Post on 25-Jun-2020
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