Related papers: Formal Ways for Measuring Relations between Concep…
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.
Concept-based explanations work by mapping complex model computations to human-understandable concepts. Evaluating such explanations is very difficult, as it includes not only the quality of the induced space of possible concepts but also…
We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of…
This paper attempts to synthesize various conceptualizations of the term "context" as found in computing literature. Ten conceptual dimensions of context thus emerge -- location; user, task, and system characteristics; physical, social,…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
Cognitive Dimensions is a framework for analyzing human-computer interaction. It is used for meta-analysis, that is, for talking about characteristics of systems without getting bogged down in details of a particular implementation. In this…
We propose a series of methods to represent the evolution of a field of science at different levels: namely micro, meso and macro levels. We use a previously introduced asymmetric measure of paradigmatic proximity between terms that enables…
This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…
In order to interact with objects in our environment, humans rely on an understanding of the actions that can be performed on them, as well as their properties. When considering concrete motor actions, this knowledge has been called the…
This paper aims to show that a simple framework, utilizing basic formalisms from set theory and category theory, can clarify and inform our theories of the relation between mind and matter.
This paper introduces the concept of spatial conceptual modeling, which allows anchoring mental world knowledge in the physical world using augmented reality technologies. For a first formal characterization, we describe a mapping from the…
With the expansion of scientific research, the number of scientific research is increasing. A new urgent problem is raised that how to keep these researches in a proper way. Therefore, knowledge mapping methods come into being, providing a…
Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions.…
Humans are able to conceive physical reality by jointly learning different facets thereof. To every pair of notions related to a perceived reality may correspond a mutual relation, which is a notion on its own, but one-level higher. Thus,…
Representing the semantics of linguistic items in a machine-interpretable form has been a major goal of Natural Language Processing since its earliest days. Among the range of different linguistic items, words have attracted the most…
Meaning can be generated when information is related at a systemic level. Such a system can be an observer, but also a discourse, for example, operationalized as a set of documents. The measurement of semantics as similarity in patterns…
Formal Concept Analysis (FCA) begins from a context, given as a binary relation between some objects and some attributes, and derives a lattice of concepts, where each concept is given as a set of objects and a set of attributes, such that…
This paper defines a new pseudometric for binary relations between finite sets that measures consensus among subsets. The main results are (1) a concise restatement of this pseudometric with an intuitively appealing interpretation via a…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…