Neurosymbolic AI (NeSy) aims to integrate the statistical strengths of neural networks with the interpretability and structure of symbolic reasoning. However, current NeSy frameworks like DeepProbLog enforce a fixed flow where symbolic reasoning always follows neural processing. This restricts their ability to model complex dependencies, especially in irregular data structures such as graphs. In this work, we introduce DeepGraphLog, a novel NeSy framework that extends ProbLog with Graph Neural Predicates. DeepGraphLog enables multi-layer neural-symbolic reasoning, allowing neural and symbolic components to be layered in arbitrary order. In contrast to DeepProbLog, which cannot handle symbolic reasoning via neural methods, DeepGraphLog treats symbolic representations as graphs, enabling them to be processed by Graph Neural Networks (GNNs). We showcase the capabilities of DeepGraphLog on tasks in planning, knowledge graph completion with distant supervision, and GNN expressivity. Our results demonstrate that DeepGraphLog effectively captures complex relational dependencies, overcoming key limitations of existing NeSy systems. By broadening the applicability of neurosymbolic AI to graph-structured domains, DeepGraphLog offers a more expressive and flexible framework for neural-symbolic integration.

Probabilistic Answer Set Programming under the credal semantics (PASP) extends Answer Set Programming with probabilistic facts that represent uncertain information. The probabilistic facts are discrete with Bernoulli distributions. However, several real-world scenarios require a combination of both discrete and continuous random variables. In this paper, we extend the PASP framework to support continuous random variables and propose Hybrid Probabilistic Answer Set Programming (HPASP). Moreover, we discuss, implement, and assess the performance of two exact algorithms based on projected answer set enumeration and knowledge compilation and two approximate algorithms based on sampling. Empirical results, also in line with known theoretical results, show that exact inference is feasible only for small instances, but knowledge compilation has a huge positive impact on the performance. Sampling allows handling larger instances, but sometimes requires an increasing amount of memory.

Solving a decision theory problem usually involves finding the actions, among a set of possible ones, which optimize the expected reward, possibly accounting for the uncertainty of the environment. In this paper, we introduce the possibility to encode decision theory problems with Probabilistic Answer Set Programming under the credal semantics via decision atoms and utility attributes. To solve the task we propose an algorithm based on three layers of Algebraic Model Counting, that we test on several synthetic datasets against an algorithm that adopts answer set enumeration. Empirical results show that our algorithm can manage non trivial instances of programs in a reasonable amount of time.

Parameter learning is a crucial task in the field of Statistical Relational Artificial Intelligence: given a probabilistic logic program and a set of observations in the form of interpretations, the goal is to learn the probabilities of the facts in the program such that the probabilities of the interpretations are maximized. In this paper, we propose two algorithms to solve such a task within the formalism of Probabilistic Answer Set Programming, both based on the extraction of symbolic equations representing the probabilities of the interpretations. The first solves the task using an off-the-shelf constrained optimization solver while the second is based on an implementation of the Expectation Maximization algorithm. Empirical results show that our proposals often outperform existing approaches based on projected answer set enumeration in terms of quality of the solution and in terms of execution time. The paper has been accepted at the ICLP2024 conference and is under consideration in Theory and Practice of Logic Programming (TPLP).

When we want to compute the probability of a query from a Probabilistic Answer Set Program, some parts of a program may not influence the probability of a query, but they impact on the size of the grounding. Identifying and removing them is crucial to speed up the computation. Algorithms for SLG resolution offer the possibility of returning the residual program which can be used for computing answer sets for normal programs that do have a total well-founded model. The residual program does not contain the parts of the program that do not influence the probability. In this paper, we propose to exploit the residual program for performing inference. Empirical results on graph datasets show that the approach leads to significantly faster inference. The paper has been accepted at the ICLP2024 conference and under consideration in Theory and Practice of Logic Programming (TPLP).

The original framework of Poole and Sato extended the logic programming language Prolog (Flach, 1994) with probabilistic facts. These are facts that are annotated with the probability that they are true; they play a role similar to the parentless nodes in Bayesian networks in that they are marginally independent of one another, and that the probabilistic dependencies are induced by the rules of the logic program. This resulted in the celebrated distribution semantics (Sato, 1995) that is the basis of probabilistic logic programming, and the corresponding learning algorithm in the PRISM language (Sato, 1995) constitutes - to the best of the authors' knowledge - the very first probabilistic programming language with built-in support for machine learning. The work of Sato and Poole has inspired many follow-up works on inference and learning, and has also introduced many variations and extensions of the probabilistic logic programming and its celebrated distribution semantics.

The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model domains with relational structure and uncertainty. Essentially, a program specifies a probability distribution over possible worlds (i.e., sets of facts). The notion of explanation is typically associated with that of a world, so that one often looks for the most probable world as well as for the worlds where the query is true. Unfortunately, such explanations exhibit no causal structure. In particular, the chain of inferences required for a specific prediction (represented by a query) is not shown. In this paper, we propose a novel approach where explanations are represented as programs that are generated from a given query by a number of unfolding-like transformations. Here, the chain of inferences that proves a given query is made explicit. Furthermore, the generated explanations are minimal (i.e., contain no irrelevant information) and can be parameterized w.r.t. a specification of visible predicates, so that the user may hide uninteresting details from explanations.

Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to account for it. The first contribution of this paper is a novel interpretation of probabilistic argumentation frameworks as probabilistic logic programs. Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. We show that the programs representing probabilistic argumentation frameworks do not satisfy a common assumption in probabilistic logic programming (PLP) semantics, which is, that probabilistic facts fully capture the uncertainty in the domain under investigation. The second contribution of this paper is then a novel PLP semantics for programs where a choice of probabilistic facts does not uniquely determine the truth assignment of the logical atoms. The third contribution of this paper is the implementation of a PLP system supporting this semantics: smProbLog. smProbLog is a novel PLP framework based on the probabilistic logic programming language ProbLog. smProbLog supports many inference and learning tasks typical of PLP, which, together with our first contribution, provide novel reasoning tools for probabilistic argumentation. We evaluate our approach with experiments analyzing the computational cost of the proposed algorithms and their application to a dataset of argumentation problems.

The power and expressivity of Probabilistic Logic Programming (PLP) [8, 18] have been utilized to represent many real world situations [2, 9, 14]. Usually, probabilistic logic programs involve only discrete random variables with Bernoulli or Categorical distributions. Numerous solutions emerged to also handle continuous distributions [10, 12, 25], increasing the expressiveness of PLP and giving birth to hybrid probabilistic logic programs, that is, programs that include discrete and continuous random variables. Inference in this type of programs is hard since it combines the complexity of the grounding computation with the intractability of a distribution defined by a mixture of random variables. Usually, inference in general hybrid probabilistic logic programs (i.e., without imposing restrictions on the type of distributions allowed) is done by leveraging knowledge compilation and using external solvers [25] or by sampling [4, 16].

Over the last years, there has been increasing research on the scaling behaviour of statistical relational representations with the size of the domain, and on the connections between domain size dependence and lifted inference. In particular, the asymptotic behaviour of statistical relational representations has come under scrutiny, and projectivity was isolated as the strongest form of domain size independence. In this contribution we show that every probabilistic logic program under the distribution semantics is asymptotically equivalent to a probabilistic logic program consisting only of range-restricted clauses over probabilistic facts. To facilitate the application of classical results from finite model theory, we introduce the abstract distribution semantics, defined as an arbitrary logical theory over probabilistic facts to bridge the gap to the distribution semantics underlying probabilistic logic programming. In this representation, range-restricted logic programs correspond to quantifier-free theories, making asymptotic quantifier results avilable for use. We can conclude that every probabilistic logic program inducing a projective family of distributions is in fact captured by this class, and we can infer interesting consequences for the expressivity of probabilistic logic programs as well as for the asymptotic behaviour of probabilistic rules.