Related papers: What do ultraproducts remember about the original …
We study tensor categories that interpolate the representation categories of finite classical groups. There are (at least) two ways to approach these categories: via ultraproducts and via oligomorphic groups. Both have strengths and…
We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and…
Ultrafinitism postulates that we can only compute on relatively short objects, and numbers beyond certain value are not available. This approach would also forbid many forms of infinitary reasoning and allow to remove certain paradoxes…
Learning from nature has been a quest of humanity for millennia. While this has taken the form of humans assessing natural designs such as bones, butterfly wings, or spider webs, we can now achieve generating designs using advanced…
Understanding and creating mathematics using natural mathematical language - the mixture of symbolic and natural language used by humans - is a challenging and important problem for driving progress in machine learning. As a step in this…
We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we study a notion of "signature" for specifying syntactic constructions. In the spirit of Initial…
Modern deep neural networks achieve impressive performance in engineering applications that require extensive linguistic skills, such as machine translation. This success has sparked interest in probing whether these models are inducing…
The author describes a conceptual study towards mapping grounded natural language discourse representation structures to instances of controlled language statements. This can be achieved via a pipeline of preexisting state of the art…
We show that numerous distinctive concepts of constructive mathematics arise automatically from an "antithesis" translation of affine logic into intuitionistic logic via a Chu/Dialectica construction. This includes apartness relations,…
A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This result generalises the ones given up to date.
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
Natural language definitions possess a recursive, self-explanatory semantic structure that can support representation learning methods able to preserve explicit conceptual relations and constraints in the latent space. This paper presents a…
We have recently begun a project to develop a more effective and efficient way to marshal inferences from background knowledge to facilitate deep natural language understanding. The meaning of a word is taken to be the entities,…
Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…
A collection of 50 open problems around the structure theory of ultraproducts of II$_1$ factors is presented, along with some annotations and references.
Large language models can perform various reasoning tasks by using chain-of-thought prompting, which guides them to find answers through step-by-step demonstrations. However, the quality of the prompts depends on the demonstrations given to…
Recently, Neural Networks have been proven extremely effective in many natural language processing tasks such as sentiment analysis, question answering, or machine translation. Aiming to exploit such advantages in the Ontology Learning…
Question Generation (QG) is fundamentally a simple syntactic transformation; however, many aspects of semantics influence what questions are good to form. We implement this observation by developing SynQG, a set of transparent syntactic…
Recent work has demonstrated that neural language models encode syntactic structures in their internal representations, yet the derivations by which these structures are constructed across layers remain poorly understood. In this paper, we…
When people interpret text, they rely on inferences that go beyond the observed language itself. Inspired by this observation, we introduce a method for the analysis of text that takes implicitly communicated content explicitly into…