements
Last revised on March 5, 2023 at 13:29:19. See the history of this page for a list of all contributions to it.