Probabilistic Logic Programming Research Articles

The generalised distribution semantics and projective families of distributions

We generalise the distribution semantics underpinning probabilistic logic programming by distilling its essential concept, the separation of a free random component and a deterministic part. This abstracts the core ideas beyond logic programming as such to encompass frameworks from probabilistic databases, probabilistic finite model theory and discrete lifted Bayesian networks. To demonstrate the usefulness of such a general approach, we completely characterise the projective families of distributions representable in the generalised distribution semantics and we demonstrate both that large classes of interesting projective families cannot be represented in a generalised distribution semantics and that already a very limited fragment of logic programming (acyclic determinate logic programs) in the deterministic part suffices to represent all those projective families that are representable in the generalised distribution semantics at all.

Semirings for probabilistic and neuro-symbolic logic programming

The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference and learning in probabilistic logic programs. While originally PLP focused on discrete probability, more recent approaches have incorporated continuous distributions as well as neural networks, effectively yielding neuro-symbolic methods. We provide an overview and synthesis of this domain, thereby contributing a unified algebraic perspective on the different flavors of PLP, showing that many if not most of the extensions of PLP can be cast within a common algebraic logic programming framework, in which facts are labeled with elements of a semiring and disjunction and conjunction are replaced by addition and multiplication. This does not only hold for the PLP variations itself but also for the underlying execution mechanism that is based on (algebraic) model counting. In order to showcase and explain this unified perspective, we focus on the ProbLog language and its extensions.

Modeling PU learning using probabilistic logic programming

Modeling PU learning using probabilistic logic programming

Scalable Neural-Probabilistic Answer Set Programming

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 programming to be carried out via the probability estimations of deep neural networks (DNNs). However, recent SOTA DPPL approaches allow only for limited conditional probabilistic queries and do not offer the power of true joint probability estimation. In our work, we propose an easy integration of tractable probabilistic inference within a DPPL. To this end, we introduce SLASH, a novel DPPL that consists of Neural-Probabilistic Predicates (NPPs) and a logic program, united via answer set programming (ASP). NPPs are a novel design principle allowing for combining all deep model types and combinations thereof to be represented as a single probabilistic predicate. In this context, we introduce a novel +/− notation for answering various types of probabilistic queries by adjusting the atom notations of a predicate. To scale well, we show how to prune the stochastically insignificant parts of the (ground) program, speeding up reasoning without sacrificing the predictive performance. We evaluate SLASH on various tasks, including the benchmark task of MNIST addition and Visual Question Answering (VQA).

Probabilistic robotic logic programming with hybrid Boolean and Bayesian inference

AbstractBayesian inference provides a probabilistic reasoning process for drawing conclusions based on imprecise and uncertain data that has been successful in many applications within robotics and information processing, but is most often considered in terms of data analysis rather than synthesis of behaviours. This paper presents the use of Bayesian inference as a means by which to perform Boolean operations in a logic programme while incorporating and propagating uncertainty information through logic operations by inference. Boolean logic operations are implemented in a Bayesian network of Bernoulli random variables with tensor-based discrete distributions to enable probabilistic hybrid logic programming of a robot. This enables Bayesian inference operations to coexist with Boolean logic in a unified system while retaining the ability to capture uncertainty by means of discrete probability distributions. Using a discrete Bayesian network with both Boolean and Bayesian elements, the proposed methodology is applied to navigate a mobile robot using hybrid Bayesian and Boolean operations to illustrate how this new approach improves robotic performance by inclusion of uncertainty without increasing the number of logic elements required. As any logical system could be programmed in this manner to integrate uncertainty into decision-making, this methodology can benefit a wide range of applications that use discrete or probabilistic logic.

Logic + probabilistic programming + causal laws.

Probabilistic planning attempts to incorporate stochastic models directly into the planning process, which is the problem of synthesizing a sequence of actions that achieves some objective for a putative agent. Probabilistic programming has rapidly emerged as a key paradigm to integrate probabilistic concepts with programming languages, which allows one to specify complex probabilistic models using programming primitives like recursion and loops. Probabilistic logic programming aims to further ease the specification of structured probability distributions using first-order logical artefacts. In this article, we briefly discuss the modelling of probabilistic planning through the lens of probabilistic (logic) programming. Although many flavours for such an integration are possible, we focus on two representative examples. The first is an extension to the popular probabilistic logic programming language PROBLOG, which permits the decoration of probabilities on Horn clauses-that is, prolog programs. The second is an extension to the popular agent programming language GOLOG, which permits the logical specification of dynamical systems via actions, effects and observations. The probabilistic extensions thereof emphasize different strengths of probabilistic programming that are particularly useful for non-trivial modelling issues raised in probabilistic planning. Among other things, one can instantiate planning problems with growing and shrinking state spaces, discrete and continuous probability distributions, and non-unique prior distributions in a first-order setting.

"Would life be more interesting if I were in AI?" Answering Counterfactuals based on Probabilistic Inductive Logic Programming

"Would life be more interesting if I were in AI?" Answering Counterfactuals based on Probabilistic Inductive Logic Programming

On the Independencies Hidden in the Structure of a Probabilistic Logic Program

On the Independencies Hidden in the Structure of a Probabilistic Logic Program

Bottom-Up Stratified Probabilistic Logic Programming with Fusemate

Bottom-Up Stratified Probabilistic Logic Programming with Fusemate

Toward Semantic Communication Protocols: A Probabilistic Logic Perspective

Classical medium access control (MAC) protocols are interpretable, yet their task-agnostic control signaling messages (CMs) are ill-suited for emerging mission-critical applications. By contrast, neural network (NN) based protocol models (NPMs) learn to generate task-specific CMs, but their rationale and impact lack interpretability. To fill this void, in this article we propose, for the first time, a semantic protocol model (SPM) constructed by transforming an NPM into an interpretable symbolic graph written in the probabilistic logic programming language (ProbLog). This transformation is viable by extracting and merging common CMs and their connections, while treating the NPM as a CM generator. By extensive simulations, we corroborate that the SPM tightly approximates its original NPM while occupying only 0.02% memory. By leveraging its interpretability and memory-efficiency, we demonstrate several SPM-enabled applications such as SPM reconfiguration for collision-avoidance, as well as comparing different SPMs via semantic entropy calculation and storing multiple SPMs to cope with non-stationary environments.

Automatic Differentiation in Prolog

AbstractAutomatic differentiation (AD) is a range of algorithms to compute the numeric value of a function’s (partial) derivative, where the function is typically given as a computer program or abstract syntax tree. AD has become immensely popular as part of many learning algorithms, notably for neural networks. This paper uses Prolog to systematically derive gradient-based forward- and reverse-mode AD variants from a simple executable specification: evaluation of the symbolic derivative. Along the way we demonstrate that several Prolog features (DCGs, co-routines) contribute to the succinct formulation of the algorithm. We also discuss two applications in probabilistic programming that are enabled by our Prolog algorithms. The first is parameter learning for the Sum-Product Loop Language and the second consists of both parameter learning and variational inference for probabilistic logic programming.

First-Order Context-Specific Likelihood Weighting in Hybrid Probabilistic Logic Programs

Statistical relational AI and probabilistic logic programming have so far mostly focused on discrete probabilistic models. The reasons for this is that one needs to provide constructs to succinctly model the independencies in such models, and also provide efficient inference.
 Three types of independencies are important to represent and exploit for scalable inference in hybrid models: conditional independencies elegantly modeled in Bayesian networks, context-specific independencies naturally represented by logical rules, and independencies amongst attributes of related objects in relational models succinctly expressed by combining rules.
 This paper introduces a hybrid probabilistic logic programming language, DC#, which integrates distributional clauses' syntax and semantics principles of Bayesian logic programs. It represents the three types of independencies qualitatively. More importantly, we also introduce the scalable inference algorithm FO-CS-LW for DC#. FO-CS-LW is a first-order extension of the context-specific likelihood weighting algorithm (CS-LW), a novel sampling method that exploits conditional independencies and context-specific independencies in ground models. The FO-CS-LW algorithm upgrades CS-LW with unification and combining rules to the first-order case.

The distribution semantics in probabilistic logic programming and probabilistic description logics: a survey

Representing uncertain information is crucial for modeling real world domains. This has been fully recognized both in the field of Logic Programming and of Description Logics (DLs), with the introduction of probabilistic logic languages and various probabilistic extensions of DLs respectively. Several works have considered the distribution semantics as the underlying semantics of Probabilistic Logic Programming (PLP) languages and probabilistic DLs (PDLs), and have then targeted the problem of reasoning and learning in them. This paper is a survey of inference, parameter and structure learning algorithms for PLP languages and PDLs based on the distribution semantics. A few of these algorithms are also available as web applications.

SmProbLog: Stable Model Semantics in ProbLog for Probabilistic Argumentation

AbstractArgumentation 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 modeling 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 PLP 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.

Meta-analysis of the functional neuroimaging literature with probabilistic logic programming

Inferring reliable brain-behavior associations requires synthesizing evidence from thousands of functional neuroimaging studies through meta-analysis. However, existing meta-analysis tools are limited to investigating simple neuroscience concepts and expressing a restricted range of questions. Here, we expand the scope of neuroimaging meta-analysis by designing NeuroLang: a domain-specific language to express and test hypotheses using probabilistic first-order logic programming. By leveraging formalisms found at the crossroads of artificial intelligence and knowledge representation, NeuroLang provides the expressivity to address a larger repertoire of hypotheses in a meta-analysis, while seamlessly modeling the uncertainty inherent to neuroimaging data. We demonstrate the language’s capabilities in conducting comprehensive neuroimaging meta-analysis through use-case examples that address questions of structure-function associations. Specifically, we infer the specific functional roles of three canonical brain networks, support the role of the visual word-form area in visuospatial attention, and investigate the heterogeneous organization of the frontoparietal control network.

Swift Markov Logic for Probabilistic Reasoning on Knowledge Graphs

AbstractWe provide a framework for probabilistic reasoning in Vadalog-based Knowledge Graphs (KGs), satisfying the requirements of ontological reasoning: full recursion, powerful existential quantification, expression of inductive definitions. Vadalog is a Knowledge Representation and Reasoning (KRR) language based on Warded Datalog+/–, a logical core language of existential rules, with a good balance between computational complexity and expressive power. Handling uncertainty is essential for reasoning with KGs. Yet Vadalog and Warded Datalog+/– are not covered by the existing probabilistic logic programming and statistical relational learning approaches for several reasons, including insufficient support for recursion with existential quantification and the impossibility to express inductive definitions. In this work, we introduce Soft Vadalog, a probabilistic extension to Vadalog, satisfying these desiderata. A Soft Vadalog program induces what we call a Probabilistic Knowledge Graph (PKG), which consists of a probability distribution on a network of chase instances, structures obtained by grounding the rules over a database using the chase procedure. We exploit PKGs for probabilistic marginal inference. We discuss the theory and present MCMC-chase, a Monte Carlo method to use Soft Vadalog in practice. We apply our framework to solve data management and industrial problems and experimentally evaluate it in the Vadalog system.

An Application of a Runtime Epistemic Probabilistic Event Calculus to Decision-making in e-Health Systems

AbstractWe present and discuss a runtime architecture that integrates sensorial data and classifiers with a logic-based decision-making system in the context of an e-Health system for the rehabilitation of children with neuromotor disorders. In this application, children perform a rehabilitation task in the form of games. The main aim of the system is to derive a set of parameters the child’s current level of cognitive and behavioral performance (e.g., engagement, attention, task accuracy) from the available sensors and classifiers (e.g., eye trackers, motion sensors, emotion recognition techniques) and take decisions accordingly. These decisions are typically aimed at improving the child’s performance by triggering appropriate re-engagement stimuli when their attention is low, by changing the game or making it more difficult when the child is losing interest in the task as it is too easy. Alongside state-of-the-art techniques for emotion recognition and head pose estimation, we use a runtime variant of a probabilistic and epistemic logic programming dialect of the Event Calculus, known as the Epistemic Probabilistic Event Calculus. In particular, the probabilistic component of this symbolic framework allows for a natural interface with the machine learning techniques. We overview the architecture and its components, and show some of its characteristics through a discussion of a running example and experiments.

Neural-Symbolic Ensemble Learning for early-stage prediction of critical state of Covid-19 patients

Recently, Artificial Intelligence (AI) and Machine Learning (ML) have been successfully applied to many domains of interest including medical diagnosis. Due to the availability of a large quantity of data, it is possible to build reliable AI systems that assist humans in making decisions. The recent Covid-19 pandemic quickly spread over the world causing serious health problems and severe economic and social damage. Computer scientists are actively working together with doctors on different ML models to diagnose Covid-19 patients using Computed Tomography (CT) scans and clinical data. In this work, we propose a neural-symbolic system that predicts if a Covid-19 patient arriving at the hospital will end in a critical condition. The proposed system relies on Deep 3D Convolutional Neural Networks (3D-CNNs) for analyzing lung CT scans of Covid-19 patients, Decision Trees (DTs) for predicting if a Covid-19 patient will eventually pass away by analyzing its clinical data, and a neural system that integrates the previous ones using Hierarchical Probabilistic Logic Programs (HPLPs). Predicting if a Covid-19 patient will end in a critical condition is useful for managing the limited number of intensive care at the hospital. Moreover, knowing early that a Covid-19 patient could end in serious conditions allows doctors to gain early knowledge on patients and provide special treatment to those predicted to finish in critical conditions. The proposed system, entitled Neural HPLP, obtains good performance in terms of area under the receiver operating characteristic and precision curves with values of about 0.96 for both metrics. Therefore, with Neural HPLP, it is possible not only to efficiently predict if Covid-19 patients will end in severe conditions but also possible to provide an explanation of the prediction. This makes Neural HPLP explainable, interpretable, and reliable.Graphical abstractRepresentation of Neural HPLP. From top to bottom, the two different types of data collected from the same patient and used in this project are represented. This data feeds the two different machine learning systems and the integration of the two systems using Hierarchical Probabilistic Logic Program.

Functional gradients in the human lateral prefrontal cortex revealed by a comprehensive coordinate-based meta-analysis.

The lateral prefrontal cortex (LPFC) of humans enables flexible goal-directed behavior. However, its functional organization remains actively debated after decades of research. Moreover, recent efforts aiming to map the LPFC through meta-analysis are limited, either in scope or in the inferred specificity of structure-function associations. These limitations are in part due to the limited expressiveness of commonly-used data analysis tools, which restricts the breadth and complexity of questions that can be expressed in a meta-analysis. Here, we adopt NeuroLang, a novel approach to more expressive meta-analysis based on probabilistic first-order logic programming, to infer the organizing principles of the LPFC from 14,371 neuroimaging studies. Our findings reveal a rostrocaudal and a dorsoventral gradient, respectively explaining the most and second most variance in meta-analytic connectivity across the LPFC. Moreover, we identify a unimodal-to-transmodal spectrum of coactivation patterns along with a concrete-to-abstract axis of structure-function associations extending from caudal to rostral regions of the LPFC. Finally, we infer inter-hemispheric asymmetries along the principal rostrocaudal gradient, identifying hemisphere-specific associations with topics of language, memory, response inhibition, and sensory processing. Overall, this study provides a comprehensive meta-analytic mapping of the LPFC, grounding future hypothesis generation on a quantitative overview of past findings.

Efficient Knowledge Compilation Beyond Weighted Model Counting

AbstractQuantitative extensions of logic programming often require the solution of so called second level inference tasks, that is, problems that involve a third operation, such as maximization or normalization, on top of addition and multiplication, and thus go beyond the well-known weighted or algebraic model counting setting of probabilistic logic programming under the distribution semantics. We introduce Second Level Algebraic Model Counting (2AMC) as a generic framework for these kinds of problems. As 2AMC is to (algebraic) model counting what forall-exists-SAT is to propositional satisfiability, it is notoriously hard to solve. First level techniques based on Knowledge Compilation (KC) have been adapted for specific 2AMC instances by imposing variable order constraints on the resulting circuit. However, those constraints can severely increase the circuit size and thus decrease the efficiency of such approaches. We show that we can exploit the logical structure of a 2AMC problem to omit parts of these constraints, thus limiting the negative effect. Furthermore, we introduce and implement a strategy to generate a sufficient set of constraints statically, with a priori guarantees for the performance of KC. Our empirical evaluation on several benchmarks and tasks confirms that our theoretical results can translate into more efficient solving in practice.