Functional Reasoning, Explanation and Analysis: A Collective View and A Proposal

Transcription

1 Functional Reasoning, Explanation and Analysis: A Collective View and A Proposal Behrouz HOMAYOUN FAR Department of Information and Computer Sciences Saitama University, Japan

2 Contents 1. Introduction. Functional reasoning research 3. Qualitative Function Formation (QFF) 4. Functional design using QFF 5. Implementation perspective 6. Discussion & Conclusion

3 Chapter 1 : Introduction

4 Skill-based (autonomus) level Prior experiences Three levels of human cognitive processes Rule-based (associative) level Information processes Basic Knowledge Analogy, deduction, induction, etc. Knowledge-based (cognitive) level Time spent Search Comparison

5 Factors affecting "cognitive overload" of human designer : 1. Information accessibility Information for decision making inferred along causal chains;. Control directness Initiating actions whose effects propagate on causal chains to a target variable 3. Counter-intuition Anticipating system behavior limited by: - Nonlinearities in device model; - Neglecting influence of overlapping procedures; - Unanticipated timing and coordination of events;

6 Definition: Function & Functional reasoning 1. Function Function 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). "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. ". Functional reasoning: [BOBROW 84] Functional reasoning enables people to reason about : Presence and function of objects in a containing system; Derive the purpose of the system; Explain how it can be achieved;

7 Chapter : Functional reasoning research

8 Functional Reasoning Research-1 Artificial Intelligence Explanation; Planning and Design; Conceptualization; Teleology; Means-End Analysis; ALLAN 5 BECKNER 69 NAGEL 77 Explaining existence of organs in an organism; HEMPEL 59 CANFIELD 64 WRIGHT 73 CUMMINS 74 Philosophy Biology

9 Planning and Design Methods Functional Reasoning Research- PU 88 MURAKAMI 88 ULRICH 88 CHANDRASEKARAN 90 BRADSHAW 91 IWASAKI 9 Explanation Based Methods FRANKE 91 DORMOY 88 DEKLEER 84 FALTINGS 87 JOSKOWICZ 87 FINK 87 ABU-HANNA 91 PUNCH 9 TEZZA 88 BYLANDER 85 SEMBUGAMOORTHY 86 SHEKAR 90 KEUNEKE 91 FAR 91 Conceptualization Methods

10 Functional Reasoning Problems 1. Identification Problem : Explaining function of a device using knowledge of structure and behavior of components;. Explanation Problem : Explaining presence of a component in a system in terms of its contribution to function of the system; 3. Selection Problem : Selecting a set of components that if used together can achieve a desired function; 4. Verification problem : Verifying whether an object can exhibit a given function in a given situation;

11 Functional Reasoning Assumptions-1 1. Functionality in State Transition a. 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 : Function concepts are defined with reference to discovering an order in the state sequence S1 S S3 Sn Function

12 Functional Reasoning Assumptions-. Functionality in Component Pair Defining function concepts in terms of interaction between pairs of components; Locality of Histories [HAYES 79]; Connectivity Hypothesis [FORBUS 87]; Paiwise Interaction of Parts [FALTINGS 87]; C1 Component C1 C4 Interaction Function C3 C Component C

13 Chapter 3 : Qualitative Function Formation (QFF) Technique

14 Qualitative Modeling Concepts 1. Qualitative Model. Qualitative Flow Graph (QFG) 3. Qualitative Process (QP) 4. Behavioral Fragment (BF)

15 Qualitative Function Formation: Qualitative Modeling The conventional qualitative model is extended to include physical and protocol based interactions. Qualitative Model (QM) : i [Y] = O[X] D L N [Y] = O[X] D O[Z] O = {M+, M-, I+, I- } D = { when, until, default, set, resert } Qualitative Process (QP): String of connected arcs of the graph representation of QM. Behavioral Fragment (BF): Characteristic behavior of the qualitative processes. Derived by: a. Dependency constraint satisfaction; b. Landmark value identification; Repetition Cycle: Repetitive behavior of the qualitative variables.

16 Clock and Dependency Constraints For each qualitative operation "clock" and "dependency" constraints are defined and evaluated to a mod-3 integer. 1. Present ( +- 1): Two events occure concurently;. Absent (0) : Two events do not occure concurently; 3. True (+1): An event has accured; 4. False (-1): An event has not yet occured; QFF expression Clock constraint Dependency constraint [Y] = O[X] + O[Z] i [Y] = O[X] when L N i [Y] = O[X] until L N (y = x ) or y = x (-n -n ) y = x (-n) (y = z ) y : [X] O [Y] y : [Z] O [Y] y : [X] O [Y] y : [X] O [Y] [Y] = O[X] default O[Z] i [Y] = O[X] set L N i [Y] = O[X] reset L N y = x + z (1 - x ) x : [X] O [Y] z (1-x ) : [Z] O [Y] y = x (-n -n ) y : [X] O [Y] y = x (-n) y : [X] O [Y]

17 Qualitative Flow Graph (QFG) QFG is a digraph represented by 4 sets: QFG = { V, A, O, C} V : nodes (qualitative variables) A : arcs (qualitative relations) A : C ---> O O : 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. -

18 EXAMPLE : Pressure Tank System Material Supply K U CV3 CV6 T S1 E1 Liquid A Liquid B T1 Liquid A T4 CV1 Compressed air F1 CV5 G1 J1 N1 To reservoir F tank CV4 CV G U1 K1 To reservoir tank Liquid C T3 Liquid C Liquid D To reservoir tank Pressure Tank

19 K To other subsystems Dependency Constraints: CV3 : CV1 : Ω U F cv3 cv1 <3> M + 1 M + Ω G F <1> M + <7> <8> M + out/t1 in/t1 I - M - F 1 I + M + H A/T F out/t F T1 I + M + H T1 H T <1> : <> : <3> : cv cv3 <7> : u ω ( ω ω ) cv4 cv3 cv cv3 <4> : ω ( ω ω ) <5> : <6> : cv1 ω ( ω ω ) ω ( ω ω ) cv5 cv1 cv cv4 cv4 ( ω ω ) cv3 cv1 ω ( ω ω ) cv6 cv5 cv5 ω ( ω ω ) g cv6 cv6 cv3 <8> : ( ω ω ) cv1 cv1 CV : Ω cv <> M + U 1 I - I + H B/T M + I + K 1 To other subsystems CV6 : Ω E F cv6 <6> M + 1 M + in/t P T1 I + A in/t1 CV4 : Ω cv4 <4> M + G I + I + A out/t I - P 1 M + P T CV5 : Ω N P cv5 <5> M + 1 I - M + I + J 1 To other subsystems

20 Qualitative Process (QP) A qualitative process (QP) is a unidirectional finite sequence of Nodes (qualitative variables) of QFG connected by Conditional arcs (qualitative relations)

21 Qualitative Behavioral Fragment (BF) "Behavioral Fragment" is the record of landmark values for qualitative variables of a qualitative process.. 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.

22 Qualitative Behavioral Fragment (BF) - 1. The simulator looks for the antecedents of conditional arcs of a qualitative process.. Only active qualitative processes can take part in simulation. 3. By clock and dependency analysis the active processes are identified. 4. A conventional qualitative simulation program derives landmark value for the qualitative variables of active processes.

23 Qualitative Function Concept 1. A "Function" is derived if a repetition cycle or persistence in the sequence of states is detected on "Behavioral Fragment".. Function has two attributes: a. Operationality b. Repetition cycle

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

25 Repetition Cycle in Qualitative Behavior 1. Repetition cycle is defined for the variables of qualitative state vector.. 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.

26 Qualitative Function Formation Technique Modeling interacting component pairs: (QM, QFG, QP) Qualitative Simulation Behavior of the processes: Behavioral Fragments (BFs) QM, QFG: QP: Qualitative Model and Qualitative Flow Graph showing the viewpoint based on which interactions are modeled, including timing and coordination of events; Qualitative Processes addressing mechanisms in component pair; Qualitative Function Formation (QFF) Function QFF: Qualitative Function Formation detecting regularity in behavior of component pairs;

27 Chapter 4 : Functional Design Using QFF

28 EXAMPLE : Pressure Tank System Material Supply K U CV3 CV6 T S1 E1 Liquid A Liquid B T1 Liquid A T4 CV1 Compressed air F1 CV5 G1 J1 N1 To reservoir F tank CV4 CV G U1 K1 To reservoir tank Liquid C T3 Liquid C Liquid D To reservoir tank Pressure Tank

29 EXAMPLE : Identification of Functions <The pressure tank system> J1 CV5 Supply S1 E1 CV6 N1 T Liquid A Liquid B F F1 CV4 CV1 G G1 To reservoir tank Pressure Tank T1 Liquid A U1 K1 U K CV CV3 Recycle To reservoir tank P"1 : P1 : Dependency Constraints [Ω ] [U ] [F ] cv3 [Ω ] cv1 <1> : <> : <1> M + M + M + cv3 [G ] ω ( ω ω ) out/t1 <> <3> <7> cv3 cv3 [F ] M - [F ] T1 I + [F ] 1 in/t1 T1 <4> <5> <6> <7> u out/t1 M + M + I + ( ω ω ) cv3 <3> : f (1-f ) <4> : cv1 [H ] T1 [H ] T1 ω ( ω ω ) cv1 cv1 <5> : g ( ω ω ) cv3 cv1 cv1 <6> : f <7> : h in/t1 in/t1 T1 Process model of the tank T1 and valves CV1 and CV3

30 EXAMPLE : Functional Explanation <The pressure tank system> J1 CV5 Supply S1 E1 CV6 N1 T Liquid A Liquid B F F1 CV4 CV1 G G1 To reservoir tank Pressure Tank T1 Liquid A U1 K1 U K CV CV3 Recycle To reservoir tank P : P3 : P4 : [Ω ] [U ] [F ] cv [Ω ] cv <1 > 1 <4 > out/t M + I + [U ] [H ] 1 B/T <1 > < > <3 > M + I - M + [Ω ] [U ] [K ] cv <1 > M + 1 Process model of the valve CV 1 [H ] T <1 > : Dependency Constraints cv ω ( ω ω ) < > : u 1 <3 > : h T <4 > : f out/t cv cv ( ω ω ) cv cv

31 Φ max Φ Φ max Φ min <Qualitative Model of the devices> [F] <1> : f (-x-x ) [G] P1: P: P3: P4: [F] [F] [F] [F] <1> M - I + <> M + I - <4> <5> : I + <3> I + <4> I - <> M + M - <3> [Φ] [Φ] [Φ] [G] [G] I + I + <> : <3> : f ( φ φ ) (-v) <5> <1> <5> max <4> : f ( φ φ )(-u) <5> : f (-y-y ) max max max g (-w-w ) ( φ ) max g (-w-w ) ( φ ) min [Φ] [Φ]

32 Chapter 5 : Implementation perspective

33 Implementation 1. Qualitative Function Formation tool. Experimental design system QFF

34 Overview of the system Library of component models Designer s goals Design input Design knowledge-base QFF reasoning engine Design output Experimental Design System QFF

35 Experimental QFF The prototype system contains: 1. Data translator for converting component model to data structure used in the knowledge base;. Reasoning (inference) engine + learning module; 3. Qualitative simulator; 4. Window-based user interface; The knowledge base contains: 1. Frame representation of component model;. Frame representation of design goals/functions; 3. Frame representation of component pairs; 4. Frame representation of customized components;

36 A Simple Component Model [F1] P1 CV1 [G1] Control Valve Model P 11 COMPONENT CV1; 1 INPUT F1; 13 CONNECT P1,CV1; 14 OUTPUT G1; 15 CONNECT CV1,P; 14 STATE S1; 15 CONDITION 16 TASK (F1 = G1); 17 ENDSTATE S1; 18 NEXTSTATE S; 19 STATE S; 0 CONDITION 1 TASK (G1 = 0); ENDSTATE S; 3 STOP; (ω >0); CV1 (ω =0); CV1

37 Frame Representation of Component Model [F1] P1 CV1 [G1] Control Valve Model P @Parts #methods #end_methods ) #ps CV1 P1 (F1) P (G1) (ω S1 CV1 >0); (ω S CV1 =0); Null slots methods

38 Frame Representation of a Device BLOCK 1 COMPONENTS 1 #PS SYSTEM 1 BLOCK... COMPONENTS... TANK_T TANK TANK_T1 VALVE_CV6 VALVE VALVE_CV5 VALVE_CV4 VALVE_CV3 VALVE_CV VALVE_CV1 Class Objects Instance Objects (Tank #ps (Tank P1 (Valve #ps (Valve CV1 S1 (Valve @Condition_1 S1 (Valve@Variables_1 (F1) CV CV1 CV1 P1 S1 (ω ) S1 S (ω @Condition_1 (F1) S1 P1 (G1) S (ω CV1 @Parts (F1) S1 S (ω >0); (G1) #methods Null S1 S (ω >0); (G1) CV1 @Condition_ #methods S (ω #end_methods (ω Null #methods #end_methods ) (ω =0); #methods #end_methods ) Null ) #methods #end_methods ) #end_methods #end_methods ) )

39 Frame Representation of Component Pairs #PS SYSTEM 1 COMP. PAIRS T, CV6 T, CV5 T, CV4 T, CV T, CV1 T, other T1, CV4 T1, CV3 T1, CV1 T1, other @Connect #methods #ps PP (CV,T) Ω CV H (,U1,K1, B/T H, T Fout/T, ) #ps PP1 (CV,T) ( Ω CV,U1,K1, H, H, F ) B/T T out/t Derived function using QFF #end_methods ) #end_methods ) Qualitative model

40 Experimental Design System QFF New & revised Input Design Input Input Pre-processing (#INPUT_TO_FRAME) Input frame structure Learning (#LEARN) Version library frame structure Functional Reasoning (#QFF) Check Design goals/ functions Component pair frame structure Function frame structure Goal Pre-processing (#GOAL_TO_FRAME) Customization (#ADJUSTMENT) Output frame structure Output Post-processing (#FRAME_TO_OUTPUT) Design Output

41 A Simple Component Model [F1] P1 CV1 [G1] P Iconic model of a control valve 11 COMPONENT CV1; 1 INPUT F1; 13 CONNECT P1,CV1; 14 OUTPUT G1; 15 CONNECT CV1,P; 14 STATE S1; 15 CONDITION (ω >0); CV1 16 TASK (F1 = G1); 17 ENDSTATE S1; 18 NEXTSTATE S; (ω =0); 19 STATE S; CV1 0 CONDITION 1 TASK (G1 = 0); ENDSTATE S; 3 STOP; @Connect_ #methods method M1( ) method M( ) #methods_end ) #ps CV1 P1 (F1) P (G1) S1 (ω CV1>0) S (ω CV1=0) Null slots methods Design input code

42 Implementation Perspective Designer Preliminary Arrangement has_parts Desired Goal/ Function has_subfunction Sub- Function has_input Interface has_joint has_version Component Pairs has_version Version Library has_function has_model Derived Function has_function Qualitative Model has_input Compare Qualitative Simulator has_record Component Library has_option has_value: Temporal & Dependency Constraints Designer s Decision: (when, until, set, reset, default) has_record has_question has_answer has_effect_on Designer Question addes_to Customized Component Design Document

43 Conclusion 1. Surveying functional reasoning research. Function formation technique (QFF): 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; 3. Implementation : Implementing QFF in an experimental design tool 4. Future works : a. Formalization of design input/output b. Automatic generation of qualitative model c. Implementing analogical learning d. Application to fault diagnosis and tool utilization