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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] [Amazon] |
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] [Amazon] |
NP (complexity)
In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems. NP is the Set (mathematics), set of decision problems for which the Computational complexity theory#Problem instances, problem instances, where the answer is "yes", have mathematical proof, proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine.''Polynomial time'' refers to how quickly the number of operations needed by an algorithm, relative to the size of the problem, grows. It is therefore a measure of efficiency of an algorithm. * NP is the set of decision problems ''solvable'' in polynomial time by a nondeterministic Turing machine. * NP is the set of decision problems ''verifiable'' in polynomial time by a deterministic Turing machine. The first definition is the basis for the abbreviation NP; "Nondeterministic alg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Footnotes
In publishing, a note is a brief text in which the author comments on the subject and themes of the book and names supporting citations. In the editorial production of books and documents, typographically, a note is usually several lines of text at the bottom of the page, at the end of a chapter, at the end of a volume, or a house-style typographic usage throughout the text. Notes are usually identified with superscript numbers or a symbol.''The Oxford Companion to the English Language'' (1992) p. 709. Footnotes are informational notes located at the foot of the thematically relevant page, whilst endnotes are informational notes published at the end of a chapter, the end of a volume, or the conclusion of a multi-volume book. Unlike footnotes, which require manipulating the page design (text-block and page layouts) to accommodate the additional text, endnotes are advantageous to editorial production because the textual inclusion does not alter the design of the publication. H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
