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Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…
A new approach to solving a class of rankconstrained semi-definite programming (SDP) problems, which appear in many signal processing applications such as transmit beamspace design in multiple-input multiple-output (MIMO) radar, downlink…
Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for its subprograms. This can be used to increase solving performance and prove program correctness. We generalize the conditions under…
Interpretability is a pressing issue for decision systems. Many post hoc methods have been proposed to explain the predictions of a single machine learning model. However, business processes and decision systems are rarely centered around a…
Answer Set Programming (ASP) is a well-established declarative paradigm. One of the successes of ASP is the availability of efficient systems. State-of-the-art systems are based on the ground+solve approach. In some applications this…
Large language models make remarkable progress in reasoning capabilities. Existing works focus mainly on deductive reasoning tasks (e.g., code and math), while another type of reasoning mode that better aligns with human learning, inductive…
This paper proposes the use of Constraint Logic Programming (CLP) to model SQL queries in a data-independent abstract layer by focusing on some semantic properties for signalling possible errors in such queries. First, we define a…
Among the hardest tasks for humans are those found in competitive programming where problems require sophisticated algorithmic thinking, puzzle solving, and the creation of effective code. As a domain to assess language models (LMs), it has…
For a large class of optimization problems, namely those that can be expressed as finite-valued constraint satisfaction problems (VCSPs), we establish a dichotomy on the number of levels of the Lasserre hierarchy of semi-definite programs…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
Data-driven algorithm selection is a powerful approach for choosing effective heuristics for computational problems. It operates by evaluating a set of candidate algorithms on a collection of representative training instances and selecting…
In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…
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…
In this paper, we propose an inexact multi-block ADMM-type first-order method for solving a class of high-dimensional convex composite conic optimization problems to moderate accuracy. The design of this method combines an inexact 2-block…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…
Strict linear feasibility or linear separation is usually tackled using efficient approximation/stochastic algorithms (that may even run in sub-linear times in expectation). However, today state of the art for solving…
LLMs face significant challenges in systematic generalization, particularly when dealing with reasoning tasks requiring compositional rules and handling out-of-distribution examples. To address these challenges, we introduce an in-context…
Despite recent advances in modern machine learning algorithms, the opaqueness of their underlying mechanisms continues to be an obstacle in adoption. To instill confidence and trust in artificial intelligence systems, Explainable Artificial…