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We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…

Abstract argumentation framework (\AFname) is a unifying framework able to encompass a variety of nonmonotonic reasoning approaches, logic programming and computational argumentation. Yet, efficient approaches for most of the decision and…

In recent years, large language models (LLMs) have made significant advancements in developing human-like and engaging dialogue systems. However, in tasks such as consensus-building and persuasion, LLMs often struggle to resolve conflicts…

Natural language explanations play a fundamental role in Natural Language Inference (NLI) by revealing how premises logically entail hypotheses. Recent work has shown that the interaction of large language models (LLMs) with theorem provers…

Large language models (LLMs) are increasingly explored for their reasoning capabilities, yet their ability to perform structured, constraint-based optimization from natural language remains insufficiently understood. This study evaluates…

We present a probabilistic logic programming framework to reinforcement learning, by integrating reinforce-ment learning, in POMDP environments, with normal hybrid probabilistic logic programs with probabilistic answer set seman-tics, that…

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…

Automated Theorem Proving (ATP) deals with the development of computer programs being able to show that some conjectures (queries) are a logical consequence of a set of axioms (facts and rules). There exists several successful ATPs where…

Large Language Models (LLMs) were shown to struggle with long-term planning, which may be caused by the limited way in which they explore the space of possible solutions. We propose an architecture where a Reinforcement Learning (RL) Agent…

Recent advances in large language models (LLMs) have enabled multi-agent reasoning systems capable of collaborative decision-making. However, in financial analysis, most frameworks remain narrowly focused on either isolated single-agent…

Answer Set Programming (ASP) is a logic programming paradigm featuring a purely declarative language with comparatively high modeling capabilities. Indeed, ASP can model problems in NP in a compact and elegant way. However, modeling…

Designing effective data manipulation methods is a long standing problem in data lakes. Traditional methods, which rely on rules or machine learning models, require extensive human efforts on training data collection and tuning models.…

This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to…

Epistemic logic programs (ELPs) are a popular generalization of standard Answer Set Programming (ASP) providing means for reasoning over answer sets within the language. This richer formalism comes at the price of higher computational…

This work presents an analytical framework for the design and analysis of LLM-based algorithms, i.e., algorithms that contain one or multiple calls of large language models (LLMs) as sub-routines and critically rely on the capabilities of…

Large Language Models (LLMs) still struggle with complex logical reasoning. While previous works achieve remarkable improvements, their performance is highly dependent on the correctness of translating natural language (NL) problems into a…

Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…

Algorithmic solutions have significant potential to improve decision-making across various domains, from healthcare to e-commerce. However, the widespread adoption of these solutions is hindered by a critical challenge: the lack of…

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…

With the development of artificial intelligence (AI), large language models (LLM) are widely used in many fields. However, the reasoning ability of LLM is still very limited when it comes to mathematical reasoning. Mathematics plays an…