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We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…

History and Overview · Mathematics 2013-07-01 Felix Nagel

A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…

Probability · Mathematics 2025-01-29 Alexander Shmyrov , Vasily Shmyrov

ZFC has sentences that quantify over all sets or all ordinals, without restriction. Some have argued that sentences of this kind lack a determinate meaning. We propose a set theory called TOPS, using Natural Deduction, that avoids this…

Logic · Mathematics 2019-06-14 Paul Blain Levy

In this paper, I have proved that for a class of polynomial differential systems of degree n+1 ( where n is an arbitrary positive integer) the composition conjecture is true. I give the sufficient and necessary conditions for these…

Classical Analysis and ODEs · Mathematics 2019-05-01 Zhengxin Zhou

G{\"o}del's second incompleteness theorem forbids to prove, in a given theory U, the consistency of many theories-in particular, of the theory U itself-as well as it forbids to prove the normalization property for these theories, since this…

Logic in Computer Science · Computer Science 2023-11-01 Gilles Dowek , Alexandre Miquel

Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…

Artificial Intelligence · Computer Science 2007-05-23 Daniel Lehmann

Matrix models are a promising candidate for a nonperturbative formulation of the superstring theory. It is possible to study how the standard model and other phenomenological models appear from the matrix model, and estimate the probability…

High Energy Physics - Theory · Physics 2016-01-20 Hajime Aoki

The new ingredient of this paper is that we consider infinitely dimensional classes of functions and instead of the relative error setting, which was used in previous papers on norm discretization, we consider the absolute error setting. We…

Numerical Analysis · Mathematics 2018-12-20 Vladimir Temlyakov

Learning word embeddings using distributional information is a task that has been studied by many researchers, and a lot of studies are reported in the literature. On the contrary, less studies were done for the case of multiple languages.…

Computation and Language · Computer Science 2020-04-15 Marco Berlot , Evan Kaplan

This paper concerns how to generate and understand discourse anaphoric noun phrases. I present the results of an analysis of all discourse anaphoric noun phrases (N=1,233) in a corpus of ten narrative monologues, where the choice between a…

cmp-lg · Computer Science 2008-02-03 Rebecca J. Passonneau

It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…

Category Theory · Mathematics 2018-10-30 Giuliano Gadioli La Guardia , Pedro Jeferson Miranda

The topic of "negative end" of change is, contrary to the fields of innovation and emergence, largely under-researched. Yet, it has lately started to gain an increasing attention from language scholars worldwide. The main focus of this…

Computation and Language · Computer Science 2025-02-10 Karolina Rudnicka

We propose a model of the speech perception of individual words in the presence of mishearings. This phenomenological approach is based on concepts used in linguistics, and provides a formalism that is universal across languages. We put…

Computation and Language · Computer Science 2020-10-19 Anita Mehta , Jean-Marc Luck

This essay discusses the idea that a Theory of Everything would not be complete without a theory of consciousness as one of its parts, and the suggestion that new physics may be needed to describe consciousness. I argue that the motivations…

General Physics · Physics 2007-05-23 Joe Henson

These notes present some elements of causality theory. While they are not as complete as other treatments of the topic, there is some originality in that the whole approach is based on a definition of causal curves which allows to simplify…

General Relativity and Quantum Cosmology · Physics 2011-11-01 Piotr T. Chruściel

Cue phrases may be used in a discourse sense to explicitly signal discourse structure, but also in a sentential sense to convey semantic rather than structural information. This paper explores the use of machine learning for classifying cue…

cmp-lg · Computer Science 2008-02-03 Diane J. Litman

Although much has been said about parallelism in discourse, a formal, computational theory of parallelism structure is still outstanding. In this paper, we present a theory which given two parallel utterances predicts which are the parallel…

cmp-lg · Computer Science 2008-02-03 Claire Gardent , Michael Kohlhase

It has been shown that NLI models are usually biased with respect to the word-overlap between premise and hypothesis; they take this feature as a primary cue for predicting the entailment label. In this paper, we focus on an overlooked…

Computation and Language · Computer Science 2022-11-09 Sara Rajaee , Yadollah Yaghoobzadeh , Mohammad Taher Pilehvar

The compositionality of meaning extends beyond the single sentence. Just as words combine to form the meaning of sentences, so do sentences combine to form the meaning of paragraphs, dialogues and general discourse. We introduce both a…

Computation and Language · Computer Science 2013-06-18 Nal Kalchbrenner , Phil Blunsom

It is claimed that a variety of facts concerning ellipsis, event reference, and interclausal coherence can be explained by two features of the linguistic form in question: (1) whether the form leaves behind an empty constituent in the…

cmp-lg · Computer Science 2008-02-03 Andrew Kehler
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