Chapter 10: Design and Analysis of PropositionalLogic RuleBased Systems - PowerPoint PPT Presentation
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Chapter 10: Design and Analysis of PropositionalLogic RuleBased Systems
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The RULES section is composed of a finite set of rules each of which is of the form: ... Rule rewriter. State-space analyzer. Special form. recognizer. No independent ... – PowerPoint PPT presentation
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Title: Chapter 10: Design and Analysis of PropositionalLogic RuleBased Systems
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Chapter 10 Design and Analysis of
Propositional-Logic Rule-Based Systems
- Albert M. K. Cheng
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Analysis of Rule-Based Systems
- The RULES section is composed of a finite set of
rules each of which is of the form - a1 b1 ! a2 b2 ! ! am bm
- IF enabling condition
- VAR set of variables on left-hand side of
the assignment, i.e., the ais - VAL expressions on right-hand side of
assignment, i.e., the bis - EC enabling condition
3
Simple Rule-Based Program
- ( 1 ) object_detected true IF sensor_a 1
AND sensor_a_status good - ( 2 ) object_detected true IF sensor_b
1 AND sensor_b_status good - ( 3 ) object_detected false IF sensor_a
0 AND sensor_a_status good - ( 4 ) object_detected false IF sensor_b
0 AND sensor_b_status good
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State Space Representation
C
A
B
L
I
D
J
M
E
F
P
K
H
N
G
FP2
FP3
FP1
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Problem Complexity
- In general, the analysis problem is undecidable
if the program variables can have infinite
domains, i.e., there is no general procedure for
answering all instances of the decision problem.
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Proof Outline
- Any two-counter machine can be encoded by an
equational rule-based program that uses only '
and -' as operations on integer variables and
gt', ' as atomic predicates such that a
two-counter machine accepts an input if and only
if the corresponding equational rule-based
program can reach a fixed point from an initial
condition determined by the input to the
two-counter machine.
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Analysis Problem is Solvable for some Cases
- All the variables of an equational rule-based
program range over finite domains. - Set of variables in VAR and set of variables in
VAL and EC are disjoint. - Enabling conditions are mutually exclusive.
- Only constants are assigned to variables in
VAR.
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Compatibility of Rules
- Let L_x denote the set of variables appearing in
LHS of rule x. - Two rules a and b are said to be compatible iff
at least one of the following conditions holds
- (CR1) Test a and test b are mutually exclusive.
- (CR2) L_a and L_b are disjoint.
- (CR3) Suppose L_a and L_b are not disjoint .
Then for every common variable v in L_a and L_b,
the same expression must be assigned to v in both
rule a and b.
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Special Form A
- Let L and T be sets of variables in VAR and EC of
rules. A set of rules are in special form A if
the following conditions hold - (1) Constant terms are assigned to all the
variables in L. - (2) All of the rules are compatible pairwise.
- (3) L and T are disjoint.
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Example
- 1. a1 true IF b true AND c true
- 2. a1 true IF b true AND c false
- 3. a2 false IF c true
- Rules 1 and 2 are compatible by conditions CR1
and CR3. Rules 1 and 3 are compatible by
condition CR2. Rules 2 and 3 are compatible by
condition CR2.
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General Analysis Strategy
Rule-based program
Special form recognizer
Simpler programs
No independent ruleset in special form
Independent rulsets in special form(s)
Rule rewriter
State-space analyzer
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Example
- input read(b, c)
- 1. a1 true IF b true AND c true
- 2.a1 true IF b true AND c false
- 3.a2 false IF c true
- 4.a3 true IF a1 true AND a2 false
- 5.a4 true IF a1 false AND a2 false
- 6.a4 false IF a1 false AND a2 true
- input read(b, c)
- 1. a1 true IF b true AND c true
- 2.a1 true IF b true AND c false
- 3.a2 false IF c true
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Applications of Analysis Tools
- Cryogenic Hydrogen Pressure Malfunction Procedure
in the Pressure Control System of the Space
Shuttle Vehicle - Integrated Status Assessment Expert System
- Fuel Cell Expert System
- Orbital Maneuvering and Reaction Control System
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