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Propositional Proof System
In propositional calculus and proof complexity a propositional proof system (pps), also called a Cook–Reckhow propositional proof system, is a system for proving classical logic, classical propositional logic, propositional tautologies. Mathematical definition Formally a pps is a polynomial-time function ''P'' whose range of a function, range is the set of all propositional tautologies (denoted TAUT). If ''A'' is a formula, then any ''x'' such that ''P''(''x'') = ''A'' is called a ''P''-proof of ''A''. The condition defining pps can be broken up as follows: * Completeness (logic), Completeness: every propositional tautology (logic), tautology has a ''P''-proof, * Soundness: if a propositional formula has a ''P''-proof then it is a tautology, * Efficiency: ''P'' runs in polynomial time. In general, a proof system for a language ''L'' is a polynomial-time function whose range is ''L''. Thus, a propositional proof system is a proof system for TAUT. Sometimes the following alterna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propositional Calculus
The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. Sometimes, it is called ''first-order'' propositional logic to contrast it with System F, but it should not be confused with first-order logic. It deals with propositions (which can be Truth value, true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives representing the truth functions of Logical conjunction, conjunction, Logical disjunction, disjunction, Material conditional, implication, Logical biconditional, biconditional, and negation. Some sources include other connectives, as in the table below. Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or Quantifier (logic), quantifiers. However, all the machinery of pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
