A Fixpoint Semantics for Rule-Base Anomalies

A Fixpoint Semantics for Rule-Base Anomalies

Du Zhang (California State University, USA)
Copyright: © 2009 |Pages: 12
DOI: 10.4018/978-1-60566-170-4.ch018
OnDemand PDF Download:


A crucial component of an intelligent system is its knowledge base that contains knowledge about a problem domain. Knowledge base development involves domain analysis, context space definition, ontological specification, and knowledge acquisition, codification and verification. Knowledge base anomalies can affect the correctness and performance of an intelligent system. In this chapter, we describe a fixpoint semantics for a knowledge base that is based on a multi-valued logic. We then use the fixpoint semantics to provide formal definitions for four types of knowledge base anomalies: inconsistency, redundancy, incompleteness, circularity. We believe such formal definitions of knowledge base anomalies will help pave the way for a more effective knowledge base verification process.
Chapter Preview


Computing plays a pivotal role in our understanding of human cognition (Pylyshyn, 1989). The classical cognitive architecture for intelligent behavior assumes that both computers and minds have at least the following three distinct levels of organization (Pylyshyn, 1989). (a) The semantic level or the knowledge level where the behavior of human beings or appropriately programmed computers can be explained through the things they know and the goals they have. It attempts to establish, in some meaningful or even rational ways, connections between the actions (by human or computer) and what they know about their world. (b) The symbol level where the semantic content of knowledge and goals is assumed to be encoded through structured symbolic expressions. It deals with representation, structure and manipulation of symbolic expressions. (c) The physical or biological level where the physical embodiment of an entire system (human or computer) is considered. It encompasses the structure and the principles by which a physical object functions.

Pylyshyn’s cognitive penetrability criterion states that “the pattern of behavior can be altered in a rational way by changing subjects’ beliefs about the task” (Pylyshyn, 1989). It is the subjects’ tacit knowledge about the world, not the properties of the architecture that enables such behavior adjustment.

The hallmark of a knowledge-based system is that by design it possesses the ability to be told facts about its world and to alter its behavior accordingly (Brachman & Levesque, 2004). It exhibits the property of cognitive penetrability.

Today, knowledge-based systems not only play an important role in furthering the study in cognitive informatics (Wang et al., 2002; Patel et al., 2003; Chan et al., 2004; Kinsner et al., 2005; Wang, 2002, 2007; Wang and Kinsner, 2006), but also have found their way into so many problem domains (Cycorp, 2006) and have been utilized to generate numerous successful applications (IBM, 2006; Ross, 2003). A crucial component of an intelligent system or a knowledge-based system is its knowledge base (KB) that contains knowledge about a problem domain (Brachman & Levesque, 2004; Fagin et al, 1995; Levesque & Lakemeyer, 2000). Knowledge base development involves domain analysis, context space definition, ontological specification, and knowledge acquisition, codification and verification (Zhang, 2005).

When developing a KB for an application, it is important to recognize the context under which we formulate and reason about domain-specific knowledge. A context is a region in some n-dimensional space (Lenat, 1998). In a KB development process, domain analysis should result in identification of the region of interest in the context space. Specifying a context entails specifying or locating a point or region along each of those n dimensions. Once the context (or contexts) for a problem domain is identified, ontological development is in order. An ontology is a formal, explicit specification of a shared conceptualization (Chandrasekaran et al, 1999; Gomez-Perez et al, 2004; O’Leary, 1998). After the conceptualization is in place, knowledge acquisition, codification and verification can be carried out to build the KB for some application. Inevitably, there will be anomalies in a KB as a result of existing practices in its development process. Knowledge base anomalies can affect the correctness and performance of an intelligent system, though some systems are robust enough to perform rationally in the presence of the anomalies. It is necessary to define KB anomalies formally before identifying where they are in a KB and deciding what to do with them.

Complete Chapter List

Search this Book:
Editorial Advisory Board
Table of Contents
Yingxu Wang
Chapter 1
Yingxu Wang
Cognitive Informatics (CI) is a transdisciplinary enquiry of the internal information processing mechanisms and processes of the brain and natural... Sample PDF
The Theoretical Framework of Cognitive Informatics
Chapter 2
Withold Kinsner
This chapter provides a review of Shannon and other entropy measures in evaluating the quality of materials used in perception, cognition, and... Sample PDF
Is Entropy Suitable to Characterize Data and Signals for Cognitive Informatics?
Chapter 3
Ismael Rodríguez, Manuel Núñez, Fernando Rubio
Finite State Machines (FSM) are formalisms that have been used for decades to describe the behavior of systems. They can also provide an intelligent... Sample PDF
Cognitive Processes by using Finite State Machines
Chapter 4
Yingxu Wang
An interactive motivation-attitude theory is developed based on the Layered Reference Model of the Brain (LRMB) and the Object-Attribute-Relation... Sample PDF
On the Cognitive Processes of Human Perception with Emotions, Motivations, and Attitudes
Chapter 5
Qingyong Li, Zhiping Shi, Zhongzhi Shi
Sparse coding theory demonstrates that the neurons in the primary visual cortex form a sparse representation of natural scenes in the viewpoint of... Sample PDF
A Selective Sparse Coding Model with Embedded Attention Mechanism
Chapter 6
Yingxu Wang
Theoretical research is predominately an inductive process, while applied research is mainly a deductive process. Both inference processes are based... Sample PDF
The Cognitive Processes of Formal Inferences
Chapter 7
Douglas Griffith, Frank L. Greitzer
The purpose of this article is to re-address the vision of human-computer symbiosis as originally expressed by J.C.R. Licklider nearly a... Sample PDF
Neo-Symbiosis: The Next Stage in the Evolution of Human Information Interaction
Chapter 8
Ray E. Jennings
Although linguistics may treat languages as a syntactic and/or semantic entity that regulates both language production and comprehension, this... Sample PDF
Language, Logic, and the Brain
Chapter 9
Yingxu Wang, Guenther Ruhe
Decision making is one of the basic cognitive processes of human behaviors by which a preferred option or a course of actions is chosen from among a... Sample PDF
The Cognitive Process of Decision Making
Chapter 10
Tiansi Dong
This chapter proposes a commonsense understanding of distance and orientation knowledge between extended objects, and presents a formal... Sample PDF
A Commonsense Approach to Representing Spatial Knowledge Between Extended Objects
Chapter 11
Natalia López, Manuel Núñez, Fernando L. Pelayo
In this chapter we present the formal language, stochastic process algebra (STOPA), to specify cognitive systems. In addition to the usual... Sample PDF
A Formal Specification of the Memorization Process
Chapter 12
Yingxu Wang
Autonomic computing (AC) is an intelligent computing approach that autonomously carries out robotic and interactive applications based on goal- and... Sample PDF
Theoretical Foundations of Autonomic Computing
Chapter 13
Witold Kinsner
Numerous attempts are being made to develop machines that could act not only autonomously, but also in an increasingly intelligent and cognitive... Sample PDF
Towards Cognitive Machines: Multiscale Measures and Analysis
Chapter 14
Amar Ramdane-Cherif
Cognitive approach through the neural network (NN) paradigm is a critical discipline that will help bring about autonomic computing (AC). NN-related... Sample PDF
Towards Autonomic Computing: Adaptive Neural Network for Trajectory Planning
Chapter 15
Lee Flax
We give an approach to cognitive modelling, which allows for richer expression than the one based simply on the firing of sets of neurons. The... Sample PDF
Cognitive Modelling Applied to Aspects of Schizophrenia and Autonomic Computing
Chapter 16
Yan Zhao, Yiyu Yao
Classification is one of the main tasks in machine learning, data mining, and pattern recognition. Compared with the extensively studied automation... Sample PDF
Interactive Classification Using a Granule Network
Chapter 17
Mehdi Najjar, André Mayers
Encouraging results of last years in the field of knowledge representation within virtual learning environments confirms that artificial... Sample PDF
A Cognitive Computational Knowledge Representation Theory
Chapter 18
Du Zhang
A crucial component of an intelligent system is its knowledge base that contains knowledge about a problem domain. Knowledge base development... Sample PDF
A Fixpoint Semantics for Rule-Base Anomalies
Chapter 19
Christine W. Chan
This chapter presents a method for ontology construction and its application in developing ontology in the domain of natural gas pipeline... Sample PDF
Development of an Ontology for an Industrial Domain
Chapter 20
Václav Rajlich, Shaochun Xu
This article explores the non-monotonic nature of the programmer learning that takes place during incremental program development. It uses a... Sample PDF
Constructivist Learning During Software Development
Chapter 21
Witold Kinsner
Many scientific chapters treat the diversity of fractal dimensions as mere variations on either the same theme or a single definition. There is a... Sample PDF
A Unified Approach to Fractal Dimensions
Chapter 22
Du Zhang, Witold Kinsner, Jeffrey Tsai, Yingxu Wang, Philip Sheu, Taehyung Wang
The 2005 IEEE International Conference on Cognitive Informatics (ICCI’05) was held during August 8th to 10th 2005 on the campus of University of... Sample PDF
Cognitive Informatics: Four Years in Practice
Chapter 23
Yiyu Yao, Zhongzhi Shi, Yingxu Wang, Witold Kinsner, Yixin Zhong, Guoyin Wang
Cognitive informatics (CI) is a cutting-edge and multidisciplinary research area that tackles the fundamental problems shared by modern informatics... Sample PDF
Toward Cognitive Informatics and Cognitive Computers: A Report on IEEE ICCI'06
About the Contributors