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Epistemics: the knowledge levelIt is now uncontroversial that knowledge can be understood in formal, computational and even mathematical terms, but also that theories of knowledge require different constructs from those needed for understanding physical or biological systems. In this section I give a short overview of current knowledge representation theory. To keep the presentation brief I use the simple image in figure 5 to explain some of the ideas.4 The most primitive epistemic convention is classification in which a symbol is assigned to some class (of object or other concept) that it is required to represent. In early computational systems the only classifications that people were interested in were mathematical types (“integer”, “string” etc). With the rise of cognitive science, however, a further classification convention emerged. Ontological assignment assigns a symbol to a conceptual category (usually a humanly intelligible category, but there is no reason why it must be). For example, the symbol "apple" can be assigned to the class "fruit" using the relationship symbol a kind of. Ontological assignment begins the transformation of meaningless symbols into meaningful concepts that can be the object of reasoning and other cognitive operations. One important cognitive operation that is usually taken to be a direct consequence of ontological assignment, for example, is epistemic inheritance: if the parent class has some interpretation then all the things that are assigned to this class also inherit this interpretation. Rules can be seen as a special kind of description. Logical implication can be viewed as a special kind of relationship between descriptions such that if one set of descriptions is true then so is the other; from the logician’s point of view one set of descriptions has the logical role of "premises" and the other the status of "conclusions". If I say “Socrates is a man” and assert that “all men are mortal” then you are entitled (under certain conventions about “all” that we agree about) to conclude that Socrates is mortal. Similarly, if I say that “Flora is an ancestor of Jane”, and “Esther is an ancestor of Flora”, then you are entitled under certain interpretations of the relationship ancestor of to conclude that “Esther is an ancestor of Jane”. Some epistemic systems support higher-order properties such as transitivity of relations, so that if we assert that some relationship is transitive, as in ancestor of, then the knowledge system is sanctioned to deduce all valid ancestor relationships To take an example from medicine we have found that a large proportion of the expertise of skilled clinicians can be modelled in terms of a small ontology of tasks: plans, actions and decisions. These models can be composed into complex goal-directed processes carried out over time. The simplest task model has a small set of critical properties, whose values can be formalised using descriptions and rules. These include preconditions (descriptions which must be true for the task to be relevant in a context), post-conditions (descriptions of the effects of carrying out the task), trigger conditions (scenarios in which the task is to be invoked) and scheduling constraints that describe sequential aspects of the process (as in finding out what is wrong with a patient before deciding what the treatment should be). Task-based representations of expertise seem to be more natural and powerful than rule-based models in complex worlds like medicine (Fox, 2003). In recent years many knowledge representation systems, from semantic networks and frame systems to rule-based systems like production systems and logic programming languages have come to be seen as members of a family of knowledge representation systems called Description Logics (Baader et al, 2003). The early ideas about knowledge representation developed by psychologists, for example (Quillian, 1968), stimulated many experimental investigations of the adequacy of particular languages. These have in turn given way to more formal theories of knowledge representation. The work of Brachman and his colleagues (1979, 1984; Nardi & Brachman, 2003) has been central in this development and has led to a much deeper understanding of the requirements on effective knowledge representation systems, and their computational and other properties.
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