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

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

tableaux Proof procedure Propositional proof system Resolution (logic) Anita Wasilewska. "General proof systems" (PDF). "Definition:Proof System - ProofWiki"...

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

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...

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...

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

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

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 be...

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...

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...

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

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

diagrammatic notation for propositional logicPages displaying short descriptions of redirect targets: a graphical syntax for propositional logic Logical determinism –...

negative existential propositions or universal propositions in logic. The irrationality of the square root of 2 is one of the oldest proofs of impossibility...

valid formulas of propositional logic. The philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921, borrowing...

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

or the proofs-as-programs and propositions- or formulae-as-types interpretation. It is a generalization of a syntactic analogy between systems of formal...

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...

to the much simpler rules of propositional calculus. In a typical argument, quantifiers are eliminated, then propositional calculus is applied to unquantified...

propositions expressed in some formal system. An alternative form of hypothetical syllogism, more useful for classical propositional calculus systems...

consequence Negation normal form Open sentence Propositional calculus Propositional formula Propositional variable Rule of inference Strict conditional...

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

Propositional logic is not concerned with the concrete meaning of propositions other than their truth values. Key rules of inference in propositional...

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

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...

axiomatic system is a set of formal statements (i.e. axioms) used to logically derive other statements such as lemmas or theorems. A proof within an axiom...

in the role that the proposition or logical connective plays within a system of inference. Gerhard Gentzen is the founder of proof-theoretic semantics...

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