Page 141 - DCAP310_INTRODUCTION_TO_ARTIFICIAL_INTELLIGENCE_AND_EXPERT_SYSTEMS

Unit 7: Probabilistic Reasoning

7.2 Possible World Representations Notes

A discrete variable is one whose domain is finite or countably infinite. One particular case of a
discrete variable is a Boolean variable, which is a variable with domain {true, false}. If X is a
Boolean variable, we write X=true as its lowercase equivalent, x, and write X=false as ¬x. We can
also have variables that are not discrete; for example, a variable whose domain corresponds to
a subset of the real line is a continuous variable.

Example: The variable Class_time may denote the starting time for a particular class.
The domain of Class_time may be the following set of possible times:
dom(Class_time)={8, 9, 10, 11, 12, 1, 2, 3, 4, 5}.

The variable Height_joe may refer to the height of a particular person at a particular time and
have as its domain the set of real numbers, in some range, that represent the height in centimeters.
Raining may be a Boolean random variable with value true if it is raining at a particular time.

7.2.1 Pointing to the Subject

Knowledge Representation is an area of artificial intelligence research aimed at representing
knowledge in symbols to facilitate inference from those knowledge elements, creating new
elements of knowledge. The KR can be made to be independent of the underlying knowledge
model or knowledge base system (KBS) such as a semantic network.

Knowledge representation (KR) research involves analysis of how to reason accurately and
effectively and how best to use a set of symbols to represent a set of facts within a knowledge
domain. A symbol vocabulary and a system of logic are combined to enable inferences about
elements in the KR to create new KR sentences. Logic is used to supply formal semantics of how
reasoning functions should be applied to the symbols in the KR system. Logic is also used to
define how operators can process and reshape the knowledge. Examples of operators and
operations include negation, conjunction, adverbs, adjectives, quantifiers and modal operators.
The logic is interpretation theory. These elements – symbols, operators, and interpretation
theory – are what give sequences of symbols meaning within a KR.
A key parameter in choosing or creating a KR is its expressivity. The more expressive a KR, the
easier and more compact it is to express a fact or element of knowledge within the semantics and
grammar of that KR. However, more expressive languages are likely to require more complex
logic and algorithms to construct equivalent inferences. A highly expressive KR is also less
likely to be complete and consistent. Less expressive KRs may be both complete and consistent.
Auto epistemic temporal modal logic is a highly expressive KR system, encompassing
meaningful chunks of knowledge with brief, simple symbol sequences (sentences). Propositional
logic is much less expressive but highly consistent and complete and can efficiently produce
inferences with minimal algorithm complexity. Nonetheless, only the limitations of an
underlying knowledge base affect the ease with which inferences may ultimately be made (once
the appropriate KR has been found). This is because a knowledge set may be exported from a
knowledge model or knowledge base system (KBS) into different KRs, with different degrees of
expressiveness, completeness, and consistency. If a particular KR is inadequate in some way,
that set of problematic KR elements may be transformed by importing them into a KBS, modified
and operated on to eliminate the problematic elements or augmented with additional knowledge
imported from other sources, and then exported into a different, more appropriate KR.

In applying KR systems to practical problems, the complexity of the problem may exceed the
resource constraints or the capabilities of the KR system.

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