Propositional proof system information

In propositional calculus and proof complexity a propositional proof system (pps), also called a Cook–Reckhow propositional proof system, is a system for...

The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes...

structures, and bunched implication. Propositional proof system Proof nets Cirquent calculus Calculus of structures Formal proof Method of analytic tableaux Resolution...

proof into a sequence of short proofs in a propositional proof system than to design short propositional proofs directly in the propositional proof system...

Efficiency of Propositional Proof Systems", in which they formalized the notions of p-simulation and efficient propositional proof system, which started...

such proof systems exist: Problem (Optimality) Does there exist a p-optimal or optimal propositional proof system? Every propositional proof system P can...

In proof complexity, a Frege system is a propositional proof system whose proofs are sequences of formulas derived using a finite set of sound and implicationally...

extend the propositional system to axiomatise classical predicate logic. Likewise, these three rules extend system for intuitionstic propositional logic (with...

system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. Some of the major areas of proof...

Logic Theorist constructed proofs from a small set of propositional axioms and three deduction rules: modus ponens, (propositional) variable substitution...

formal language for classical propositional logic can be expressed using just negation (¬), implication (→) and propositional symbols. A well-known axiomatization...

In mathematical logic, the implicational propositional calculus is a version of classical propositional calculus that uses only one connective, called...

logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to...

formal proof is a complete rendition of a mathematical proof within a formal system. An axiomatic system is said to be consistent if it lacks contradiction...

non-constructive proofs show that if a certain proposition is false, a contradiction ensues; consequently the proposition must be true (proof by contradiction)...

statement holds is not enough for a proof, which must demonstrate that the statement is true in all possible cases. A proposition that has not been proved but...

models of arithmetic. Early logic systems includes Indian logic of Pāṇini, syllogistic logic of Aristotle, propositional logic of Stoicism, and Chinese logic...

truth-functional tautology or theorem of propositional logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia...

truth-functional propositional logic (Paul Bernays 1918), (Emil Post 1920) Proof of the syntactic completeness of truth-functional propositional logic (Emil...

impossible?". In classical logic, particularly in propositional and first-order logic, a proposition φ {\displaystyle \varphi } is a contradiction if and...

false) of a truth function. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher-order logics...

In propositional logic, the double negation of a statement states that "it is not the case that the statement is not true". In classical logic, every...

redirect targetss: a graphical syntax for propositional logic Logical determinism – view that a proposition about the future is either necessarily true...

proved, or can be proved. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem...

calculus. This is similar to a way of axiomatizing classical propositional logic. In propositional logic, the inference rule is modus ponens MP: from ϕ → ψ...

see if the proposition in question holds. This is a method of direct proof. A proof by exhaustion typically contains two stages: A proof that the set...