On Concept Algebra

2009 ◽  
pp. 3055-3075
Author(s):  
Yingxu Wang
Keyword(s):  
System Modeling ◽  
Formal Theory ◽  
Mathematical Structure ◽  
Abstract Concept ◽  
Abstract Concepts ◽  
Formal Knowledge ◽  
Adaptive Capability ◽  
Algebraic Operations ◽  
Complex Knowledge ◽  
Object Attribute

Concepts are the most fundamental unit of cognition that carries certain meanings in expression, thinking, reasoning, and system modeling. In denotational mathematics, a concept is formally modeled as an abstract and dynamic mathematical structure that encapsulates attributes, objects, and relations. The most important property of an abstract concept is its adaptive capability to autonomously interrelate itself to other concepts. This article presents a formal theory for abstract concepts and knowledge manipulation known as “concept algebra.” The mathematical models of concepts and knowledge are developed based on the object-attribute-relation (OAR) theory. The formal methodology for manipulating knowledge as a concept network is described. Case studies demonstrate that concept algebra provides a generic and formal knowledge manipulation means, which is capable to deal with complex knowledge and software structures as well as their algebraic operations.

On Concept Algebra

2011 ◽  
pp. 126-148
Author(s):  
Yingxu Wang
Keyword(s):  
System Modeling ◽  
Formal Theory ◽  
Mathematical Structure ◽  
Abstract Concept ◽  
Abstract Concepts ◽  
Formal Knowledge ◽  
Adaptive Capability ◽  
Algebraic Operations ◽  
Complex Knowledge ◽  
Object Attribute

Concepts are the most fundamental unit of cognition that carries certain meanings in expression, thinking, reasoning, and system modeling. In denotational mathematics, a concept is formally modeled as an abstract and dynamic mathematical structure that encapsulates attributes, objects, and relations. The most important property of an abstract concept is its adaptive capability to autonomously interrelate itself to other concepts. This article presents a formal theory for abstract concepts and knowledge manipulation known as “concept algebra.” The mathematical models of concepts and knowledge are developed based on the object-attribute-relation (OAR) theory. The formal methodology for manipulating knowledge as a concept network is described. Case studies demonstrate that concept algebra provides a generic and formal knowledge manipulation means, which is capable to deal with complex knowledge and software structures as well as their algebraic operations.

ON CONCEPT ALGEBRA FOR COMPUTING WITH WORDS (CWW)

2010 ◽  
Vol 04 (03) ◽  
pp. 331-356 ◽  
Author(s):  
YINGXU WANG
Keyword(s):  
Computing Methodology ◽  
System Modeling ◽  
Formal Theory ◽  
Mathematical Structure ◽  
Computing With Words ◽  
Linguistic Variables ◽  
Cognitive Computing ◽  
Human Beings ◽  
Intelligent Computing ◽  
Concrete Entity

Computing with words (CWW) is an intelligent computing methodology for processing words, linguistic variables, and their semantics, which mimics the natural-language-based reasoning mechanisms of human beings in soft computing, semantic computing, and cognitive computing. The central objects in CWW techniques are words and linguistic variables, which may be formally modeled by abstract concepts that are a basic cognitive unit to identify and model a concrete entity in the real world and an abstract object in the perceived world. Therefore, concepts are the most fundamental linguistic entities that carries certain meanings in expression, thinking, reasoning, and system modeling, which may be formally modeled as an abstract and dynamic mathematical structure in denotational mathematics. This paper presents a formal theory for concept and knowledge manipulations in CWW known as concept algebra. The mathematical models of abstract and concrete concepts are developed based on the object-attribute-relation (OAR) theory. The formal methodology for manipulating knowledge as a concept network is described. Case studies demonstrate that concept algebra provides a generic and formal knowledge manipulation means, which is capable of dealing with complex knowledge and their algebraic operations in CWW.

scholarly journals Drawing with Metaphors. Mediating ideational content in drawing through metaphors

2013 ◽  
Vol 6 (3) ◽  
Author(s):  
Berit Ingebrethsen
Keyword(s):  
Abstract Concept ◽  
Abstract Concepts ◽  
Visual Metaphors ◽  
Linguistic Research ◽  
Cognitive Linguistic ◽  
Educational Issue ◽  
Metaphor Theory ◽  
Different Types ◽  
George Lakoff ◽  
The Subject

It is not easy to express abstract concepts, such as time and society, in a drawing. The subject of this article is rooted in the educational issue of visually expressing themes represented by abstract concepts. However, it is possible to find means and devices to express such ideas. This article shows how metaphors can be used to express such ideas visually. Cognitive linguistic research argues that metaphors are crucial in the verbal communication of abstract concepts. This article also attempts to show that metaphors are important in visual communication. The cognitive linguistic metaphor theory of George Lakoff and Mark Johnson is used here to investigate how metaphors are used to construct meaning in the drawings of cartoonist and illustrator Finn Graff and artist Saul Steinberg. The article presents a few examples of how visual devices structure the abstract concept of time. It then proceeds to explain how symbols function as metonymies and provides an overview of the different types of metaphors and how they are used to express meaning in drawings. The article concludes by attempting to provide new insights regarding the use of visual metaphors.

scholarly journals Exploring Geometric Feature Hyper-Space in Data to Learn Representations of Abstract Concepts

2020 ◽  
Vol 10 (6) ◽  
pp. 1994 ◽  
Author(s):  
Rahul Sharma ◽  
Bernardete Ribeiro ◽  
Alexandre Miguel Pinto ◽  
F. Amílcar Cardoso
Keyword(s):  
Training Data ◽  
Geometric Feature ◽  
Automatic Identification ◽  
Computational Domain ◽  
Abstract Concept ◽  
Abstract Concepts ◽  
Concept Representation ◽  
Data Problem ◽  
Rans Modeling ◽  
Concrete Concepts

The term concept has been a prominent part of investigations in psychology and neurobiology where, mostly, it is mathematically or theoretically represented. Concepts are also studied in the computational domain through their symbolic, distributed and hybrid representations. The majority of these approaches focused on addressing concrete concepts notion, but the view of the abstract concept is rarely explored. Moreover, most computational approaches have a predefined structure or configurations. The proposed method, Regulated Activation Network (RAN), has an evolving topology and learns representations of abstract concepts by exploiting the geometrical view of concepts, without supervision. In the article, first, a Toy-data problem was used to demonstrate the RANs modeling. Secondly, we demonstrate the liberty of concept identifier choice in RANs modeling and deep hierarchy generation using the IRIS dataset. Thirdly, data from the IoT’s human activity recognition problem is used to show automatic identification of alike classes as abstract concepts. The evaluation of RAN with eight UCI benchmarks and the comparisons with five Machine Learning models establishes the RANs credibility as a classifier. The classification operation also proved the RANs hypothesis of abstract concept representation. The experiments demonstrate the RANs ability to simulate psychological processes (like concept creation and learning) and carry out effective classification irrespective of training data size.

Using abstract concepts in impact-focussed organisational research

2017 ◽  
Vol 12 (1) ◽  
pp. 18-34 ◽  
Author(s):  
Peter Lugosi
Keyword(s):  
Design Methodology ◽  
Applied Research ◽  
Data Generation ◽  
Abstract Concept ◽  
Abstract Concepts ◽  
Business Research ◽  
Content Type ◽  
Change In Practice ◽  
Organisational Research ◽  
Context Specific

Purpose The purpose of this paper is to conceptualise and examine the processes through which abstract concepts, or abstractions, can be utilised in co-creating knowledge within “impact-focussed” organisational and business research, i.e. applied research that primarily seeks to promote change in practice rather than principally aiming to make theoretical contributions to academic debates. The paper uses the abstraction “hospitality” as an empirical example and discusses the techniques used to “operationalise” this concept, i.e. make it understandable for research participants enabling researchers to use it within data generation and the creation of practical insights in organisational enquiry. Design/methodology/approach The study employed two methods: first, participant-generated photos; and second, two interactive workshops with 38 practitioners where the abstract concept “hospitality” was used to generate practical organisational insights. Findings The paper distinguishes between four stages: the elaboration of abstraction, concretisation of abstraction, probing perspectives on abstraction and exploring experiences of abstraction. It is argued that utilising specific techniques within these four stages facilitates: recognisability: the extent to which organisational stakeholders understand the content and meanings of the abstraction; and relatability: the extent to which stakeholders appreciate how the abstract concepts are relevant to interpreting their own practices and experiences. Research limitations/implications This is an exploratory study, used to develop and refine elicitation techniques, rather than to draw definitive conclusions about the applicability of specific abstract concepts. Nevertheless, reflecting on the processes and techniques used in the utilisation of abstractions here can help to operationalise them in future impact-focussed research. Originality/value The paper conceptualises the processes through which abstract concepts can be made apprehendable for non-specialist, non-academic practitioners. In doing so, it discusses how various elicitation techniques support the utilisation of abstractions in generating insights that can support the development of constructive, context-specific practices in organisations and businesses.

scholarly journals Contributions of different prefrontal cortical regions to abstract rule acquisition and reversal in monkeys

2017 ◽  
Author(s):  
Giancarlo La Camera ◽  
Sebastien Bouret ◽  
Barry J. Richmond
Keyword(s):  
Orbitofrontal Cortex ◽  
Brain Regions ◽  
Abstract Concept ◽  
Abstract Concepts ◽  
Prefrontal Cortical ◽  
Rule Acquisition ◽  
Learning Rules ◽  
Association Task ◽  
Abstract Rule ◽  
Cortical Regions

AbstractThe ability to learn and follow abstract rules relies on intact prefrontal regions including the lateral prefrontal cortex (LPFC) and the orbitofrontal cortex (OFC). Here, we investigate the specific roles of these brain regions in learning rules that depend critically on the formation of abstract concepts as opposed to simpler input-output associations. To this aim, we tested monkeys with bilateral removals of either LPFC or OFC on a rapidly learned task requiring the formation of the abstract concept of same vs. different. While monkeys with OFC removals were significantly slower than controls at both acquiring and reversing the concept-based rule, monkeys with LPFC removals were not impaired in acquiring the task, but were significantly slower at rule reversal. Neither group was impaired in the acquisition or reversal of a delayed visual cue-outcome association task without a concept-based rule. These results suggest that OFC is essential for the implementation of a concept-based rule, whereas LPFC seems essential for its modification once established.

scholarly journals Abstract concept learning in a simple neural network inspired by the insect brain

2018 ◽  
Author(s):  
Alex J. Cope ◽  
Eleni Vasilaki ◽  
Dorian Minors ◽  
Chelsea Sabo ◽  
James A.R. Marshall ◽  
...  
Keyword(s):  
Executive Control ◽  
Honey Bees ◽  
Mushroom Body ◽  
Insect Brain ◽  
Abstract Concept ◽  
Abstract Concepts ◽  
Top Down ◽  
Learning Tasks ◽  
Learning Rates ◽  
Simple Neural Network

AbstractThe capacity to learn abstract concepts such as ‘sameness’ and ‘difference’ is considered a higher-order cognitive function, typically thought to be dependent on top-down neocortical processing. It is therefore surprising that honey bees apparantly have this capacity. Here we report a model of the structures of the honey bee brain that can learn same-ness and difference, as well as a range of complex and simple associative learning tasks. Our model is constrained by the known connections and properties of the mushroom body, including the protocerebral tract, and provides a good fit to the learning rates and performances of real bees in all tasks, including learning sameness and difference. The model proposes a novel mechanism for learning the abstract concepts of ‘sameness’ and ‘difference’ that is compatible with the insect brain, and is not dependent on top-down or executive control processing.

DYING IS HARD TO DESCRIBE: METONYMIES AND METAPHORS OF DEATH IN THEILIAD

2018 ◽  
Vol 68 (2) ◽  
pp. 359-383 ◽  
Author(s):  
Fabian Horn
Keyword(s):  
Cognitive Linguistics ◽  
Figurative Language ◽  
Human Mind ◽  
Abstract Concept ◽  
Abstract Concepts ◽  
Epic Poem ◽  
Recent Developments ◽  
Battle Scenes

Homer'sIliadis an epic poem full of war and battles, but scholars have noted that ‘[t]he Homeric poems are interested in death far more than they are in fighting’. Even though long passages of the poem, particularly the so-called ‘battle books’ (Il.Books 5–8, 11–17, 20–2), consist of little other than fighting, individual battles are often very short with hardly ever a longer exchange of blows. Usually, one strike is all it takes for the superior warrior to dispatch his opponent, and death occurs swiftly. The prominence of death in Homeric battle scenes raises the question of how and in which terms dying in battle is being depicted in theIliad: for while fighting can be described in a straightforward fashion, death is an abstract concept and therefore difficult to grasp. Recent developments in cognitive linguistics have ascertained that, when coping with difficult and abstract concepts, such as emotions, the human mind is likely to resort to figurative language and particularly to metaphors.

Simulation and Visualization of Concept Algebra in MATLAB

2014 ◽  
Vol 6 (1) ◽  
pp. 30-55 ◽  
Author(s):  
Xiaoyu Lin ◽  
Yingxu Wang
Keyword(s):  
Natural Language Processing ◽  
Natural Language ◽  
Mathematical Models ◽  
Language Processing ◽  
Real World ◽  
Formal Knowledge ◽  
Design And Implementation ◽  
Visualization Software ◽  
Formal Concepts ◽  
Algebraic Operations

Concept algebra (CA) is a denotational mathematics for formal knowledge manipulation and natural language processing. In order to explicitly demonstrate the mathematical models of formal concepts and their algebraic operations in CA, a simulation and visualization software is developed in the MATLAB environment known as the Visual Simulator of Concept Algebra (VSCA). This paper presents the design and implementation of VSCA and the theories underpinning its development. Visual simulations for the sets of reproductive and compositional operations of CA are demonstrated by real-world examples throughout the elaborations of CA and VSCA.

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