Related papers: Numbers Extensions
In problem solving, understanding the problem that one seeks to solve is an essential initial step. In this paper, we propose computational methods for facilitating problem understanding through the task of recognizing the unknown in…
Solving classification with graph methods has gained huge popularity in recent years. This is due to the fact that the data can be intuitively modeled with graphs to utilize high level features to aid in solving the classification problem.…
To provide an explanation of the evolution of scientific knowledge, I start from the assumption that knowledge is based on concepts, and propose that each concept about reality is affected by vagueness. This entails a paradox, which I term…
This extended abstract presents a logic, called Lp, that is capable of representing and reasoning with a wide variety of both qualitative and quantitative statistical information. The advantage of this logical formalism is that it offers a…
Machine Learning has been a big success story during the AI resurgence. One particular stand out success relates to unsupervised learning from a massive amount of data, albeit much of it relates to one modality/type of data at a time. In…
Two different approaches to dealing with probabilistic knowledge are examined -models and inductive inference. Examples of the first are: influence diagrams [1], Bayesian networks [2], log-linear models [3, 4]. Examples of the second are:…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial…
Two major areas of interest in the era of Large Language Models regard questions of what do LLMs know, and if and how they may be able to reason (or rather, approximately reason). Since to date these lines of work progressed largely in…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
In this paper, we delve into the study of epistemic logics, interpreted through similarity models based on weighted graphs. We explore eight languages that extend the traditional epistemic language by incorporating modalities of common,…
We investigate an extension of ZFC set theory (in an extended language) that stipulates the existence of a proper class of indiscernibles over the universe. One of the main results of the paper shows that the purely set-theoretical…
In a game of incomplete information, an infinite state space can create problems. When the space is uncountably large, the strategy spaces of the players may be unwieldly, resulting in a lack of measurable equilibria. When the knowledge of…
Our goal is to study the pseudo-intersection and tower numbers on uncountable regular cardinals, whether these two cardinal characteristics are necessarily equal, and related problems on the existence of gaps. First, we prove that either…
We consider the problem where a set of individuals has to classify $m$ objects into $p$ categories by aggregating the individual classifications, and no category can be left empty. An aggregator satisfies \emph{Expertise} if individuals are…
In this article, I focus on the resiliency of the P=?NP problem. The main point to deal with is the change of the underlying logic from first to second-order logic. In this manner, after developing the initial steps of this change, I can…
We revisit the challenging problem of resolving prepositional-phrase (PP) attachment ambiguity. To date, proposed solutions are either rule-based, where explicit grammar rules direct how to resolve ambiguities; or statistical, where the…
As the quantity of human knowledge increasing rapidly, it is harder and harder to evaluate a knowledge worker's knowledge quantitatively. There are lots of demands for evaluating a knowledge worker's knowledge. For example, accurately…