Animated miracles by Yigal Mesika; Anthony Brahams; Ori Ashkenazy; Menny

By Yigal Mesika; Anthony Brahams; Ori Ashkenazy; Menny Lindenfield

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It follows that P has to adhere to the conditional independence {b}⊥ ⊥P {c} | {a} (among others). Moreover, the probability of a possible world such as abcde can be written as P (abcde) = P (e | c) · P (d | bc) · P (c | a) · P (b | a) · P (a). 36 G. Kern-Isberner et al. Therefore, P can be completely described by e. g. 05 Note that the probabilities of negated variables derive from the above equations via e. g. P (e | c) = 1−P (e | c). By only defining the above conditional probabilities the function P can be compactly stored.

While comparing the different approaches is a difficult task due to the variety of the available concepts and to the absence of a common interface, we address this problem from both a conceptual and practical point of view. On a conceptual layer we propose and discuss several criteria by which first-order probabilistic methods can be distinguished, and apply these criteria to a series of approaches. On the practical layer, we briefly describe some systems for probabilistic reasoning, and go into more details on the KReator system as a versatile toolbox for various approaches to first-order probabilistic relational learning, modelling, and reasoning.

It is extended to formulas in the usual way, e. , we define θ(p(X, Y ) ∧ q(X)) = p(θ(X), θ(Y )) ∧ q(θ(X)). A grounding substitution θ is legal if any variable of type S in r is mapped to a constant of type S. We extend this relational language L to a probabilistic conditional language by introducing conditionals and probabilities. Definition 4 (Relational probabilistic conditional). A relational probabilistic conditional r is an expression of the form r = (φ | ψ)[α] with formulas φ, ψ ∈ L and α ∈ [0, 1].

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