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Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…

To comprehensively evaluate the mathematical reasoning capabilities of Large Language Models (LLMs), researchers have introduced abundant mathematical reasoning datasets. However, most existing datasets primarily focus on linear reasoning,…

Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic…

Our study demonstrates the effective use of Large Language Models (LLMs) for automating the classification of complex datasets. We specifically target proposals of Decentralized Autonomous Organizations (DAOs), as the clas-sification of…

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…

Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…

Logistic regression is one of the most popular methods in binary classification, wherein estimation of model parameters is carried out by solving the maximum likelihood (ML) optimization problem, and the ML estimator is defined to be the…

Statistical relational models provide compact encodings of probabilistic dependencies in relational domains, but result in highly intractable graphical models. The goal of lifted inference is to carry out probabilistic inference without…

We present CLP(BN), a novel approach that aims at expressing Bayesian networks through the constraint logic programming framework. Arguably, an important limitation of traditional Bayesian networks is that they are propositional, and thus…

Automating the translation of natural language to first-order logic (FOL) is crucial for knowledge representation and formal methods, yet remains challenging. We present a systematic evaluation of fine-tuned LLMs for this task, comparing…

We introduce DeepPSL a variant of probabilistic soft logic (PSL) to produce an end-to-end trainable system that integrates reasoning and perception. PSL represents first-order logic in terms of a convex graphical model -- hinge-loss Markov…

Bayesian networks are a canonical formalism for representing probabilistic dependencies, yet their integration within logic programming frameworks remains a nontrivial challenge, mainly due to the complex structure of these networks. In…

Motivated by the need for rigorous and scalable evaluation of large language models, we study contextual preference inference for pairwise comparison functionals of context-dependent preference score functions across domains. Focusing on…

Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…

In probabilistic reasoning, the traditionally discrete domain has been elevated to the hybrid domain encompassing additionally continuous random variables. Inference in the hybrid domain, however, usually necessitates to condone trade-offs…

In this paper, we propose a new Soft Confidence-Weighted (SCW) online learning scheme, which enables the conventional confidence-weighted learning method to handle non-separable cases. Unlike the previous confidence-weighted learning…

Large language models (LLMs) are known for their exceptional performance across a range of natural language processing tasks, but their deployment comes at a high computational and financial cost. On the other hand, smaller language models…

Reconciling the tension between inductive learning and deductive reasoning in first-order relational domains is a longstanding challenge in AI. We study the problem of answering queries in a first-order relational probabilistic logic…

Large Language Models (LLMs) have rapidly transformed the landscape of artificial intelligence, enabling natural language interfaces and dynamic orchestration of software components. However, their reliance on probabilistic inference limits…

Effectful programs interact in ways that go beyond simple input-output, making compositional reasoning challenging. Existing work has shown that when such programs are ``separate'', i.e., when programs do not interfere with each other, it…