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Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design, implementation and their use in…
We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations,…
Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…
Language serves as a vehicle for conveying thought, enabling communication among individuals. The ability to distinguish between diverse concepts, identify fairness and injustice, and comprehend a range of legal notions fundamentally relies…
Large Language Models (LLMs) have been shown to achieve breakthrough performance on complex logical reasoning tasks. Nevertheless, most existing research focuses on employing formal language to guide LLMs to derive reliable reasoning paths,…
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of…
We face the problems of correctness, optimality and precision for the static analysis of logic programs, using the theory of abstract interpretation. We propose a framework with a denotational, goal-dependent semantics equipped with two…
Large Language Model (LLM) based coding tools have been tremendously successful as software development assistants, yet they are often designed for general purpose programming tasks and perform poorly for more specialized domains such as…
Graphical models with High Order Potentials (HOPs) have received considerable interest in recent years. While there are a variety of approaches to inference in these models, nearly all of them amount to solving a linear program (LP)…
Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
Recent advancements in Large Language Models have sparked interest in their potential for robotic task planning. While these models demonstrate strong generative capabilities, their effectiveness in producing structured and executable plans…
Recent advancements in cognitive science and multi-round reasoning techniques for Large Language Models (LLMs) suggest that iterative thinking processes improve problem-solving performance in complex tasks. Inspired by this, approaches like…
The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well founded semantics corresponds to the…
Large language models (LLMs) have exhibited remarkable capabilities in learning from explanations in prompts, but there has been limited understanding of exactly how these explanations function or why they are effective. This work aims to…
Recently, language models (LMs), especially large language models (LLMs), have revolutionized the field of deep learning. Both encoder-decoder models and prompt-based techniques have shown immense potential for natural language processing…
Epistemic Logic Programs (ELPs), extend Answer Set Programming (ASP) with epistemic operators. The semantics of such programs is provided in terms of world views, which are sets of belief sets, i.e., syntactically, sets of sets of atoms.…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
In this paper we examine the limitations of Large Language Models (LLMs) for complex reasoning tasks. Although recent works have started to employ formal languages as an intermediate representation for reasoning tasks, they often face…
We present a logical framework to represent and reason about stochastic optimization problems based on probability answer set programming. This is established by allowing probability optimization aggregates, e.g., minimum and maximum in the…