The Expert System Shell SPIRIT

Presented by Poom SamaharnI-MMIS 51-7038-0066

Agenda

Background Probabilistic expert system

What is SPIRIT? Expert system’s architecture

Knowledge processing in SPIRIT Query and response

Terminology Summarization

Background

The early 70’s : Develop knowledge based system with purely deterministic rule processing.

Today : Knowledge based systems are able to manage uncertain, subjective, and vague knowledge.

Involved probabilistic facts and rules must be either estimated by an expert or calculated from statistical data.

SPIRIT uses subjective estimations of probabilities in a knowledge domain and statistical data to construct a knowledge base.

Probabilistic Expert System

The probabilistic expert system represents the experts knowledge by a probability distribution.

The probability distribution is defined with a finite set of discrete random variables for the space of attributes.

Stochastic or random dependencies between the variables can be specified by– Rules– Conditionals– Facts

Probabilistic Expert System (cont.)

For example : If the test result is positive (Fact), the monitor display is o.k. with probability 0.9 (Rule). => the space of attributes of the discrete variables will be

  TESTRESULT  and  DISPLAY_CONDITION  {positive, negative} {ok, defect}

Conditionals generate a fair distribution for probabilistic knowledge base.

Probabilistic expert systems are graphical networks that support the modeling of uncertainty and decisions in complex domains.

What is SPIRIT?

Symmetrical Probabilistic Intensional Reasoning in Inference Networks in Transition.

The expert-system-shell SPIRIT is a sophisticated tool to build up knowledge bases.

SPIRIT allows to use rich communication language with the user. For example, user informs the system that the car's speed is very high then there is an increased danger of accident.

Interactive explanation with dependency graph and LEG-structure.

Expert System’s Architecture

Figure 1. Expert system architecture

Knowledge Processing in SPIRIT

The following four steps are description about how to generate a probabilistic knowledge base:  Step 1 : Define variables and its attributes.

Step 2 : Enter facts and rules and assign probabilities.

Step 3 : Generate an internal structure to enable inference.

Step 4 : Generate a joint probability distribution to complete the knowledge base.

Step 1 : Define variables

Define the knowledge domain by specifying variables Vl and their values vl.

Variable types and their attributes  - Boolean variable : (yes = 1/no = 0)

- Nominal variable : (an unsorted set of values e.g. red/green/blue) ) - Utility variable : (a sorted list of numeric values e.g. -8614,

-29, 0,25,388,1466)

Variables and attributes form the domain on which a probability distribution will be generated by facts and rules.

Step 1 : Define variables(cont.)

s

Figure 2. A view of variable and its values

Step 2 : Set facts and rules

Define suitable facts and rules, according to the SPIRIT syntax of propositions.

Propositions are formed by the junctors

^ = ‘and’ v = ‘or’ ¬ = ‘not( ) = ‘parenthesis’ | = ‘given’

Variable’s dependencies are informed to the system with the probabilistic conditionals.

e.g. MARITAL=s |YOUNG => P = 0.80(Rules can be set as active or inactive)

Step 2 : Set facts and rules(cont.)

Conditional conventions

T = True F = False i = inapplicable

B|A[x] is valid in P , iff P(BA) = x.P(A)When x is the probabilistic conditional and P is probability distribution. (the epistemic state with valid conditionals)

^t f i v t f i ¬ | t f i

t t f t t t t t t f t t i t

f f f f f f f t f f i f

i i i i i i i i i I

Step 2 : Set facts and rules(cont.)

Facts about the domain => Knowledge acquisition

The knowledge engineer supplies conditionals Bi|Ai i = 1,...,I and estimate their probabilities xi to be true in the population.

This knowledge ,supplied by the rules and facts, is then implemented in a distribution P*.

P* = arg minR(Q,P0), s.t. Q |= RWhen P* is the basic knowledge generated under MinREnt.R is the relative entropy of distribution of variable Q.P0 is the uniform probability distribution.

Step 2 : Set facts and rules(cont.)

SPIRIT provides entropies H(P0) and H(P*) , so the shell informs the amount of acquired knowledge (H(P0) - H(P*)) in [bit].

Figure 3. Knowledge acquisition

Step 3 : Generate a structure to enable inference

SPIRIT provides the dependency structure of a model’s variables with Markov net and optional inference net.

Inference is the result of logical assumption about the vague population (e.g. all animals).

Inference takes place in spite of incomplete information about this population.

Knowledge adaptation is inference and answering questions is based on inference as well.

Step 3 : Generate a structure to enable inference

Figure 4. Markov net on dependencies window

Step 4 : Generate a joint probability distribution

SPIRIT calculates a special joint distribution(global distribution).

However, global distribution, formed in a hypertree, suffers to store an exponential growth of the number of probabilities with an increasing number of variables.

Global distribution is decomposed in marginal distributions(Local Events Groups – LEGs). LEGs form a knowledge base’s junction tree where edges(links) can connect any number of vertices(nodes).

Step 4 : Generate a joint probability distribution(cont.)

Figure 5. Junction tree in SPIRIT

Query and Response

Query has three parts– Focus– The addition to focus– A question plus response

Focus (E) is about domain’s temporary assumptions with a rich set of probabilistic conditionals. Focus will be discarded when query is over.

E = {Fj|Ej [yi], j=1,…,J}

When Fj|Ej are further conditionals and yi are their probabilities.

Query and Response(cont.)

The addition to focus => The adaptation of P** to focus E

P** = arg minR(Q,P*), s.t. Q |= E

P** is the probability distribution that preserves the indefiniteness of P* as much as possible, but adapts it to hypothetical facts and rules.

This inference process respects the principle of minimum

relative entropy.

Query and Response(cont.)

A question plus response

P**(H|G) = z

A question is any conditional(H|G) and the response or answer to the question is represented by z.

The goal is to evaluate the probabilities of conditional questions from user.

The response is about the probability of H given G derived from the knowledge subjective in P* and from the evident situation.

Query and Response(cont.)

Figure 6. (Un)certainty query and response

Terminology

P presc = The prescribed probability of the rule in range [0..1].

P act = The current probability of the rule in the distribution. When P presc = P act, the rule is valid.

Entropy = A measure of the uncertainty associated with random variable. The relative entropy is changed by the rule.

Knowledge base = a database created by experts that can be retrieve and update in machine language and human language.

Terminology(cont.)

Expert system = The system that provide an answer or clarify uncertainties with existing knowledge bases.

Statistical inference = The use of statistics and facts from random data to make inferences of unknown aspect of a population.

Conditional probability = The probability of some event (B), given the occurrence of another event(A) => P(B|A)

Summarization

The shell XSPIRIT 3.0, a Java-version, is a professional tool for information and knowledge processing.

SPIRIT processes probabilities rather than information measures, but an additional module allows to handle both.

Knowledge processing in 4 steps : Define variables, set

rules and facts, generate a structure for inference, and create joint probability distribution.

Particular query can be answered based on a knowledge model.

References

Rodder, W. and Xu, L. 1999. Entropy-driven Inference and Inconsistency, Proc. Artificial Intelligence and Statistics, Fort Lauderdale, 272-279.

Rodder, W. and Kern-Isberner, G. (2003a). From Information to Probability - An Axiomatic Approach. International Journal of Intelligent Systems, 18-4, 383–403.

Rodder, W., Reucher, E., Kulmann, F. Features of the Expert-System Shell SPIRIT, Logic Journal of the IGPL, 14-3 (2006) 483-500.

References (cont.)

Reucher, E. and Kulmann, F. Probabilistic Knowledge Processing and Remaining Uncertainty, Proc. 20th International FLAIRS Conference -FLAIRS-20, May 7-9, Key West, Florida (2007) 122-127.

Spirit (2009). http://www.xspirit.de., access 18/09/2009