Large language models (LLMs) can already identify patterns and reason effectively, yet their variable accuracy hampers adoption in high-stakes decision-making applications. In this paper, we study this issue from a venture capital perspective by predicting idea-stage startup success based on founder traits. (i) To build a reliable prediction model, we introduce LLM-AR, a pipeline inspired by neural-symbolic systems that distils LLM-generated heuristics into probabilistic rules executed by the ProbLog automated-reasoning engine. (ii) An iterative policy-evolution loop incorporates association-rule mining to progressively refine the prediction rules. On unseen folds, LLM-AR achieves 59.5% precision and 8.7% recall, 5.9x the random baseline precision, while exposing every decision path for human inspection. The framework is interpretable and tunable via hyperparameters, showing promise to extend into other domains.

ProbLog is a popular probabilistic logic programming language/tool, widely used for applications requiring to deal with inherent uncertainties in structured domains. In this paper we study connections between ProbLog and a variant of another well-known formalism combining symbolic reasoning and reasoning under uncertainty, i.e. probabilistic argumentation. Specifically, we show that ProbLog is an instance of a form of Probabilistic Abstract Argumentation (PAA) that builds upon Assumption-Based Argumentation (ABA). The connections pave the way towards equipping ProbLog with alternative semantics, inherited from PAA/PABA, as well as obtaining novel argumentation semantics for PAA/PABA, leveraging on prior connections between ProbLog and argumentation. Further, the connections pave the way towards novel forms of argumentative explanations for ProbLog's outputs.

This paper introduces the Fusemate probabilistic logic programming system. Fusemate's inference engine comprises a grounding component and a variable elimination method for probabilistic inference. Fusemate differs from most other systems by grounding the program in a bottom-up way instead of the common top-down way. While bottom-up grounding is attractive for a number of reasons, e.g., for dynamically creating distributions of varying support sizes, it makes it harder to control the amount of ground clauses generated. We address this problem by interleaving grounding with a query-guided relevance test which prunes rules whose bodies are inconsistent with the query. We present our method in detail and demonstrate it with examples that involve "time", such as (hidden) Markov models. Our experiments demonstrate competitive or better performance compared to a state-of-the art probabilistic logic programming system, in particular for high branching problems.

Quantitative extensions of logic programming often require the solution of so called second level inference tasks, i.e., 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. Under consideration for acceptance in TPLP.

This paper presents a probabilistic extension of the well-known cellular automaton, Game of Life. In Game of Life, cells are placed in a grid and then watched as they evolve throughout subsequent generations, as dictated by the rules of the game. In our extension, called ProbLife, these rules now have probabilities associated with them. Instead of cells being either dead or alive, they are denoted by their chance to live. After presenting the rules of ProbLife and its underlying characteristics, we show a concrete implementation in ProbLog, a probabilistic logic programming system. We use this to generate different images, as a form of rule-based generative art.

We introduce SMProbLog, a generalization of the probabilistic logic programming language ProbLog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly sampled program, and these probabilities are mutually independent. The semantics of ProbLog is given by the success probability of a query, which corresponds to the probability that the query succeeds in a randomly sampled program. It is well-defined when each random sample uniquely determines the truth values of all logical atoms. Argumentation problems, however, represent an interesting practical application where this is not always the case. SMProbLog generalizes the semantics of ProbLog to the setting where multiple truth assignments are possible for a randomly sampled program, and implements the corresponding algorithms for both inference and learning tasks. We then show how this novel framework can be used to reason about probabilistic argumentation problems. Therefore, the key contribution of this paper are: a more general semantics for ProbLog programs, its implementation into a probabilistic programming framework for both inference and parameter learning, and a novel approach to probabilistic argumentation problems based on such framework.

We present Probabilistic Decision Model and Notation (pDMN), a probabilistic extension of Decision Model and Notation (DMN). DMN is a modeling notation for deterministic decision logic, which intends to be user-friendly and low in complexity. pDMN extends DMN with probabilistic reasoning, predicates, functions, quantification, and a new hit policy. At the same time, it aims to retain DMN's user-friendliness to allow its usage by domain experts without the help of IT staff. pDMN models can be unambiguously translated into ProbLog programs to answer user queries. ProbLog is a probabilistic extension of Prolog flexibly enough to model and reason over any pDMN model.

This paper argues the need for research to realize uncertainty-aware artificial intelligence and machine learning (AI\&ML) systems for decision support by describing a number of motivating scenarios. Furthermore, the paper defines uncertainty-awareness and lays out the challenges along with surveying some promising research directions. A theoretical demonstration illustrates how two emerging uncertainty-aware ML and AI technologies could be integrated and be of value for a route planning operation.

The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives in logic programming, which is now increasingly seen to provide a declarative background to complex machine learning applications. While many systems offer inference capabilities, the more significant challenge is that of learning meaningful and interpretable symbolic representations from data. In that regard, inductive logic programming and related techniques have paved much of the way for the last few decades. Unfortunately, a major limitation of this exciting landscape is that much of the work is limited to finite-domain discrete probability distributions. Recently, a handful of systems have been extended to represent and perform inference with continuous distributions. The problem, of course, is that classical solutions for inference are either restricted to well-known parametric families (e.g., Gaussians) or resort to sampling strategies that provide correct answers only in the limit. When it comes to learning, moreover, inducing representations remains entirely open, other than "data-fitting" solutions that force-fit points to aforementioned parametric families. In this paper, we take the first steps towards inducing probabilistic logic programs for continuous and mixed discrete-continuous data, without being pigeon-holed to a fixed set of distribution families. Our key insight is to leverage techniques from piecewise polynomial function approximation theory, yielding a principled way to learn and compositionally construct density functions. We test the framework and discuss the learned representations.

We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as resolving inconsistencies in answer set programs, ranking stable models, associating probability to stable models, and applying statistical inference to computing weighted stable models. We also present formal comparisons with related formalisms, such as answer set programs, Markov Logic, ProbLog, and P-log.