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Test-time scaling has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs) by allocating additional computational resources during inference. However, this paradigm is inherently…

The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often,…

Standard answer set programming (ASP) targets at solving search problems from the first level of the polynomial time hierarchy (PH). Tackling search problems beyond NP using ASP is less straightforward. The class of disjunctive logic…

Disentangling the encodings of neural models is a fundamental aspect for improving interpretability, semantic control and downstream task performance in Natural Language Processing. Currently, most disentanglement methods are unsupervised…

Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…

A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques. Alternatively, the non-binary problem can be translated into an equivalent binary one. In this case, it is generally…

To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…

Providing explanations for the outputs of artificial neural networks (ANNs) is crucial in many contexts, such as critical systems, data protection laws and handling adversarial examples. Logic-based methods can offer explanations with…

We define an isomorphism between the group of points of a conic and the set of integers modulo a prime equipped with a non-standard product. This product can be efficiently evaluated through the use of R\'edei rational functions. We then…

While large language models (LLMs) have shown strong performance in math and logic reasoning, their ability to handle combinatorial optimization (CO) -- searching high-dimensional solution spaces under hard constraints -- remains…

Code search is vital in the maintenance and extension of software systems. Past works have used separate language models for the natural language and programming language artifacts on models with multiple encoders and different loss…

Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…

Large Language Models (LLMs) have revolutionized natural language processing by understanding and generating human-like text. However, the increasing demand for more sophisticated LLMs presents significant computational challenges due to…

Encoding and decoding models are widely used in systems, cognitive, and computational neuroscience to make sense of brain-activity data. However, the interpretation of their results requires care. Decoding models can help reveal whether…

Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…

We apply the sample average approximation (SAA) method to risk-neutral optimization problems governed by nonlinear partial differential equations (PDEs) with random inputs. We analyze the consistency of the SAA optimal values and SAA…

Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…

Chain-of-thought (CoT) reasoning not only enhances large language model performance but also provides critical insights into decision-making processes, marking it as a useful tool for monitoring model intent and planning. However, recent…

Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly…

Neural program embedding can be helpful in analyzing large software, a task that is challenging for traditional logic-based program analyses due to their limited scalability. A key focus of recent machine-learning advances in this area is…