Nitesh Kumar

Nitesh Kumar

This thesis focuses on advancing probabilistic logic programming (PLP), which combines probability theory for uncertainty and logic programming for relations. The thesis aims to extend PLP to support both discrete and continuous random variables, which is necessary for applications with numeric data. The first contribution is the introduction of context-specific likelihood weighting (CS-LW), a new sampling algorithm that exploits context-specific independencies for computational gains. Next, a new hybrid PLP, DC#, is introduced, which integrates the syntax of Distributional Clauses with Bayesian logic programs and represents three types of independencies: i) conditional independencies (CIs) modeled in Bayesian networks; ii) context-specific independencies (CSIs) represented by logical rules, and iii) independencies amongst attributes of related objects in relational models expressed by combining rules. The scalable inference algorithm FO-CS-LW is introduced for DC#. Finally, the thesis addresses the lack of approaches for learning hybrid PLP from relational data with missing values and (probabilistic) background knowledge with the introduction of DiceML, which learns the structure and parameters of hybrid PLP and tackles the relational autocompletion problem. The conclusion discusses future directions and open challenges for hybrid PLP.

Nitesh Kumar, Usashi Chatterjee, Steven Schockaert

Conceptual spaces represent entities in terms of their primitive semantic features. Such representations are highly valuable but they are notoriously difficult to learn, especially when it comes to modelling perceptual and subjective features. Distilling conceptual spaces from Large Language Models (LLMs) has recently emerged as a promising strategy, but existing work has been limited to probing pre-trained LLMs using relatively simple zero-shot strategies. We focus in particular on the task of ranking entities according to a given conceptual space dimension. Unfortunately, we cannot directly fine-tune LLMs on this task, because ground truth rankings for conceptual space dimensions are rare. We therefore use more readily available features as training data and analyse whether the ranking capabilities of the resulting models transfer to perceptual and subjective features. We find that this is indeed the case, to some extent, but having at least some perceptual and subjective features in the training data seems essential for achieving the best results.

Nitesh Kumar, Usashi Chatterjee, Steven Schockaert

Conceptual spaces represent entities and concepts using cognitively meaningful dimensions, typically referring to perceptual features. Such representations are widely used in cognitive science and have the potential to serve as a cornerstone for explainable AI. Unfortunately, they have proven notoriously difficult to learn, although recent LLMs appear to capture the required perceptual features to a remarkable extent. Nonetheless, practical methods for extracting the corresponding conceptual spaces are currently still lacking. While various methods exist for extracting embeddings from LLMs, extracting conceptual spaces also requires us to encode the underlying features. In this paper, we propose a strategy in which features (e.g. sweetness) are encoded by embedding the description of a corresponding prototype (e.g. a very sweet food). To improve this strategy, we fine-tune the LLM to align the prototype embeddings with the corresponding conceptual space dimensions. Our empirical analysis finds this approach to be highly effective.

Nitesh Kumar, Ondrej Kuzelka, Luc De Raedt

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.

Pedro Zuidberg Dos Martires, Nitesh Kumar, Andreas Persson et al.

Robotic agents should be able to learn from sub-symbolic sensor data, and at the same time, be able to reason about objects and communicate with humans on a symbolic level. This raises the question of how to overcome the gap between symbolic and sub-symbolic artificial intelligence. We propose a semantic world modeling approach based on bottom-up object anchoring using an object-centered representation of the world. Perceptual anchoring processes continuous perceptual sensor data and maintains a correspondence to a symbolic representation. We extend the definitions of anchoring to handle multi-modal probability distributions and we couple the resulting symbol anchoring system to a probabilistic logic reasoner for performing inference. Furthermore, we use statistical relational learning to enable the anchoring framework to learn symbolic knowledge in the form of a set of probabilistic logic rules of the world from noisy and sub-symbolic sensor input. The resulting framework, which combines perceptual anchoring and statistical relational learning, is able to maintain a semantic world model of all the objects that have been perceived over time, while still exploiting the expressiveness of logical rules to reason about the state of objects which are not directly observed through sensory input data. To validate our approach we demonstrate, on the one hand, the ability of our system to perform probabilistic reasoning over multi-modal probability distributions, and on the other hand, the learning of probabilistic logical rules from anchored objects produced by perceptual observations. The learned logical rules are, subsequently, used to assess our proposed probabilistic anchoring procedure. We demonstrate our system in a setting involving object interactions where object occlusions arise and where probabilistic inference is needed to correctly anchor objects.