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・ Markov
・ Markov (crater)
・ Markov additive process
・ Markov algorithm
・ Markov blanket
・ Markov brothers' inequality
・ Markov chain
・ Markov chain approximation method
・ Markov chain geostatistics
・ Markov chain mixing time
・ Markov chain Monte Carlo
・ Markov chains on a measurable state space
・ Markov decision process
・ Markov information source
・ Markov kernel
Markov logic network
・ Markov model
・ Markov number
・ Markov partition
・ Markov perfect equilibrium
・ Markov process
・ Markov Processes International
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・ Markov random field
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・ Markov reward model
・ Markov Reward Model Checker
・ Markov spectrum
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・ Markov switching multifractal


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Markov logic network : ウィキペディア英語版
Markov logic network
A Markov logic network (or MLN) is a probabilistic logic which applies the ideas of a Markov network to first-order logic, enabling uncertain inference. Markov logic networks generalize first-order logic, in the sense that, in a certain limit, all unsatisfiable statements have a probability of zero, and all tautologies have probability one.
==Description==
Briefly, it is a collection of formulas from first order logic, to each of which is assigned a real number, the weight. Taken as a Markov network, the vertices of the network graph are atomic formulas, and the edges are the logical connectives used to construct the formula. Each formula is considered to be a clique, and the Markov blanket is the set of formulas in which a given atom appears. A potential function is associated to each formula, and takes the value of one when the formula is true, and zero when it is false. The potential function is combined with the weight to form the Gibbs measure and partition function for the Markov network.
The above definition glosses over a subtle point: atomic formulas do not have a truth value unless they are grounded and given an interpretation; that is, until they are ground atoms with a Herbrand interpretation. Thus, a Markov logic network becomes a Markov network only with respect to a specific grounding and interpretation; the resulting Markov network is called the ground Markov network. The vertices of the graph of the ground Markov network are the ground atoms. The size of the resulting Markov network thus depends strongly (exponentially) on the number of constants in the domain of discourse.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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