RuleML Technical Webinar

1. RuleML Telecon – Nov.27th, 2009
Degrees (of freedom)
in Uncertain Reasoning
Davide Sottara
DEIS, Faculty of Engineering, University of Bologna
40100 Bologna (BO), Italy
davide.sottara2@unibo.it
ENEA

2. Imperfect Information
Different types of “afflictions”:
 Reliability (Confidence)
• E.g.: Temperature = 25° ( = 70/100)
 Measures the “strength” of the estimate
 (Conflicting) alternatives may be considered
 Uncertainty, proper (Probability, “prior”)
Both subjective (bayesian) and objective (frequentist)
• E.g.: Temperature = 25° ( = 70%)
 Temperature is expected to be (precisely) 25°
 May be completely different
 Vagueness (Fuzzy, “posterior”)
• E.g.: Temperature ≈ 25° ( = 0.7)
 The value, e.g. 22°, is known to be “similar” to 25°.
 Data known precisely, but expressed vaguely.
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3. Simple Examples
rule "Bet - Fuzzy"
when
$b: Bet( $a : amount is high, $n : number )
Extraction( outcome == $n )
then
insert(new Win($a),”very high”);
end
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4. Simple Examples
rule "Bet - Fuzzy"
when
rule "Bet - Probabilistic"
$b: Bet( $a : amount is high, $n : number )
when
Extraction( outcome == $n ): number )
$b: Bet( $a : amount, $n
then Extraction( outcome == $n )
insert(new Win($a),”very high”);
then
end gain = $a / 
end
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5. Simple Examples
rule "Bet - Fuzzy"
when
rule "Bet - Probabilistic"
$b: Bet( $a : amount is high, $n : number )
when
rule "Bet - Mixed"
Extraction( outcome == $n ): number )
$b: Bet( $a : amount, $n
when
then Extraction( outcome == $n high, $n : number )
$b: Bet( $a : amount is )
insert(new Extraction( outcome”); $n )
then neg Win($a),”very high ==
end gain = $a / 
then
end ExpectedRisk r = ...
end
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6. vs
Benefits Drawbacks
 Robustness  Complexity
 Handle Inaccurate inputs  In writing rules
 Avoid arbitrary thresholds  In evaluating rules
 Convenience  Coherence
 Knowledge is rarely precise  Maintain soundness
 Conciseness
 Compact expressions
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7. Expressing Imperfection
Damasio, Pan, Stoilos & Straccia (2008)
 Different non-boolean rules can be encoded
 Generalize the idea of (truth) degree
 Generalize the idea of logic operator
Their work has led to fuzzyRuleML
What about Evaluation?
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8. (Truth) Degrees
 Different models generalize {T,F}
 High order models may combine different types
 Real Value [0,1]
0 1
“false” “true”
 Interval [0,1]2
0 1
“false” “true”
 Distribution [0,1] → [0,1] 0 1
 Type II fuzzy set “false” “true”
 Imprecise Distribution [0,1] → [0,1]3 0 1
 Type III fuzzy set “false” “true”
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9. Evaluators
 Predicates are no longer “just” true (or false)
Information may come from different sources:
 Facts : “a priori” information ⇒ ⇒
 Embedded Evaluator
• Possibly external
 Rules : chaining
Age > 18
 Degrees have to be merged (∩ )
 May be missing* (⊘)
 May be discounted* () by confidence
 May override* others ()
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10. Operators
 Literal and Logical Evaluators (Operators) are configurable
 Implementation kind* chosen individually
• With default*
• Refined using arguments*
Bet( $a : amount is high, $n : number
Extraction( value == 3 )
amount
α ⊗ ∧ $n high isA
number Bet
value
α ⊗ =3 isA
Extract
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11. Full Entailment
 Generalized
α
Propagation* policy
 “Propagate iff true” not suitable
β
α
⊗
β
 Implication is evaluated
→
 Modus Ponens is evaluated
⇒
 Using Premise and Implication
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12. Engine extension
 Core component : Factory
 Builds Degrees
 Builds (coherent) Operators
 Provides Propagation Policy
• PASS, HOLD, DROP
 Provides Merge Strategy
• Handles missing values
• Discounts and Overrides
Attributes are passed to the factory
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13. f-RuleML Attributes / 1
 @degree
 Applies-to : Evaluators, Operators, Rules
 Value : any
 Role : prior, constant value (may be merged with
other contributions)
 Factory: parses the value to return a Degree
 @kind
 Applies-to : Operators, (Evaluators), Rules
 Value : depends on logic family
 Role : select the type of operator
 Factory: chooses the actual implementation
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14. f-RuleML Attributes / 2
 @args
 Applies-to : Evaluators, (Operators), (Rules)
 Value : String
 Role : additional initialization parameters for the
evaluator / operator
 Factory: passes the String to the constructor
 @default
 Applies-to : Operators, Evaluators, Rules
 Value : n.a.
 Role : forces the default options
 Factory: ignores other initialization parameters
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15. Examples / 1
rule "Attr1"
when
Toss ( side == @[ degree=0.5 ] “heads”)
then
// ...
end rule "Attr2"
when
Coin( weight
< @[args=”tol=0.2,unit=g”]
10 ])
or @[ kind=”Max” ]
Dice( faces == 4)
then ... end
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16. f-RuleML Attributes / 3
 @id
 Applies-to : Evaluators, Operators
 Value : ID
 Role : unique identifier.
May be used to chain rules
(i.e. a rule entails the truth of a constraint)
 Factory: n.a.
 @filter
 Applies-to : Operators, Evaluators, Rules
 Value : *
 Role : selects the rule-propagation strategy
 Factory: chooses the actual implementation
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17. f-RuleML Attributes / 4
 @boolean
 Applies-to : Evaluators, Operators, Rules
 Value : “true” | “false” (optional)
 Role : the result is approximated with a boolean
 Factory: casts the actual Degree to a Degree
modelling T (resp. F)
 @crisp
 Applies-to : Operators, Evaluators, Rules
 Value : “true” | “false” (optional)
 Role : forces the canonical evaluation
 Factory: the result is cast to boolean and
propagation is halted on false
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18. Examples / 2
rule "Attr3"
when
$c : Coin( )
Toss ( coin == @[ crisp] $c )
then
insert($c,”id_lucky”)
end
rule "Attr4"
when
$c : Coin( this
is @[ id=”id_lucky”] “lucky”)
then
...
end
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19. f-RuleML Attributes / 5
 @merge
 Applies-to : Evaluators, Operators, Rules
 Value : *
 Role : Degree fusion strategy
 Factory: chooses the actual implementation
 @missing
 Applies-to : Evaluators, Operators, Rules
 Value : *
 Role : Missing value completion strategy
 Factory: chooses the actual implementation
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20. f-RuleML Attributes / 5
 @override
 Applies-to : Evaluators, Operators, Rules
 Value : *
 Role : “Defeat” degree strategy
 Factory: chooses the actual implementation
 @discount
 Applies-to : Evaluators, Operators, Rules
 Value : *
 Role : Confidence-based strategy
 Factory: chooses the actual implementation
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21. Examples / 3
rule "Attr5"
when
Toss( side == “heads”,
this
is @[ degree=”[0.4,0.6]”,
merge=”Intersect”,
missing=”OWA” ]
“probable” )
then
...
end
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22. Work–in–progress
 Extending RETE:
Evaluator
(@kind,
@id @args)
@filter
∩,,⊘
Degree[ ]
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23. Conclusions
 f-RuleML supports Imperfect Rules:
 Rules define the abstract constraints
 Attributes specify the concrete semantics
 Evaluation requires more customizations
 Additional attributes can be used
 Different logics can be used by setting the
default values appropriately
 Individual rules can override them
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