Related papers: IST is more than an algorithm to prove ZFC theorem…
This thesis argues that the currently widely used Natural Language Processing algorithms possibly have various limitations related to the properties of the texts they handle and produce. With the wide adoption of these tools in rapid…
Can a machine understand the meanings of natural language? Recent developments in the generative large language models (LLMs) of artificial intelligence have led to the belief that traditional philosophical assumptions about machine…
A folk theorem says higher order arithmetic has the proof theoretic strength of set theory with limited power set. This paper makes the theorem precise in terms of several axiom system based on ZF.
Information field theory (IFT) is the application of probabilistic reasoning to fields. Physical fields are mathematical functions over continuous spaces that exhibit certain properties of regularity, such as limited variance and finite…
A rather easy yet rigorous proof of a version of G\"odel's first incompleteness theorem is presented. The version is "each recursively enumerable theory of natural numbers with 0, 1, +, *, =, logical and, logical not, and the universal…
Sentence embedding methods offer a powerful approach for working with short textual constructs or sequences of words. By representing sentences as dense numerical vectors, many natural language processing (NLP) applications have improved…
Sentence Simplification aims to rephrase complex sentences into simpler sentences while retaining original meaning. Large Language models (LLMs) have demonstrated the ability to perform a variety of natural language processing tasks.…
We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by…
In real world everything is an object which represents particular classes. Every object can be fully described by its attributes. Any real world dataset contains large number of attributes and objects. Classifiers give poor performance when…
For the sake of reliability, the kernels of Interactive Theorem Provers (ITPs) are generally kept relatively small. On top of the kernel, additional symbols and inference rules are defined. This paper presents an analysis of how kernel…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
Transformer-based models are nowadays state-of-the-art in ad-hoc Information Retrieval, but their behavior is far from being understood. Recent work has claimed that BERT does not satisfy the classical IR axioms. However, we propose to…
Natural Language Processing has moved rather quickly from modelling specific tasks to taking more general pre-trained models and fine-tuning them for specific tasks, to a point where we now have what appear to be inherently generalist…
Recently many efforts have been devoted to interpreting the black-box NMT models, but little progress has been made on metrics to evaluate explanation methods. Word Alignment Error Rate can be used as such a metric that matches human…
The purpose of this article is to give a presentation of the method of forcing aimed at someone with a minimal knowledge of set theory and logic. The emphasis will be on how the method can be used to prove theorems in ZFC.
Modern statistical machine translation (SMT) systems usually use a linear combination of features to model the quality of each translation hypothesis. The linear combination assumes that all the features are in a linear relationship and…
The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…
Stop words, which are considered non-predictive, are often eliminated in natural language processing tasks. However, the definition of uninformative vocabulary is vague, so most algorithms use general knowledge-based stop lists to remove…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…
We analyze inexact fixed point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed point…