Related papers: Five Basic Concepts of Axiomatic Rewriting Theory
We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
This text is reproduced with the kind permission of Fran\c{c}ois Ap\'ery. It was originally edited by Fran\c{c}ois Gu\'enard and Gilbert Leli\`evre for the book "Penser les math\'ematiques". It is the modified and abridged version of a text…
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…
The rational base number system, introduced by Akiyama, Frougny, and Sakarovitch in 2008, is a generalization of the classical integer base number system. Within this framework two interesting families of infinite words emerge, called…
Referring is one of the most basic and prevalent uses of language. How do speakers choose from the wealth of referring expressions at their disposal? Rational theories of language use have come under attack for decades for not being able to…
Text generation has become more accessible than ever, and the increasing interest in these systems, especially those using large language models, has spurred an increasing number of related publications. We provide a systematic literature…
We study the combination of the following already known ideas for showing confluence of unconditional or conditional term rewriting systems into practically more useful confluence criteria for conditional systems: Our syntactical separation…
We develop a new thermodynamic approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules called generating rules, a finite set of connected graphs P called energy patterns and an energy…
Lately there has been a lot of discussion about why deep learning algorithms perform better than we would theoretically suspect. To get insight into this question, it helps to improve our understanding of how learning works. We explore the…
Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…
Algorithmic information theory roots the concept of information in computation rather than probability. These lecture notes were constructed in conjunction with the graduate course I taught at Universit\`a della Svizzera italiana in the…
When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them,…
Rewriting systems on words are very useful in the study of monoids. In good cases, they give finite presentations of the monoids, allowing their manipulation by a computer. Even better, when the presentation is confluent and terminating,…
Generating an article automatically with computer program is a challenging task in artificial intelligence and natural language processing. In this paper, we target at essay generation, which takes as input a topic word in mind and…
This paper is about (first order) query rewritability in the context of theory-mediated query answering. The starting point of our journey is the FUS/FES conjecture, saying that if a theory is core-terminating (FES) and admits query…
Born from years of teaching undergraduate and graduate algebra courses at Chongqing University, this text is designed to introduce Galois theory while minimizing prerequisites. It seeks to reconnect the abstract machinery of modern algeba:…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
This short paper compiles the big ideas behind some philosophical views, definitions, and examples of causality. This collection spans the realms of the four commonly adopted approaches to causality: Humes regularity, counterfactual,…
Human experts write summaries using different techniques, including extracting a sentence from the document and rewriting it, or fusing various information from the document to abstract it. These techniques are flexible and thus difficult…