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Proof assistant. In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details ...
The propositional calculus [a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [1] or sometimes zeroth-order logic. [4] [5] It deals with propositions [1] (which can be true or false) [6] and relations between propositions, [7] including the construction of ...
The concept of proof is formalized in the field of mathematical logic. [ 12] A formal proof is written in a formal language instead of natural language. A formal proof is a sequence of formulas in a formal language, starting with an assumption, and with each subsequent formula a logical consequence of the preceding ones.
Usually a given proof calculus encompasses more than a single particular formal system, since many proof calculi are under-determined and can be used for radically different logics. For example, a paradigmatic case is the sequent calculus , which can be used to express the consequence relations of both intuitionistic logic and relevance logic .
Formal proof. In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (known as well-formed formulas when relating to formal language ), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence, according to the rule of inference. It differs from a natural language ...
Intuitionistic logic. Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems of intuitionistic logic do not assume the law of the excluded middle and ...
Distributive property. In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality is always true in elementary algebra . For example, in elementary arithmetic, one has Therefore, one would say that multiplication distributes over addition .
Formal calculation. In mathematical logic, a formal calculation, or formal operation, is a calculation that is systematic but without a rigorous justification. It involves manipulating symbols in an expression using a generic substitution without proving that the necessary conditions hold. Essentially, it involves the form of an expression ...
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