Knowledge Science - Natural and Artificial Reasoning - page 46

different models may be derived from a single theory. Thus, a set of models is the
extension of a theory in the same way that a set of facts is an extension of a concept.
An extension is a relationship between a set of symbols and a symbol which is not
itself a member of the set. The meaning of the symbol is the set. Since every symbol
of the set can itself have an extension, the relationship of a concept to a set of facts
(or a theory to a set of models) is relative and not absolute (Addis 1990 ).

4.2.3 Heuristic Knowledge

Heuristic knowledge is that knowledge which indicates how a deductive process
should be performed. Given a number of facts and hypotheses, many potential paths
of deduction are possible. The heuristic knowledge uses extra-logical information to
guide the deductive process towards 'useful' results. What is useful depends upon
the purpose of the system.

4.2.4 Inferential Knowledge

C. S. Peirce pointed out there are three types of deduction . Since there is only
one formal process of deduction based upon 'modus ponens' (although there are
many mechanisms such as resolution that can achieve the same result), the distinc-
tions he identified can be related to the different classes of heuristics identified in
Fig. 4.1 . Exactly how these may be identified within a knowledge system is yet to
be understood.
We can note that inference , in general, can be divided into two styles:

• Open : 'Open' inference does not necessarily have identifying formal mechanisms

associated with it. In general, open inference is related to the creation or the
construction of insights.

• Closed : Closed inference identifies the process of selection from pre-formed or

pre-determined set of insights.

The problem with most artificial intelligence systems is that it simulates intelligence
through an inference that appears open (capable of learning) but which is in fact
closed. Closed inference is usually found in both intelligent mechanisms and many
established skills (such as navigation, engineering and mathematics).
Inference , as Peirce observed, has three distinct forms. These are abduction ,
induction and deduction . Their roles are simply described as:
Generate a hypothesis ( abduction )- >
Validate a hypothesis ( induction )- >
Infer new facts from a hypothesis ( deduction ).