Related papers: Probability Aggregates in Probability Answer Set P…
Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic…
Logic programs with aggregates (LPA) are one of the major linguistic extensions to Logic Programming (LP). In this work, we propose a generalization of the notions of unfounded set and well-founded semantics for programs with monotone and…
Queries with aggregation and arithmetic operations, as well as incomplete data, are common in real-world database, but we lack a good understanding of how they should interact. On the one hand, systems based on SQL provide ad-hoc rules for…
We elaborate upon the formal foundations of hybrid Answer Set Programming (ASP) and extend its underlying logical framework with aggregate functions over constraint values and variables. This is achieved by introducing the construct of…
In this paper, a possibilistic disjunctive logic programming approach for modeling uncertain, incomplete and inconsistent information is defined. This approach introduces the use of possibilistic disjunctive clauses which are able to…
A method is presented for computing minimal answers in disjunctive deductive databases under the disjunctive stable model semantics. Such answers are constructed by repeatedly extending partial answers. Our method is complete (in that every…
Aggregates are among the most frequently used linguistic extensions of answer set programming. The result of an aggregation may introduce new constants during the instantiation of the input program, a feature known as value invention. When…
Assumption-based argumentation (ABA) is a central structured argumentation formalism. As shown recently, answer set programming (ASP) enables efficiently solving NP-hard reasoning tasks of ABA in practice, in particular in the commonly…
The goal of combining the robustness of neural networks and the expressiveness of symbolic methods has rekindled the interest in Neuro-Symbolic AI. Deep Probabilistic Programming Languages (DPPLs) have been developed for probabilistic logic…
Probabilistic programming and the formal analysis of probabilistic algorithms are active areas of research, driven by the widespread use of randomness to improve performance. While functional correctness has seen substantial progress,…
This paper introduces Probabilistic Deduction (PD) as an approach to probabilistic structured argumentation. A PD framework is composed of probabilistic rules (p-rules). As rules in classical structured argumentation frameworks, p-rules…
We propose a new formal language for the expressive representation of probabilistic knowledge based on Answer Set Programming (ASP). It allows for the annotation of first-order formulas as well as ASP rules and facts with probabilities and…
In this paper we explore the application of methods for classical judgment aggregation in pooling probabilistic opinions on logically related issues. For this reason, we first modify the Boolean judgment aggregation framework in the way…
Answer Set Programming (ASP) is logic programming under the stable model or answer set semantics. During the last decade, this paradigm has seen several extensions by generalizing the notion of atom used in these programs. Among these,…
The Acceptance Probability Estimation Problem (APEP) is to additively approximate the acceptance probability of a Boolean circuit. This problem admits a probabilistic approximation scheme. A central question is whether we can design a…
Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…
We present a logical framework to represent and reason about stochastic optimization problems based on probability answer set programming. This is established by allowing probability optimization aggregates, e.g., minimum and maximum in the…
This report outlines an approach to learning generative models from data. We express models as probabilistic programs, which allows us to capture abstract patterns within the examples. By choosing our language for programs to be an…
Weight constraint and aggregate programs are among the most widely used logic programs with constraints. In this paper, we relate the semantics of these two classes of programs, namely the stable model semantics for weight constraint…
Hamiltonian Monte Carlo (HMC) is arguably the dominant statistical inference algorithm used in most popular "first-order differentiable" Probabilistic Programming Languages (PPLs). However, the fact that HMC uses derivative information…