The Role of Deterministic and Non-Deterministic Rule ...

Submitted to the Sixth National Conference on Artificial Intelligence

The Role of Deterministic and Non-Deterministic Rule Scheduling in Expert Systems

Arthur B Baskin Departmenl of ledicaJ Information Science University of TlIinois at Lrbana-Champaign

1408 W University Avenue t rbana IL 61801

Telephone (217) 333-8007 Arpanet aisungbaskinacsuiucedu

Robert E Stepp Artificial Intelligence Research Group

Coordinaled Science Laboratory University of Illinois at Crbana-Champaign

1101 Wesl Springfield Avenue LrbanaIL 61801

Telephone (217) 333-6071 Arpanet uicslsteppacsuiucedu

Topic Area Automated Reasoning Subtopic Area RUle-based Reasoning

Science Track

Keywords Control Scheme Rule Scheduling Expert Systems

ABSTRACT Expert system problem solving ability depend on knowledge comprising both inferential relations between concepts and a strategy for their application Existing expert sytcms Uie a fe generic conllol strategies such as forard anu backvard chaining to reduce the amount of procedural knovdedge that is supplied by a domain expert Systems generally do not accept much meta-knoledge about 110 to manage the rules in the knoledge bae and in so doing they cannot follo rule scheduling strategi based on explicit problem rohing expertise coming from the domain expert This is most usually noticed a inadequacies in expressing heuristics for problem decomposition and the solicitation of input data A knovmiddotledge engineer may try to overcome the inadfquaci by using splaquoially engineered rul that have scheduling side elflaquot~ but at the cost of time underltanclability and maintainability

The mis~ing element in present expert ystem~ is a formalirm that can provide explicit kno4ledyene engineer cont 101 oer rule cequendng as ~ell at the customary cheduling chemes Explicit conllol adds a l)rocEdural mlaquohanism that can hi used in an organized 4ay to determini~tically inlJuence the ltlthedulinyen of ylttem acthmiddotities The idea of a nle group a~ a control ltcheme annotated knowledge block is introduced for calHuring and manipulating both procedural and declarative knoJ-Iedge in a well structulEd objectmiddotorientcd way

Major ~upport for thi research is provided by the Olftce of Nanl Research under grant NOOOI4-X2-KmiddotOllSb and hy the Ndtional Science Foundation lnder grant NSF 1ST ~S-ll1iO additional support is prolded hy the IA-panment of Delense Adnnced Research Projects Agency under ~rant NOOO14-I5SmiddotK-0078 and by iI contract for the study 01 llmplettness and conSIStency checking in rule hases from Compagnie Goneral Electric European Support Ccnter

1 Introduction

The now common paradigm of expert systems evolved from the inadequacies of purely

procedural approaches to building problem solving systems Human expertise expressed as

procedures (eg as conventional computer programs) was sufficient when available in complete

detail [Bleich 1972] but such problem solving knowledge is very difficult to acquire critique

refine and interpret The modularized structure provided by production rules their improved ease

of interpretation and critiquing and their non-procedural deductive evaluation made them much

more effident than procedural languages for building large problem solving systems

The very concise non-deterministic statement of rule scheduling that makes non-procedural

knowledge bases easier to build leads to problems when domain specific procedural knowledge

needs to be taken into account The difficulty presently experienced is the unpredictability of rule

firing order as it affects problem decomposition the acquisition of data and search effort

Knowledge engineers presently need to handcraft clever rules that affect rule precedence (order of

use) as side effects of the way they fit in the inference chains Such rules require great skill to

write and they are very difficult to interpret because they do not contain domain expertise but

engineering tricks to make the non-procedural approach have a procedural effect The indirect

encoding of this procedural information effectively obscures it in much the same way that encoding

knowledge directly in program code obscured it in the past

The above observations are important because experience with expert systems has shown that

the bottleneck is the acqUisition and refinement of knowledge [Ginsberg Weiss and Politakis

1985] Knowledge acquisition aids have grown in importance including the development of

intelligent knowledge engineering tools to search and edit large complex knowledge bases and the

application of inductive inference techniques to the knowledge acquisition task The hurden of

maintaining massive knowledge bases has also led to new design ideas for further structuring the

knowledge Even with these aids the acquiSition and management of expertise still demands a

formalism that makes plain those parts of the knowledge that encode domain expertise and those

2

that manage and direct system behavior and consultation session dynamics A casual mixture of

the two confounds system maintenance and limits knowledge base size simply because of

knowledge engineer confusion

In this paper the role of procedural knowledge that is processed in a deterministic way

(sequenced a priori) and the role of inferential knowledge that is processed in a non-deterministic

way (sequenced in the context of a particular problem) are explored The view taken is that both

types of knowledge are required to varying degrees and that th~y are to be woven together to best

carture expertise rather than to rigidly force a particular knowledge structure

2 Structuring large numbers of rules

In complex expert systems rules are profitably organized into rule sets called rule groups

The immediate advantage to such an organization stems from the connectedness of the rules

certain subsets of rules perform chunks of inference that solve subproblems and are best organized

into a functionality hierarchy built of rule groups The rule group thus possesses a perceived goal

and that plus their modest size makes knowledge engineering over rule groups easier than

manipulating individual rules in the universe of the entire knowledge base

Rule groups also provide a way to carefully fit the rule dynamics to the subproblem they

address For example inference over some sets of rules works much better in a forward-chained

environment While for other sets of rules the better strategy may be backwards-chaining As

knowledge bases grow it is less and less acceptable to pick just one single rule scheduling scheme

for all the rules

The choice of forward versus backwards chaining scheme is but one of a number of rule

retrievalevaluationapplication control parameters that may need to vary from one part of the

knowledge base to another A currtntly missing dimension to controlling rule use goes back to the

first historical perspective mentioned above the need to facilitate both declarative inferential

knowledge and procedural knowledge for solving problems In many domains there is important

heuristic ~xrertise embodied as wise procedure-driven (sequence structured) inferences

3

3 Scheduling large numbers of rules

Rules can be viewed as declared implicative statements and as IF THEl programming

constructs depending on the way they are used to capture expertise The system must be capable

of handling rules in a variety of ways with the knowledge engineer able to specify the appropriate

view A rule group is defined as the the smallest unit of rules with a common knowledge engineer

defined control mechanism Thus a rule group is composed of zero or more rules each having a

condicion part and an actum part The condition part can be any logical combination of predicates

The action part ~an he a conjunction of assertions (variable value asltiignmentlt) andor invocations

of other rule groups

The rule processing mechanism in an expert system needs to perform three fundamental

proce~ses

bull Rule retrieval the selection of one or more relevant candidate rules from th~ rule group to be

explored in more detail

bull Rule evaluation the evaluation of one or more of the condition parts of candidate rules to

determine a set of satisfied rules

bull Rule application the selection of one or more of the satisfied rules and the performance of the

rules action part

Thus the rule interpreter operates by asserting a precedence relation over rules for retrieval

condition evaluation and action performance A particular rule scheduling strategy defines the

precedence relations in a particular problem-oriented way

31 Deterministic rule scheduling

Deterministic rule scheduling makes an explicit procedural statement about rule precedence

This may be a linear sequence of rules to consider or it may he a graph precedence using any of the

conditional and iterative How control mechanisms in modern programming languages A sample

deterministic rule group is shown in Figure 1 Statements of the form IF ltconditiongt THE

lt rule-groupgt act in this setting like subroutines in a conventional programming environment

Whereas a subroutine is a deterministic procedural form the rule group may be either like a

deterministic subroutine or a non-deterministic inference subprocess that plays a particular role in

the decomposition of the problem

32 Non-Deterministic rule scheduling

ion-deterministic rule scheduling makes a declarative statement about rule precedence The

order of rule selection is implicitly defined by the non-deterministic strategy and ultimately

determined by the state of the system during problem solving in conjunction with the capabilities

of competing rules Typical strategies give precedence LO the rules with the greatest utility or the

rules that can most likely progress from currently available information or the rules that can

most likely infer currently needed information A sample non-deterministic rule group is shown

in Figure 2

DEGI~-RLLE-GROLP rg-one AliOTA TI01 use-deterministic-sc heduling

IF ltcond gt THE ltaction 1gt IF ltcond2gt THEi BEGIIl

IF ltcond3gt THEi ltaction3gt EiD

ELSE BEGI~

IF ltcond4gt THEN ltaction4gt EIlD

WHILE lt cond5 gt DO BEGIJ IF ltcond6gt THE-J ltaction6gt E~D

ED

Each ltcondgt form may be a conditional statement or TRLE Each ltactiongt may be a set of assertions or the activation of another rule group

Fig 1 A sample deterministic rule group

BEGIX-RLLE-GROUP rg-two AOTATIO use-forward-chaining

IF lt cond 1 gt THE lt action 1 gt IF ltcond2gt THEl ltaction2 gt IF lt cond3 gt THEl ltaction3 gt

EO

All rules are under consideration by the forward-chaining control scheme at all times The actual order of rule use cannot be determined until inference is actually attempted in the context estashyblished by presenting a particular problem The precedence relation over a particular rule is influenced by its contribution to the current state of the inference process in the presence of other competing rules

Fig 2 A sample non-deterministic rule group

33 Deterministic versus non-deterministic scheduling

Figure 3 illustrates the relationships between the degree of scheduling imprecision (ie degree

of non-determinism) versus a host of other rule group aspects At the left-hand extreme are the

purely non-deterministic scheduling mechanisms normally found in expert systems The purely

non-deterministic mode provides for concise statements of expert knowledge in which rule

scheduling is in the hands of the selected control scheme and no explicit statements of rule

precedence are given This type of rule group is well suited to capturing shallow knowledge often

found in the inference network of a typical knowledge base

on-deterministic scheduling is particularly ill suited to the task of specifying system

behavior during inference For example many a knowledge engineer has tried to write rules to

influence the order of solicitation of input data or evaluation of certain rules In conventional

systems that only practice non-deterministic rule scheduling this is an alien goal and such

attempts to introduce explicit precedence relations ihvariably lead to brittle systems with expert

knowledge and system behavior directives inextricably woven together The result is confusion

and hardship in maintaining and understanding the two as separate facets of the system-one often

6

needs to adjust system behavior without compromising the expert knowledge and vice-a-versa

The non-deterministic end of the scheduling envelope in Figure 3 is the widest to account for

scheduling freedoms in the choices of

bull forward-chaining versus backward-chaining

bull backtracking through rule interpretation choice points versus the hill-climbing approach

bull one-shot rule firing versus repeated rule firing

The right-hand side of Figure 3 corresponds to purely deterministic rule scheduling Here the

knowledge engineer provides an explicit statement of rule precedence for retrieval evaluation and

application This statement is verbose and possibly difficult to write Because there are explicit

rule scheduling instructions rule groups with purely deterministic scheduling are best for

Envelope of rule scheduling flexibility

on-deterministic

Other dimensions

or scheduling control

Degree 0

Iterative and recur~ive control

Deterministic

implicit rule precedence explicit rule precedence

more concise more control

shallow know ledge deep knowledge

Fig 3 l portrait of some relationships on rule scheduling

7

capturing deep procedure based domain knowledge The enclosing envelope is narrowist at the

right because rule order is totally constrained by the explicit control of the knowledge engineer

Ioving a little left of the deterministic extreme one finds the introduction of structured

deterministic control such as iteration and recursion over rules and rule groups Moving right to

left the verboseness changes gradually into conciseness and explicit precedence over rules changes

into implicit precedence The middle region between the pure deterministic and non-deterministic

extremes is an area that corresponds to systems with mixed control strategies ie with some rule

groups that handle a non-deterministic part of the solution calling on and called from rule groups

that handle a deterministic part For example a mostly non-deterministic approach (near the left

end of the drawing) would have traditional inference behavior (non-deterministically scheduled

rules) with system behavior control vested in deterministic rule groups

4 Inter-rule scheduling to meet the demands of problem domains

The knowledge base for a large complex expert system requires the structure here described

as the rule group Each rule group is captured by the knowledge engineer and checked for

completeness and consistency (tasks that are simplified via the rule group approach) The

knowledge engineer may dial any desired degree of scheduling impreciSion as We decides what level

of scheduling control versus conciseness is appropriate

Deterministic rule scheduling is most likely to be used for the rule group or groups near the

root (beginning subproblems) in the tree of all rule groups This corresponds to the presence of real

world knowledge that dictates the gross decomposition of the problem and choice of strategy

Important procedural information might be captured to determine the appropriate order of

subproblem investigation or the choice of the best solution strategy from among several alternative

inference chains This type of knowledge can be clearly and concisely stated in a deterministicly

scheduled rule group containing rules processed in a knowledge engineer specified order to activate

other rule groups according to problem specific conditions

8

This can ~ illustrated by considering the stereotypical problem of bin packing With

complete knowledge of the packing rules (packing constraints) but without procedural expertise

extensive searches must be conducted to find a solution A non-deterministic control strategy by

itself lacks the domain specific knowledge to equip it with an expert provided sequence of relevant

subproblems that can reach a solution with much less searching Heuristic knowledge for grocery

packing such as separate items into hard and soft categories then pack hard objects then pack soft

objects is a piece of top level problem decomposition expertise that is most easily captured by a

deterministic formalism

The other place where deterministic scheduling is of great importance is the solicitation of

input data To achieve a satisfying user dialogue data requests need to be ordered in a domain

sensitive way by the knowledge engineer Ordering of requests to please the user should not affect

the inferential knowledge content of the system but only its order of rule application Rules

pertaining to related concepts should be scheduled together so that input requests they spawn are

intellectually satisfying Deterministicly scheduled rule groups make the job easy and well

managed whereas an imposed non-deterministic strategy forces the knowledge engineer to corrupt

the inference structure with special effect rules that break easily and have no problem relevance

other than to to perturb rule order

S Intra-rule scheduling to meet the demands of problem domains

Individual rules possess their own deterministic versus non-deterministic control possibilities

In rule right hand sides a conjunctive form is normally a non-deterministic structure ie its

semantics say nothing about the order of evaluation of the conjuncts There may be times when

evaluation order may need to be explicitly stated for the well structured management of

evaluation side effects attached to external real world data (such as managing the user dialogue)

-t other times it may be best for the order to be determined dynamically by the system to

minimize the demand for data for which alternative sources exist Again no one scheme covers all

cases

9

It may be that certain conjuncts carry more weight that others so that a system with limited

resources may wish to evaluate some variables used in the left hand side of a rule while assuming

default values for others according to a preplanned way to get an approximate evaluation that is

as good as possible under the imposed timecomputation constraints This within rule control

strategy could practice a form of variable precision logic [Collins and 1ichalski 1986]

Knowledge engineers are becoming increasingly aware that merely constructing a knowledge

base that will support certain inferences is not enough The knowledge base must be maintainable

(ie able to be automatically checked for consistency and completenes-) and understandable In

both regards the structure of the knowledge becomes as important as its ability to sustain

inference Structure in a knowledge base includes grouping related knowledge tog~ther and

proposing a precedence relation on it for optimized use

6 Combined scheduling schemes

The idea of this paper is that an important part of the knowledge base is the expression of the

precedence relation on rules for retrieval evaluation and application The precedence relation is

part of the meta-knowledge of the system The knowledge engineer should be able to specify the

precedence himself (deterministic scheduling) or have the system do it through an established

strategy (non-determinist scheduling) The approach taken in theory and in practice is the

decomposition of the knowledge base into rule groups that have annotations giving control scheme

information This approach is being taken in the latest versions of the ADVISE tool for building

expert systems [-lichalski and Baskin 19~3]

The annotated rule group provides the basic control over rule scheduling As illustrated in

Figs 1 and 2 the rules in a rule group are subjected to either a non-deterministic scheme or a

deterministic one Presently twelve non-deterministic schemes are known to the ADVISE system

These are built from strategies that combine the four dimensions forward-chainingbackwardshy

chaining depth-firstibreadth-firstmiddot rule activation backtrackinghill-climbing and singleshy

shotmulti-shot rule firings For deterministic rule scheduling the rules are taken in the order

10

presented in the rule group as modified by iteration constructs

A series of initialization actions such as the acquisition of labdata values that are always

required is performed by a deterministly scheduled rule group containing imperative statements of the form

IF TRLE THE ltactiongt

For data acquisition the action may be a system primitive that triggers prompting and input from

the user For data initiali8tion the action can be an assertion of the form [variablename value]

61 Rule groups as objects

It is profitable to view rule groups as instances in an object-oriented world such as the Flavors

system [Weinreb 1980] A rule group thus consists of values to instance variables along with

method procedures defining computations over rule groups Both instance variable and method

definitions may be inherited from a hierarchy of superclasses

The rules in a rule group are assigned as a list to the rgCONT AI~ED-RCLES instance

variable where rg is the name of the rule group and the double colon sets off an internal symbol

within the rg structure The control scheme is embodied in the method rgoo where rg is again the

name of the rule group and the single colon sets off an external symbol within the rg structure

The 00 method may be inherited or it may be unique to a particular rule group

By object-oriented design a rule is also cast as an object but of a different type A rule

(simplified to our purposes here) is an object with three basic parts a condition an action and

strength-of-inference parameters The condition part is an object having among other things a

method condEVALLATE for evaluating the degree of satisfaction of the condition The action

part is an object having a method actoo for performing conjunctive actions (by invoking DO for

each conjunct object) In this way rules containing rule group names in their left hand side fit well

the standard rule semantics and implementation when application of a rule group is needed its

DO method is invoked

11

A rule groups 00 method contains its control scheme-either a non-deterministic one or a

deterministic one Thus the activation of the 00 method causes rules to be processed under some

precedence relation In a deterministic 00 the rule (objects) are processed in list order as written

Iterative constructs lead to the recursive application of 00 to the internal parts of the construct

(ie to invoke the rules in the body of the iteration)

Invoking the 00 method for a non-deterministicly scheduled rule group works in the same

way except that the method is the control procedure that dynamically determines rule precedence

and takes rules inmiddot that order rather than definition order Thus the 00 method serves two

purposes

1 it makes operational in an object-driven way the system interpretation of the various

knowledge forms comprising the knowledge base (Le bull it provides the appropriate processing

semantics to each form)

2 it provides a place to store explicit meta-knowledge for each rule group that is separate from

the knowledge itself The one mechanism provides the full range of possibilities depicted in

Fig 3

jow let us consider the encoding of the 00 method itself While the practiced LISP programmer

would immediately think if it as just a LISP function or an attached procedure another interesting

possibility exists the 00 method could be a rule group When thinking of the 00 method as a

rule group it would seem obvious that circularity of methods should be avoided since execution of

a rule group requires another 00 method to schedule the rules

Assume that purely deterministic rule groups have a system defined [)() method that is not

another rule group Such rule groups can then be used (in a procedural way) to define 00 methods

for other rule groups Thus non-deterministic control schemes may be written within the language

of the knowledge system as deterministic rule groups When control schemes are written as rule

groups inference over control logic becomes possible for better understanding the control metashy

knowledge and for its optimization revision and consistency and completeness checking

12

Whether to code 00 methods as LISP procedures or as rule groups in the knowledge base

depends on the perceived balance of processing speed against knowledge engineer control and

understanding It would seem likely that some special kinds of expertise would sometimes require

adapting the control scheme in a problem dependent way The mechanism of method based rule

group control schemes has this flexibility

7 Conclusion

The rule group construct provides a knowledge block for structuring rules in large complex

knowledge bases The rule group focuses the knowledge engineer on knowledge subsets that solve

application subproblems Annotation of the rule group by the object-oriented scheme of inherited

methods provides a powerful way to use both implicit non-deterministic control strategies with

explicit deterministic control strategies The latter form has all the power of contemporary

programming languages and can even be used to procedurally describe the inference control scheme

applied to non-deterministic rule groups In an object-oriented approach the various control

strategies are alternative bodies for a rule groups fX) method

The benefits of this approach to rule precedence control are

bull separation of knowledge and control (meta) knowledge consistency and completeness

checking is made easier interpretation of the rule is not confused by myriad special side

effects otherwise needed to control rule firing order

bull more flexible control strategies each rule group in the knowledge base may have its own

most appropriate control strategy applied to the rules within it

bull built-in and knowledge engineer defined control schemes the knowledge engineer may use

either a built-in (underlying languaged coded) control scheme for a common strategy or he

may use a specially defined (rule language coded) control scheme for special effect

The object-oriented approach to separate but yet linked knowledge and control can be applied to

expert systems in many ways TheOO method from the previous section was said to operate both

13

with rule group objects and with rule objects This gives rise to further flexibility evaluation and

application schemes for rules that can be system or knowledge engineer defined Current research

on the ADVISE tool for building expert systems involves developing this approach

Precedence control (obtained via explicit or implicit control schemes) serves to increase the

efficiency of the human user of the system and of the system itself By specifying intelligent

precedences over data acquisition the dialogue between the machine and the user better serves the

user By specifying intelligent precedences over high level rule groups the basic subproblem

solution strategy is better captured making the system focus more keenly on the users type of

problem By specifying appropriate precedences over rules within each rule group the system

applies the scheme that is most efficient for that set of rules as determined by the knowledge

engineer for a particular problem By specifying appropriate precedences over elements within the

left- and right-hand sides of rules the system can more efficiently process the rule without

compromising any problem implied rule semantics or side effects

In a nutshell knowledge is power and power requires control The techniques outlined here

provide flexible new approaches for managing large complex expert systems

8 References

Bleich HL Computer-based consultation tmerican Journal of Medicine Vol 53 Pp 285-291 1972

Collins A and Michalski RSbull The logic of plausible reasoning A core theory Cognitive Science Vol 11 1987

Ginsberg A Weiss Sbull and Politakis P SEEK2 A generalized approach to automatic knowledge base refinement Proc of the Ninth l1Uem Jvint Con on Arliftcio1 l1Uelligence Los Angeles CA Pp 367-374 1985

Gordon J and Shortliffe E A Method for ylanaging Evidential Reasoning in a Hierarchical Hypothesis Space Artiftciallntelligence Vol 26 Pp 323-357 1985

Ylkhalski RS and Baskin AB 1ntegrating Multiple Knowledge Representations and Learning Capabilities in an Expert System Proceedings of Intern Joiru Conf on Arriftcial Intelligence Pp 256-258 1983

14

Srackman K bull A Program for Machine Learning of Counting Criteria Computer Methods and Programs in Biomedicine Vol 21 Pp 221-226 1985

Sridharan~ Evolving Systems of Knowledge AI Maga=ine Pp IOS-120 Fall 1985

Weinreb D and Ioon D Flavors Iesiage Passing in the Lisp Machine lemo 602 MIT AI Lab Cambridge 1A ~ovember 1980

IS

1 Introduction

The now common paradigm of expert systems evolved from the inadequacies of purely

procedural approaches to building problem solving systems Human expertise expressed as

procedures (eg as conventional computer programs) was sufficient when available in complete

detail [Bleich 1972] but such problem solving knowledge is very difficult to acquire critique

refine and interpret The modularized structure provided by production rules their improved ease

of interpretation and critiquing and their non-procedural deductive evaluation made them much

more effident than procedural languages for building large problem solving systems

The very concise non-deterministic statement of rule scheduling that makes non-procedural

knowledge bases easier to build leads to problems when domain specific procedural knowledge

needs to be taken into account The difficulty presently experienced is the unpredictability of rule

firing order as it affects problem decomposition the acquisition of data and search effort

Knowledge engineers presently need to handcraft clever rules that affect rule precedence (order of

use) as side effects of the way they fit in the inference chains Such rules require great skill to

write and they are very difficult to interpret because they do not contain domain expertise but

engineering tricks to make the non-procedural approach have a procedural effect The indirect

encoding of this procedural information effectively obscures it in much the same way that encoding

knowledge directly in program code obscured it in the past

The above observations are important because experience with expert systems has shown that

the bottleneck is the acqUisition and refinement of knowledge [Ginsberg Weiss and Politakis

1985] Knowledge acquisition aids have grown in importance including the development of

intelligent knowledge engineering tools to search and edit large complex knowledge bases and the

application of inductive inference techniques to the knowledge acquisition task The hurden of

maintaining massive knowledge bases has also led to new design ideas for further structuring the

knowledge Even with these aids the acquiSition and management of expertise still demands a

formalism that makes plain those parts of the knowledge that encode domain expertise and those

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