In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A newpossibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming...

The field of Probabilistic Logic Programming (PLP) has seen significant advances in the last 20 years, with many proposals for languages that combine probability with logic programming. Since the start, the problem of learning probabilistic logic programs has been the focus of much attention and a special issue of Theory and Practice of Logic Programming on Probability, Logic, and Learning has ...

We propose Edward, a Turing-complete probabilistic programming language. Edward builds on two compositional representations—random variables and inference. By treating inference as a first class citizen, on a par with modeling, we show that probabilistic programming can be as flexible and computationally efficient as traditional deep learning. For flexibility, Edward makes it easy to fit the sa...

In our recently published article, we investigated the behavioral addiction model of obsessive-compulsive disorder (OCD), by assessing three core dimensions of addiction in patients with OCD healthy participants. Similar to the common findings in addiction, OCD patients demonstrated increased impulsivity, risky decision-making, and biased probabilistic reasoning compared to healthy controls. Th...

A temporal logic for reasoning about probabilistic systems is considered exogenous probabilistic computation tree logic (EpCTL). Both a syntactic and a semantic approach to verify systems with EpCTL are introduced. For the first approach a (weakly) complete Hilbert calculus is given. The completeness result capitalizes in the decidability of the existential theory of the real numbers and in a P...

We introduce a notion of probability to the graph programming language GP2 which resolves nondeterministic choices of graph transformation rules and their matches. With our programming model Probabilistic GP2 (P-GP2), rule and match decisions are assigned uniform distributions over their domains. In this paper, we present an implementation of P-GP2 as an extension of an existing GP2 compiler. A...

In this paper we propose a framework for combining Disjunctive Logic Programming and Poole's Probabilistic Horn Abduction. We use the concept of hypothesis to spec­ ify the probability structure. We consider the case in which probabilistic information is not available. Instead of using probability intervals, we allow for the specification of the probabilities of disjunctions. Because mini­ mal ...

We extend cc to allow the specification of a discrete probability distribution for random variables. We demonstrate the expressiveness of pcc by synthesizing combinators for default reasoning. We extend pcc uniformly over time, to get a synchronous reactive probabilistic programming language, Timed pcc. We describe operational and denotational models for pcc (and Timed pcc). The key feature of ...

We present a new approach to probabilistic logic programs with a possible worlds semantics. Classical program clauses are extended by a subinterval of [0; 1] that describes the range for the conditional probability of the head of a clause given its body. We show that deduction in the defined probabilistic logic programs is computationally more complex than deduction in classical logic programs....

First-order model counting emerged recently as a novel reasoning task, at the core of efficient algorithms for probabilistic logics such as MLNs. For certain subsets of first-order logic, lifted model counters were shown to run in time polynomial in the number of objects in the domain of discourse, where propositional model counters require exponential time. However, these guarantees apply only...