The CHR-based Implementation of the SCIFF Abductive System

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The CHR-based Implementation of the
SCIFFAbductive System

• Marco Gavanelli Università di Ferrara, Italy
• Marco Alberti Universidade nova de Lisboa,
  Portugal
• Evelina Lamma Università di Ferrara, Italy

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Abductive Logic Programming

• ALP lt KB, A, IC gt
• KB logic program (set of clauses)
• A atoms without definitions, can be assumed
• IC Integrity constraints (usually,
  implications)
• KB ? ? - G KB ? ? - IC
• Reasoning from effects to causes

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Diagnosis

• headache- flu.
• headache- period.
• headache- hangover.
• flu, vaccine -gt false.
• hangover -gt drank.
• period, sex(male) -gt false.
• ?- headache.
• Yes, flu More?
• Yes, period

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Event Calculus

• holdsat(Fluent,Time)- initially(Fluent),
  not(clipped(0,Fluent,Time)).
• holdsat(Fluent,Time)- initiates(Action,Fluent),
• happens(Action,T1), not(clipped(T1,Fluent,Time)).
  
• clipped(T1,Fluent,T2)- terminates(Action),
  happens(Action,T), T1ltTltT2.
• initially(f1). initially(f2).

happens(c,7)
happens(a,2)
happens(b,4)
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Abductive Event Calculus

• holdsat(Fluent,Time)- initially(Fluent),
  not(clipped(0,Fluent,Time)).
• holdsat(Fluent,Time)- initiates(Action,Fluent),
• happens(Action,T1), not(clipped(T1,Fluent,Time)).
  
• clipped(T1,Fluent,T2)- terminates(Action),
  happens(Action,T), T1ltTltT2.
• initially(f1). initially(f2).

happens(c,7)
happens(a,2)
happens(b,4)
?

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Sound negation

• p(1).
• p(f(X))- q(X).
• q(2).
• ?- not(p(Y)).
• yes, Y\1, Y\f(2)

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Abduction constraint solvingKowalski, Toni,
Wetzel 98

• headache - flu.
• headache - hangover.
• flu, vaccine -gt false

Constraint Store
?- , headache.
vaccine
Constraint Solver
flu
fail
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Abduction constraint solvingKowalski, Toni,
Wetzel 98

• headache - flu.
• headache - hangover.
• headache - period.
• flu, vaccine -gt false.
• hangover -gt drank.
• period, sex(male) -gt false.

Constraint Store
Constraint Solver
?- , headache.
vaccine
fail
flu
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Constraint Handling Rules (CHR)

• Declarative language for defining constraint
  solvers
• Simplification rules
• c1, c2, ..., cn ltgt guard body
• activated if some constraints in the store match
  with c1, c2, ..., cn and guard is true
• removes c1, c2, ..., cn from the store and
  executes body
• Propagation rules
• c1, c2, ..., cn gt guard body
• activated if some constraints in the store match
  with c1, c2, ..., cn and guard is true
• executes body

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Example leq (less or equal)

• reflexivity_at_ leq(X,X) ltgt true.
• antisymmetry_at_ leq(X,Y), leq(Y,X) ltgt XY.
• transitivity_at_ leq(X,Y), leq(Y,Z) gt leq(X,Z).

leq(A,B), leq(B,C), leq(C,A)
leq(A,B), leq(B,C), leq(C,A), leq(A,C)
leq(A,B), leq(B,A), AC
AB, AC
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Abduction in CHR Abdennadher, Christiansen,
Dahl

• Abducibles mapped to CHR constraints
• headache - flu.
• headache - hangover.
• flu, vaccine -gt false

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Abduction in CHR

• headache - flu.
• headache - ...
• flu, vaccine gt false

Constraint Store
?- , headache.
vaccine
fail
flu
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Abduction in CHR

• headache - hangover.
• headache - ...
• drank.
• hangover gt drank

Constraint Store
?- headache.
hangover
drank
success
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Abduction in CHR

• headache - period.
• headache - ...
• sex(male).

Constraint Store

• period, sex(male) gt false

! CHR invalid syntax "sex(male)" ! Undeclared
constraint sex/1 in head of rule
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Problem
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Operational semantics

• Propagation
• a(X) a(Y), b -gt c (XY, b) -gt c
• Case analysis
• (XY, b) -gt c XY, (b -gt c) \/ X\Y
• Equality rewriting
• p(A,B,C)p(D,E,F) AD, BE, CF
• Unfolding
• p(X) -gt Goal p(X)- a. p(X)-b.
• a -gt Goal. b -gt Goal
• ...
• Constraint solving

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Abduction in CHR (SCIFF)
Constraint Store

• headache - flu.
• headache - ...

ic( )
vaccine, flu -gt false
?- , headache.
vaccine
fail
flu
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Abduction in CHR (SCIFF)
Constraint Store

• headache - flu.
• headache - ...

ic( flu -gt false)
ic( )
vaccine, flu -gt false
?- , headache.
vaccine
fail
flu
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Transitions

• Propagation transition ( case analysis)
• abd(X), ic(abd(Y)Rest-gt Head)
• gt
• copy(ic(abd(Y) Rest -gt Head) ,
• ic(abd(Y)Rest-gt Head)),
• reif_unify(X,Y,Boolean),
• ( Boolean1, ic(Rest-gtHead)
• Boolean0).

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Transitions

• Propagation transition ( case analysis)
• abd(X), ic(abd(Y)Rest-gt Head)
• gt
• copy(ic(abd(Y) Rest -gt Head) ,
• ic(abd(Y)Rest-gt Head)),
• reif_unify(X,Y,Boolean),
• ( Boolean1, ic(Rest-gtHead)
• Boolean0).

ic(abd(vaccine),abd(flu)-gt false)
ic(abd(period),sex(male)-gt false)
ic(abd(hangover)-gt drank)
abd(hangover)
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No hashing

• Does not use CHRs hashing
• Solution abducibles are represented with
  redundant information
• abd(Functor, Arity, Atom)
• So to abduce atom X
• abd(X)- functor(F, A, X),
• abd(F, A, X).
• E.g., if I abduce atom mother(X,john), the
  constraint store contains
• abd(mother, 2, mother(X,john))

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Hashing

• Propagation transition ( case analysis)
• abd(F,A,X), ic(abd(F,A,Y)Rest-gt Head)
• gt
• copy(ic(abd(Y) Rest -gt Head) ,
• ic(abd(Y)Rest-gt Head)),
• reif_unify(X,Y,Boolean),
• ( Boolean1, ic(Rest-gtHead)
• Boolean0).

Requires the first two arguments identical
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Hashing

• Propagation transition ( case analysis)
• abd(F,A,X), ic(abd(F,A,Y)Rest-gt Head)
• gt
• copy(ic(abd(Y) Rest -gt Head) ,
• ic(abd(Y)Rest-gt Head)),
• reif_unify(X,Y,Boolean),
• ( Boolean1, ic(Rest-gtHead)
• Boolean0).

ic(abd(vaccine,1,vaccine),abd(flu,1,flu)-gt
false)
ic(abd(period,1,period),sex(male)-gt false)
ic(abd(hangover,1,hangover)-gt drank)
abd(hangover,1,hangover)
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Postpone choices

• new CHR constraint
• nondeterministic(Goal)
• says that Goal can open a choice point, so
  should be called as late as possible.
• Two phases, declared by a CHR constraint phase/1
• phase(deterministic) only deterministic goals
  are executed
• phase(nondeterministic) exactly ONE
  nondeterministic goal can be executed
• switch2det _at_ phase(nondeterministic),
  nondeterministic(G) ltgt
• call(G), phase(deterministic).
• switch2nondet _at_ phase(deterministic) ltgt
  phase(nondeterministic)

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Postponing nondet.

• Propagation transition ( case analysis)
• abd(F,A,X), ic(abd(F,A,Y)Rest-gt Head)
• gt
• copy(ic(abd(Y) Rest -gt Head) ,
• ic(abd(Y)Rest-gt Head)),
• reif_unify(X,Y,B),
• ( B1, ic(Rest-gtHead)
• B0).

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Postponing nondet.

• Propagation transition ( case analysis)
• abd(F,A,X), ic(abd(F,A,Y)Rest-gt Head)
• gt
• copy(ic(abd(Y) Rest -gt Head) ,
• ic(abd(Y)Rest-gt Head)),
• reif_unify(X,Y,B),
• (B 1 -gt ic(Rest, Head)
• B 0 -gt true
• nondeterministic((B1,ic(Rest,Head))
  B0))
• ).

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Results
Experiment SCIFF 2005 SCIFF 2011
Auction protocol 2.27 s 0.37 s
Block world 45.0 s 15.7 s
AlLoWS Feeble Conformance 84.4 s 36.8 s
AlLoWS non-conformant 3.7 s 3.3 s
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Conclusions

• CHR implementation of an abductive
  proof-procedure
• Sound, complete, sound treatment of negation
• Well integrated with constraint solving, CLP(FD),
  CLP(R), universally quantified variables,
  quantifier restrictions, etc.
• Easy to extend for other features (see other talk
  after coffee break)

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Thank you for your attention!

• Questions?