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PH was first defined by Larry Stockmeyer. [1] It is a special case of hierarchy of bounded alternating Turing machine. It is contained in P #P = P PP and PSPACE. PH has a simple logical characterization: it is the set of languages expressible by second-order logic.
The union of the classes in the hierarchy is denoted PH. Classes within the hierarchy have complete problems (with respect to polynomial-time reductions ) that ask if quantified Boolean formulae hold, for formulae with restrictions on the quantifier order.
SO, unrestricted second-order logic, is equal to the Polynomial hierarchy PH. More precisely, we have the following generalisation of Fagin's theorem: The set of formulae in prenex normal form where existential and universal quantifiers of second order alternate k times characterise the k th level of the polynomial hierarchy.
PH is the set of languages definable by second-order formulas. ... Foundations without Foundationalism: A Case for Second-Order Logic. Oxford: Clarendon Press.
Archaic form of Phi. Phi (/ f aɪ /; [1] uppercase Φ, lowercase φ or ϕ; Ancient Greek: ϕεῖ pheî; Modern Greek: φι fi) is the twenty-first letter of the Greek alphabet.. In Archaic and Classical Greek (c. 9th to 4th century BC), it represented an aspirated voiceless bilabial plosive ([pʰ]), which was the origin of its usual romanization as ph .
The Gettier problem, in the field of epistemology, is a landmark philosophical problem concerning the understanding of descriptive knowledge.Attributed to American philosopher Edmund Gettier, Gettier-type counterexamples (called "Gettier-cases") challenge the long-held justified true belief (JTB) account of knowledge.
Stumpp’s case is of the most infamous in history, for the heinousness of his alleged crimes and the brutality of the punishment he’d later face after a quarter-century of rumors. Convicted of ...
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds. [1]
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