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Arguing for the need to combine declarative and probabilistic programming, Barany et al. (TODS 2017) recently introduced a probabilistic extension of Datalog as a purely declarative probabilistic programming language. We revisit this language and propose a more principled approach towards defining its semantics based on stochastic kernels and Markov processes - standard notions from probability theory. This allows us to extend the semantics to continuous probability distributions, thereby settling an open problem posed by Barany et al. We show that our semantics is fairly robust, allowing both parallel execution and arbitrary chase orders when evaluating a program. We cast our semantics in the framework of infinite probabilistic databases (Grohe and Lindner, ICDT 2020), and show that the semantics remains meaningful even when the input of a probabilistic Datalog program is an arbitrary probabilistic database.
Statistical models of real world data typically involve continuous probability distributions such as normal, Laplace, or exponential distributions. Such distributions are supported by many probabilistic modelling formalisms, including probabilistic d
We study termination of higher-order probabilistic functional programs with recursion, stochastic conditioning and sampling from continuous distributions. Reasoning about the termination probability of programs with continuous distributions is hard
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In this paper, a new technique for the optimization of (partially) bound queries over disjunctive Datalog programs with stratified negation is presented. The technique exploits the propagation of query bindings and extends the Magic Set (MS) optimiza
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