Related papers: A Tribute to Alain Colmerauer
A programming tactic involving polyhedra is reported that has been widely applied in the polyhedral analysis of (constraint) logic programs. The method enables the computations of convex hulls that are required for polyhedral analysis to be…
The logics of knowledge are modal logics that have been shown to be effective in representing and reasoning about knowledge in multi-agent domains. Relatively few computational frameworks for dealing with computation of models and useful…
The goal of mechanistic interpretability is discovering simpler, low-rank algorithms implemented by models. While we can compress activations into features, compressing nonlinear feature-maps -- like MLP layers -- is an open problem. In…
The aim of this paper is to honor Ivo G. Rosenberg by describing some of his most influential results and their impact in logic, discrete mathematics, algebra, and computer science.
There is an increasing number of algorithmic computations in theoretical physics. These, while conceptually simple, can nevertheless be time-consuming and contain subtleties that should not be overlooked. Given the recent improvement of…
This paper, which is dedicated to Alan Turing on the 50th anniversary of his death, gives an overview and discusses the philosophical implications of incompleteness, uncomputability and randomness.
Recent advances in AI, machine learning, and NLP have led to the development of a new generation of Large Language Models (LLMs) that are trained on massive amounts of data and often have trillions of parameters. Commercial applications…
Common criticisms of state-of-the-art machine learning include poor generalisation, a lack of interpretability, and a need for large amounts of training data. We survey recent work in inductive logic programming (ILP), a form of machine…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
We give an overview of several of the mathematical works of Gilles Lachaud and provide a historical context. This is interspersed with some personal anecdotes highlighting many facets of his personality.
This article surveys recent advances in applying algebraic techniques to constraint satisfaction problems.
The purpose of this paper is to present a fresh idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form "$P$ transforms into $Q$ as…
An outline of J\"org Eschmeier's main mathematical contributions is organized both on a historical perspective, as well as on a few distinct topics. The reader can grasp from our essay the dynamics of spectral theory of commutative tuples…
Constraint logic grammars provide a powerful formalism for expressing complex logical descriptions of natural language phenomena in exact terms. Describing some of these phenomena may, however, require some form of graded distinctions which…
The paper discusses what is needed to address the limitations of current LLM-centered AI systems. The paper argues that incorporating insights from human cognition and psychology, as embodied by a computational cognitive architecture, can…
Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…
Inductive logic programming (ILP) has been a deeply influential paradigm in AI, enjoying decades of research on its theory and implementations. As a natural descendent of the fields of logic programming and machine learning, it admits the…
We study a class of countably-infinite-dimensional linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined spaces of measures. The optimal value, optimal points, and minimal points of these CILPs can be…
Similarity-based Logic Programming (briefly, SLP ) has been proposed to enhance the LP paradigm with a kind of approximate reasoning which supports flexible information retrieval applications. This approach uses a fuzzy similarity relation…
Linear programming is now included in algorithm undergraduate and postgraduate courses for computer science majors. We give a self-contained treatment of an interior-point method which is particularly tailored to the typical mathematical…