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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 ...
t. e. Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power.
Formal verification is a key incentive for formal specification of systems, and is at the core of formal methods . It represents an important dimension of analysis and verification in electronic design automation and is one approach to software verification. The use of formal verification enables the highest Evaluation Assurance Level ( EAL7 ...
e. In artificial intelligence, symbolic artificial intelligence (also known as classical artificial intelligence or logic-based artificial intelligence) [1] [2] is the term for the collection of all methods in artificial intelligence research that are based on high-level symbolic (human-readable) representations of problems, logic and search. [3]
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 ...
Automated theorem proving. Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science .
propositional logic, Boolean algebra, first-order logic. ⊥ {\displaystyle \bot } denotes a proposition that is always false. The symbol ⊥ may also refer to perpendicular lines. The proposition. ⊥ ∧ P {\displaystyle \bot \wedge P} is always false since at least one of the two is unconditionally false. ∀.
Symbolic statement. In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as " given any ", " for all ", or " for any ". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every ...