Related papers: What do ultraproducts remember about the original …

We explore the features of a user interface where formal proofs can be built through gestural actions. In particular, we show how proof construction steps can be associated to drag-and-drop actions. We argue that this can provide quick and…

We present some new methods for logical deduction, based on ideas from ground theory. Roughly speaking, in our calculi a typical deduction will proceed as follows: we first analyse the premiss down to its ultimate grounds; then we discard…

Reactive synthesis transforms a specification of a reactive system, given in a temporal logic, into an implementation. The main advantage of synthesis is that it is automatic. The main disadvantage is that the implementation is usually very…

Syntax is a latent hierarchical structure which underpins the robust and compositional nature of human language. In this work, we explore the hypothesis that syntactic dependencies can be represented in language model attention…

Subtraction is a powerful technique for creating new bijections from old. Let's reinvent it! While we're at it, let's reinvent division as well.

Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete…

We propose a constructive interpretation of truth which resolves the standard semantic paradoxes.

This is a review article on the development of the probe and enclosure methods from past to present, focused on their central ideas together with various applications.

This collection of sums and integrals has been harvested from the mathematical and physical literature in unstructured ways. Its main use is backtracking the original sources whenever an integral of the reader's application resembles one of…

Present language understanding methods have demonstrated extraordinary ability of recognizing patterns in texts via machine learning. However, existing methods indiscriminately use the recognized patterns in the testing phase that is…

The use of nonstandard methods to characterize properties of weak, strong and mixed extensions of congruences to ultrafilters has been the main topic of several recent papers. We show that similar methods can be used to characterize the…

We use nonstandard methods, based on iterated hyperextensions, to develop applications to Ramsey theory of the theory of monads of ultrafilters. This is performed by studying in detail arbitrary tensor products of ultrafilters, as well as…

Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…

We introduce a novel data generation method for contradiction detection, which leverages the generative power of large language models as well as linguistic rules. Our vision is to provide a condensed corpus of prototypical contradictions,…

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 approach concludes finally the problem of the…

Human speakers have an extensive toolkit of ways to express themselves. In this paper, we engage with an idea largely absent from discussions of meaning in natural language understanding--namely, that the way something is expressed reflects…

In the wake of responsible AI, interpretability methods, which attempt to provide an explanation for the predictions of neural models have seen rapid progress. In this work, we are concerned with explanations that are applicable to natural…

We aim to provide an explanation for how the human brain might connect words for sentence formation. A novel approach to modeling syntactic representation is introduced, potentially showing the existence of universal syntactic structures…

The generating series of a number of different objects studied in arithmetic statistics can be built out of Euler products. Euler products often have very nice analytic properties, and by constructing a meromorphic continuation one can use…

This tutorial provides a comprehensive and in-depth view of the research on procedures, primarily in Natural Language Processing. A procedure is a sequence of steps intended to achieve some goal. Understanding procedures in natural language…