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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 ...
Resolution (logic) In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation-complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts as a decision procedure for formula ...
Universal generalization / instantiation. Existential generalization / instantiation. In propositional logic and Boolean algebra, De Morgan's laws, [ 1][ 2][ 3] also known as De Morgan's theorem, [ 4] are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British ...
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 motivating factor for the development of computer science .
Propositional formula. In propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, or a sentential formula .
In proof theory and mathematical logic, sequent calculus is a family of formal systems sharing a certain style of inference and certain formal properties. The first sequent calculi systems, LK and LJ, were introduced in 1934/1935 by Gerhard Gentzen [1] as a tool for studying natural deduction in first-order logic (in classical and intuitionistic versions, respectively).
Proof complexity. In logic and theoretical computer science, and specifically proof theory and computational complexity theory, proof complexity is the field aiming to understand and analyse the computational resources that are required to prove or refute statements. Research in proof complexity is predominantly concerned with proving proof ...
Although intuitionistic logic retains the trivial propositions {,} from classical logic, each proof of a propositional formula is considered a valid propositional value, thus by Heyting's notion of propositions-as-sets, propositional formulae are (potentially non-finite) sets of their proofs.