foundational proof
1Mathematical proof — In mathematics, a proof is a convincing demonstration (within the accepted standards of the field) that some mathematical statement is necessarily true.[1][2] Proofs are obtained from deductive reasoning, rather than from inductive or empirical… …
2Formal proof — See also: mathematical proof, proof theory, and axiomatic system A formal proof or derivation is a finite sequence of sentences (called well formed formulas in the case of a formal language) each of which is an axiom or follows from the… …
3Twelf — is an implementation of the logical framework LF. It is used for logic programming and for the formalization of programming language theory.Introduction At its simplest, a Twelf program (called a signature ) is a collection of declarations of… …
4Scientific evidence (law) — This article is about the legal concept. For scientific evidence in pure science, see Scientific evidence. History Educating witness Role The educating witness teaches the fact finder (jury or, in a bench trial, judge) about the underlying… …
5Mathematical logic — (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… …
6mathematics, foundations of — Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods. It began with Euclid s Elements as an inquiry into the logical and philosophical basis of mathematics in essence, whether the axioms of any system… …
7Cessationism versus Continuationism — is a Christian theological dispute concerned with the question whether the charismatic gifts are currently in operation. Contents 1 Problems in the dispute 2 Restrictions on the topics 3 Cessationist U …
8Natural deduction — In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the natural way of reasoning. This contrasts with the axiomatic systems which instead use… …
9Foundations of mathematics — is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. The search for foundations of mathematics is also a central question of the philosophy …
10List of important publications in mathematics — One of the oldest surviving fragments of Euclid s Elements, found at Oxyrhynchus and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.[1] This is a list of important publications in mathematics, organized by field. Some… …
