In this paper, a Multi-Choice Stochastic Bi-Level Programming Problem (MCSBLPP) is considered where all the parameters of constraints are followed by normal distribution. The cost coefficients of the objective functions are multi-choice types. At first, all the probabilistic constraints are transformed into deterministic constraints using stochastic programming approach. Further, a general tran...

We introduce DeepProbLog, a neural probabilistic logic programming language that incorporates deep learning by means of predicates. show how existing inference and techniques the underlying ProbLog can be adapted for new language. theoretically experimentally demonstrate DeepProbLog supports (i) both symbolic subsymbolic representations inference, (ii) program induction, (iii) (logic) programmi...

We make a formal analogy between random sampling and fresh name generation. show that quasi-Borel spaces, model for probabilistic programming, can soundly interpret the ν-calculus, calculus Moreover, we prove this semantics is fully abstract up to first-order types. This surprising an ‘off-the-shelf’ model, requires novel analysis of probability distributions on function spaces. Our tools are d...