Related papers: Numbers Extensions
This article explores the model-dependent nature of set cardinality, emphasizing that cardinality is not absolute but varies across different axiomatic frameworks. Although Cantor's diagonal argument shows the real numbers are…
We show that the affirmation $P\subseteq NP$ (in computer science) erroneously and we prove the justice of the hypotesis J.Edmonds's $P\neq NP$. We show further that all the $NP$-complete problems is not polynomial and we give the…
Knowledge is only good if it is sound, consistent and complete. The same holds true for conceptual knowledge, which holds knowledge about concepts and its association. Conceptual knowledge no matter what format they are represented in, must…
Probing and enhancing large language models' reasoning capacity remains a crucial open question. Here we re-purpose the reverse dictionary task as a case study to probe LLMs' capacity for conceptual inference. We use in-context learning to…
We study the connection between kappa calculus and probabilistic reasoning in diagnosis applications. Specifically, we abstract a probabilistic belief network for diagnosing faults into a kappa network and compare the ordering of faults…
Concepts play a pivotal role in various human cognitive functions, including learning, reasoning and communication. However, there is very little work on endowing machines with the ability to form and reason with concepts. In particular,…
Can language models (LM) ground question-answering (QA) tasks in the knowledge base via inherent relational reasoning ability? While previous models that use only LMs have seen some success on many QA tasks, more recent methods include…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
There is a strong consensus that combining the versatility of machine learning with the assurances given by formal verification is highly desirable. It is much less clear what verified machine learning should mean exactly. We consider this…
In this thesis we shall present two logical systems, MP and MP, for the purpose of reasoning about knowledge and effort. These logical systems will be interpreted in a spatial context and therefore, the abstract concepts of knowledge and…
Knowledge is fundamental to the overall capabilities of Large Language Models (LLMs). The knowledge paradigm of a model, which dictates how it encodes and utilizes knowledge, significantly affects its performance. Despite the continuous…
The reliability of large language models (LLMs) is greatly compromised by their tendency to hallucinate, underscoring the need for precise identification of knowledge gaps within LLMs. Various methods for probing such gaps exist, ranging…
Commonsense datasets have been well developed in Natural Language Processing, mainly through crowdsource human annotation. However, there are debates on the genuineness of commonsense reasoning benchmarks. In specific, a significant portion…
The study of machine learning-based logical query answering enables reasoning with large-scale and incomplete knowledge graphs. This paper advances this area of research by addressing the uncertainty inherent in knowledge. While the…
This article critically reappraises arguments in support of Cantor's theory of transfinite numbers. The following results are reported: i) Cantor's proofs of nondenumerability are refuted by analyzing the logical inconsistencies in…
Given a strong limit cardinal $\lambda$ of countable cofinality, we show that if every $\lambda$-coanalytic subset of the generalised Cantor space ${}^{\lambda}2$ has the $\lambda$-$\mathsf{PSP}$, then there is an inner model with…
Language has been a dynamic system and word meanings always have been changed over times. Every time a novel concept or sense is introduced, we need to assign it a word to express it. Also, some changes have happened because the result of a…
Closed-source frontier labs do not disclose parameter counts, and the standard alternative -- inference economics -- carries $2\times$+ uncertainty from hardware, batching, and serving-stack assumptions external to the model. We exploit a…
Probabilistic Logic Programming (PLP) under the Distribution Semantics is a leading approach to practical reasoning under uncertainty. An advantage of the Distribution Semantics is its suitability for implementation as a Prolog or Python…
We show that the problem of deciding whether the vertex set of a graph can be covered with at most two bicliques is in NP$\cap$coNP. We thus almost determine the computational complexity of a problem whose status has remained open for quite…