Functional Reasoning,Explanation and Analysis:

A Collective View and A Proposal

Behrouz HOMAYOUN FAR

Department of Information and Computer SciencesSaitama University, Japan

Contents

1. Introduction

5. Implementation perspective

3. Qualitative Function Formation (QFF)

4. Functional design using QFF

6. Discussion & Conclusion

2. Functional reasoning research

Introduction

Chapter 1 :

Three levels of human cognitive processes

BasicKnowledge

Timespent

Priorexperiences

Information processes

Analogy, deduction, induction, etc.

Search

Comparison

Knowledge-based(cognitive)

level

Knowledge-based(cognitive)

level

Skill-based(autonomus)

level

Skill-based(autonomus)

level

Rule-based(associative)

level

Rule-based(associative)

level

Factors affecting "cognitive overload" of human designer :

1. Information accessibility

2. Control directness

3. Counter-intuition

Information for decision making inferred along causal chains;

Initiating actions whose effects propagate on causal chains to a target variable

Anticipating system behavior limited by: - Nonlinearities in device model; - Neglecting influence of overlapping procedures; - Unanticipated timing and coordination of events;

Definition: Function & Functional reasoning

1. FunctionFunction is usually mentioned together with "behavior" , "goal" or "purpose".Making effort to obtain a certain "result" or "good".Tied with intention of humans (in design).

Functional reasoning enables people to reason about :

2. Functional reasoning:

Presence and function of objects in a containing system;Derive the purpose of the system;Explain how it can be achieved;

"Function is a relation between the goal of a human user and the behavior of a system. In an assembly, the function of a component relates the behavior of that component to the function of the assembly. "

[BOBROW 84]

Chapter 2 :

Functional reasoningresearch

Explanation;Planning and Design;Conceptualization;

Artificial Intelligence

Biology

Functional Reasoning Research-1

ALLAN’ 52BECKNER’ 69NAGEL’ 77

Philosophy

HEMPEL’ 59CANFIELD’ 64 WRIGHT’ 73 CUMMINS’ 74

Explaining existence oforgans in an organism;

Teleology;Means-End Analysis;

DEKLEER’ 84FALTINGS’ 87JOSKOWICZ’ 87FINK’ 87ABU-HANNA’ 91PUNCH’ 92

PU’ 88MURAKAMI’ 88ULRICH’ 88CHANDRASEKARAN’ 90BRADSHAW’ 91 IWASAKI’ 92

SEMBUGAMOORTHY’ 86SHEKAR’ 90KEUNEKE’ 91FAR’ 91

BYLANDER’ 85FRANKE’ 91DORMOY’ 88

Pla

nnin

g an

d D

esig

n M

etho

ds

Con

cept

ualiz

atio

n M

etho

ds

Explanation Based Methods

Functional Reasoning Research-2

TE

ZZ

A’ 8

8

Functional Reasoning Problems

1. Identification Problem :

2. Explanation Problem :

3. Selection Problem :

4. Verification problem :

Explaining function of a device using knowledge of structure and behavior of components;

Explaining presence of a component in a system in terms of its contribution to function of the system;

Selecting a set of components that if used together can achieve a desired function;

Verifying whether an object can exhibit a given function in a given situation;

Functional Reasoning Assumptions-1

1. Functionality in State Transitiona. A physical phenomena can be explained in terms of ‘histories’ and ‘states’ [HAYES 79];b. History that leads to a function displays certain patterns [BIGELOW87];c. A state representation addresses a certain characteristic of ite refered object [MATTEN 88];Therefore :

S1 S2 S3 Sn

Function concepts are defined with reference to discovering an order in the state sequence

Function

2. Functionality in Component PairDefining function concepts in terms of interactionbetween pairs of components; Locality of Histories [HAYES 79]; Connectivity Hypothesis [FORBUS 87]; Paiwise Interaction of Parts [FALTINGS 87];

Functional Reasoning Assumptions-2

Component C1 Component C2

Function

InteractionC1

C4 C3

C2

Qualitative FunctionFormation (QFF)Technique

Chapter 3 :

Qualitative Modeling Concepts

2. Qualitative Flow Graph (QFG)

3. Qualitative Process (QP)

4. Behavioral Fragment (BF)

1. Qualitative Model

Qualitative Function Formation:Qualitative Modeling

The conventional qualitative model is extended to includephysical and protocol based interactions.

Qualitative Process (QP):String of connected arcs of the graph representation of QM.

Characteristic behavior of the qualitative processes.Derived by: a. Dependency constraint satisfaction; b. Landmark value identification;

Behavioral Fragment (BF):

Repetition Cycle:Repetitive behavior of the qualitative variables.

Qualitative Model (QM) :

Ni

[Y] = O[X] ‘D’ L

[Y] = O[X] ‘D’ O[Z]

O = M+ , M- , I+ , I-

D = ‘when’ , ‘until’ , ‘default’ , ‘set’ , ‘resert’

QFF expression Clock constraint Dependency constraint

[Y] = O[X] + O[Z]

[Y] = O[X] ‘when’ LN

i

[Y] = O[X] ‘until’ LN

i

[Y] = O[X] ‘default’ O[Z]

(y = x ) or22

y = x (-n -n )22 2

y = x (-n)22

2 y = x + z (1 - x )22 2

y : [X] O [Y]2

y : [X] O [Y]2

y : [X] O [Y]2

x : [X] O [Y]2

y : [Z] O [Y]2

z (1-x ) : [Z] O [Y]2 2

(y = z )22

Clock and Dependency Constraints

[Y] = O[X] ‘set’ LN

i y = x (-n -n )22 2 y : [X] O [Y]2

[Y] = O[X] ‘reset’ LN

i y = x (-n)22 y : [X] O [Y]2

For each qualitative operation "clock" and "dependency" constraints are defined and evaluated to a mod-3 integer.

1. Present ( 1): Two events occure concurently;

2. Absent (0) : Two events do not occure concurently;

3. True (+1): An event has accured;

4. False (-1): An event has not yet occured;

+-

Qualitative Flow Graph (QFG)

QFG is a digraph represented by 4 sets:

QFG = V, A, O, CV : nodes (qualitative variables)A : arcs (qualitative relations)

A : C ---> OO : ordinary qualitative relations

O = M+ , M- , I+ , I- C : dependency constraints for coordinative qualitative relations

For each A when C is evaluated to either(+1) or (+1) then O is enabled.-

EXAMPLE : Pressure Tank System

G1

J1

N1CV5

S1

E1CV6

F2

G2

F1

U1 K1

U2K2

Pressure Tank

T2

T1

CV4 CV2

CV3

To reservoir tank

To reservoir tank

Material Supply

T4

T3

To reservoir tank

CV1Liquid B

Liquid A

Liquid A

Liquid C

Liquid D

Liquid C

Compressedair

FT1out/T12cv3Ω U F HT1

I +M-M+M+<3>

CV3 :ω (−ω −ω )cv3

2cv3 cv3

2<3> :

<7> :

<4> : ω (−ω −ω )cv42

cv4 cv42

(−ω − ω )22u

cv3 cv32

in/T11cv1Ω G F

M+M+<1>

CV1 :

F1

I +

1cv2Ω U

M+<2>

CV2 :

B/T2H

1K

in/T21cv6Ω E F

M+M+<6>

CV6 :

2cv4Ω G Aout/T2

M+

M+<4>

CV4 :

P1PT2

21cv5Ω N P

M+<5>

CV5 :

HA/T2

HT2

in/T1

PT1

J 1

K2

I -

M+

M+

out/T2F

I -

M+

A

I +

I +

I +

I -

I +

I -M+

To other subsystems

To other subsystems

To other subsystems

I +

I +

ω (−ω −ω )cv22

cv2 cv22

<2> :

ω (−ω −ω )cv12

cv1 cv12

<1> :

ω (−ω −ω )cv52

cv5 cv52

<5> :

ω (−ω −ω )cv62

cv6 cv62

<6> :

<8> : (−ω − ω )22g

cv1 cv12

<8>

<7>

Dependency Constraints:

Qualitative Process (QP)

A qualitative process (QP) is a uni-directional finite sequence of Nodes (qualitative variables) of QFG

connected by Conditional arcs (qualitative relations)

1. "Behavioral Fragment" is the record of landmark values for qualitative variables of a qualitative process.

Qualitative Behavioral Fragment (BF) -1

2. BF is derived by "Qualitative Simulation" in two steps :

a. Dependency constraint satisfaction for the arcs of qualitative process.b. Landmark value identification of qualitative variables.

1. The simulator looks for the antecedents of conditional arcs of a qualitative process.

Qualitative Behavioral Fragment (BF) -2

3. By clock and dependency analysis the active processes are identified.

2. Only active qualitative processes can take part in simulation.

4. A conventional qualitative simulation program derives landmark value for the qualitative variables of active processes.

1. A "Function" is derived if a repetition cycle or persistence in the sequence of states is detected on "Behavioral Fragment".

Qualitative Function Concept

2. Function has two attributes:

a. Operationality

b. Repetition cycle

Operationality is the sum ofenabling conditions for the arcs of qualitative processes whose "Behavioral Fragments" lead to a "Function".

Operationality

1. Repetition cycle is defined for the variables of qualitative state vector.

Repetition Cycle in Qualitative Behavior

2. Qualitative state vector for a component pair is composed of "Landmark values" of the "Behavioral Fragments" for qualitative variables of active processes.

3. Different repetition cycles can be detected each representing a "function" from a different viewpoint.

Qualitative Simulation

Qualitative FunctionFormation (QFF)

Qualitative Processesaddressing mechanisms in component pair;

Qualitative Model andQualitative Flow Graphshowing the viewpointbased on which interactionsare modeled, including timingand coordination of events;

Qualitative Function Forma-tion detecting regularity inbehavior of component pairs;

QP:

QM, QFG:

QFF:

Behavior of the processes:Behavioral Fragments

(BFs)

Function

Qualitative Function Formation Technique

Modeling interactingcomponent pairs:

(QM, QFG, QP)

Chapter 4 :

Functional DesignUsing QFF

EXAMPLE : Pressure Tank System

G1

J1

N1CV5

S1

E1CV6

F2

G2

F1

U1 K1

U2K2

Pressure Tank

T2

T1

CV4 CV2

CV3

To reservoir tank

To reservoir tank

Material Supply

T4

T3

To reservoir tank

CV1Liquid B

Liquid A

Liquid A

Liquid C

Liquid D

Liquid C

Compressedair

[H ]T1out/T12cv3[Ω ] [U ] [F ]

M+ M +

M+

I+

<1>

ω (−ω −ω )cv3 cv3

22cv3<1> :

[F ]T1<2> <3> <7>

M-

M+ M+ I+

[H ]T1<4> <5> <6> <7>

[F ]T1[F ]in/T11[G ]cv1[Ω ]

(−ω −ω )cv3 cv3

222<2> :

ω (−ω −ω )cv1 cv1

22cv1<4> :

(−ω −ω )cv1 cv1

222<5> : gu

2out/T1

<3> : f (1-f )in/T12 <6> : <7> :

in/T12f

T12h

Dependency

Constraints

P"1 :

P1 :

Process model of the tank T1 and valves CV1 and CV3

J1 N1CV5

S1 E1

CV6

F2 G2

F1 G1

U1 K1 U2 K2

Pressure Tank

T2 T1CV4

CV1

CV2 CV3

Recycle

To reservoir tank

To reservoir tank

Supply

Liquid A

Liquid B

Liquid A

<T

he pressure tank system>

EXAMPLE : Identification of Functions

out/T21cv2[Ω ] [U ] [F ]

M+ I +

M+

<1’>

ω (−ω −ω )cv2 cv2

22cv2<1’> :

<4’>

I - M+<1’> <2’> <3’>

[H ]T2[H ]B/T21[U ]cv2[Ω ]

(−ω −ω )cv2 cv2

221

<2’> : u2T2

<3’> : h

<4’> :out/T22f

P2 :

P3 :

Process model of the valve CV2

11cv2[Ω ] [U ] [K ]

M+

<1’>P4 :

J1 N1CV5

S1 E1

CV6

F2 G2

F1 G1

U1 K1 U2 K2

Pressure Tank

T2 T1CV4

CV1

CV2 CV3

Recycle

To reservoir tank

To reservoir tank

Supply

Liquid A

Liquid B

Liquid A

<T

he pressure tank system>

Dependency Constraints

EXAMPLE : Functional Explanation

<Qualitative Model of the devices>

Φmin

Φmax

ΦΦmax

<1> :22

f (-x-x )

<4> : (−φ −φ )max max

22f (-u)

<3> : (−φ −φ )max max

22f (-v)

<2> :22

f (-y-y )

<5> :

22g (-w-w ) (−φ )

max22

g (-w-w ) (−φ )min[Φ]

[Φ]

[Φ]

[Φ]

I+

I+

I+

I-

M+

M-

[F]

[F]

[F]

[F]

[G]

[G]

<3>

<4>

<2>

<1> <5>

<5>

P1:

P2:

P3:

P4:

[Φ]

[F]

[G]

M+

I+

M-I+

I-

<1>

<2> <4>

<3>

<5> :

Chapter 5 :

Implementationperspective

Implementation

1. Qualitative Function Formation tool

2. Experimental design system QFF2

Overview of the system

Designoutput

Experimental Design System QFF2

Design knowledge-base

QFF reasoning engine

Library ofcomponent

models

Designinput

Designer’sgoals

The prototype system contains:1. Data translator for converting component model to data structure used in the knowledge base;2. Reasoning (inference) engine + learning module;

3. Qualitative simulator;

4. Window-based user interface;

The knowledge base contains:1. Frame representation of component model;

3. Frame representation of component pairs;

Experimental QFF2

4. Frame representation of customized components;

2. Frame representation of design goals/functions;

A Simple Component Model

Control ValveModel

[F1]

CV1

[G1]

P1 P2

11 COMPONENT CV1;12 INPUT F1;13 CONNECT P1,CV1;14 OUTPUT G1;15 CONNECT CV1,P2;14 STATE S1;15 CONDITION 16 TASK (F1 = G1);17 ENDSTATE S1;18 NEXTSTATE S2;19 STATE S2;20 CONDITION 21 TASK (G1 = 0);22 ENDSTATE S2;23 STOP;

(ω >0);CV1

(ω =0);CV1

Frame Representation of Component Model

Control ValveModel

[F1]

CV1

[G1]

P1 P2

(Valve CV1 @super_class @name @Connect_1 @Variables_1 @Connect_2 @Variables_2 @State_1 @Condition_1 @State_2 @Condition_2 @Parts#methods

#end_methods)

(ω >0);CV1

(ω =0);CV1

#psCV1P1(F1)P2(G1)S1

S2

Null

slot

sm

etho

ds

(Tank T2

@super_class

@name

@Connect_1

@Variables_1

@Connect_2

@Variables_2

@State_1

@Condition_1

@State_2

@Condition_2

)

#ps

T2

P1

(F1)

P2

(G1)

S1

S2

(Tank T1

@super_class

@name

@Connect_1

@Variables_1

@Connect_2

@Variables_2

@State_1

@Condition_1

@State_2

@Condition_2

)

#ps

T1

P1

(F1)

P2

(G1)

S1

S2

(Valve CV6

@super_class

@name

@Connect_1

@Variables_1

@Connect_2

@Variables_2

@State_1

@Condition_1

@State_2

@Condition_2

@Parts

#methods

#end_methods

)

#ps

CV1

P1

(F1)

P2

(G1)

S1

S2

Null

(ω >0);CV1

(ω =0);CV1

(Valve CV5

@super_class

@name

@Connect_1

@Variables_1

@Connect_2

@Variables_2

@State_1

@Condition_1

@State_2

@Condition_2

@Parts

#methods

#end_methods

)

#ps

CV1

P1

(F1)

P2

(G1)

S1

S2

Null

(ω >0);CV1

(ω =0);CV1

(Valve CV4

@super_class

@name

@Connect_1

@Variables_1

@Connect_2

@Variables_2

@State_1

@Condition_1

@State_2

@Condition_2

@Parts

#methods

#end_methods

)

#ps

CV1

P1

(F1)

P2

(G1)

S1

S2

Null

(ω >0);CV1

(ω =0);CV1

(Valve CV3

@super_class

@name

@Connect_1

@Variables_1

@Connect_2

@Variables_2

@State_1

@Condition_1

@State_2

@Condition_2

@Parts

#methods

#end_methods

)

#ps

CV1

P1

(F1)

P2

(G1)

S1

S2

Null

(ω >0);CV1

(ω =0);CV1

(Valve CV2

@super_class

@name

@Connect_1

@Variables_1

@Connect_2

@Variables_2

@State_1

@Condition_1

@State_2

@Condition_2

@Parts

#methods

#end_methods

)

#ps

CV1

P1

(F1)

P2

(G1)

S1

S2

Null

(ω >0);CV1

(ω =0);CV1

Frame Representation of a Device

Class Objects Instance Objects

VALVE_CV5

TANK_T2

TANK_T1

VALVE_CV6

CO

MP

ON

EN

TS

...

VALVE_CV4

VALVE_CV3

VALVE_CV2

VALVE_CV1

#PS

SY

ST

EM

1

BLO

CK

1B

LOC

K ..

.

CO

MP

ON

EN

TS

1 TANK

VALVE

(Valve CV1

@super_class

@name

@Connect_1

@Variables_1

@Connect_2

@Variables_2

@State_1

@Condition_1

@State_2

@Condition_2

@Parts

#methods

#end_methods

)

#ps

CV1

P1

(F1)

P2

(G1)

S1

S2

Null

(ω >0);CV1

(ω =0);CV1

(Pair PP2

@super_class

@name

@Connect

@Variables

@State_1

@Condition_1

@State_2

@Condition_2

@Function

#methods

#end_methods

)

#ps

PP2

(CV2,T2)

( ,U1,K1, ,

, )

B/T2HT2H out/T2FCV2Ω

Frame Representation of Component Pairs

Der

ived

fu

nct

ion

usi

ng

QF

F

(Pair PP1

@super_class

@name

@Connect

@Variables

@State_1

@Condition_1

@State_2

@Condition_2

@Function

#methods

#end_methods

)

#ps

PP1

(CV2,T2)

( ,U1,K1, ,

, )B/T2H

T2H out/T2FCV2Ω

Qu

alit

ativ

em

odel

T2, CV6T2, CV5T2, CV4T2, CV2T2, CV1T2, other#P

S

SY

ST

EM

1

CO

MP

. PA

IRS

T1, CV4T1, CV3T1, CV1T1, other

Experimental Design System QFF2

DesignInput

DesignOutput

Designgoals/

functions

Version libraryframe structure

Component pairframe structure

Input framestructure

(#LEARN)Learning

Input Pre-processing(#INPUT_TO_FRAME)

Functional Reasoning(#QFF)

Customization(#ADJUSTMENT)

Ou

tpu

t P

ost-

pro

cess

ing

(#FRAME_TO_OUTPUT)

Function frame structure

Check

Goal Pre-processing(#GOAL_TO_FRAME)

Output frame structure

New &revisedInput

11 COMPONENT CV1;12 INPUT F1;13 CONNECT P1,CV1;14 OUTPUT G1;15 CONNECT CV1,P2;14 STATE S1;15 CONDITION 16 TASK (F1 = G1);17 ENDSTATE S1;18 NEXTSTATE S2;19 STATE S2;20 CONDITION 21 TASK (G1 = 0);22 ENDSTATE S2;23 STOP;

(ω >0);CV1

(ω =0);CV1

Iconic model ofa control valve

[F1]

CV1

[G1]

P1 P2

slot

sm

etho

ds

Design input code

(Valve CV1 @super_class @name @Connect_1 @Variables_1 @Connect_2 @Variables_2 @State_1 (when_asked M1()) @Condition_1 @State_2 (when_asked M2()) @Condition_2 @Parts#methods method M1( ) method M2( )#methods_end)

#psCV1P1(F1)P2(G1)S1

S2

Null

(ω >0)CV1

(ω =0)CV1

A Simple Component Model

QualitativeModel

has

_mod

el

has_version

has

_joi

nt

has_record

Designer’sDecision:

(when, until, set, reset, default)

has

_opt

ion

has_value: Temporal & Dependency Constraints

DerivedFunction

has

_fu

nct

ion

PreliminaryArrangement

has_parts

has_function

Desired Goal/Function

has

_su

bfu

nct

ion

Sub-Function

Compare

has_input

has

_in

put

has_effect_on

Inte

rfac

e

QualitativeSimulator

Designer

Designer

ComponentLibrary

ComponentPairs

has

_ver

sion

VersionLibrary

CustomizedComponent

DesignDocumentad

des

_to

has_record

Question

has

_qu

esti

on

has_answer

Implementation Perspective

Conclusion

a. Extending common qualitative models to include interactions and timing of events by defining temporal and dependency constraints;b. Defining function concepts as interpretation of a persistance or a cycle in sequence of qualitative states;

1. Surveying functional reasoning research

3. Implementation :

2. Function formation technique (QFF):

4. Future works :

Implementing QFF in an experimental design tool

a. Formalization of design input/outputb. Automatic generation of qualitative modelc. Implementing analogical learningd. Application to fault diagnosis and tool utilization