A Fixpoint Semantics for Rule-Base Anomalies

Introduction

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.