Using answer set programming to answer complex queries

1
Using answer set programming to answer complex
queries

• Chitta Baral
• (joint work with Michael Gelfond, Texas Tech U
  and Richard Scherl, Monmouth U)
• Arizona State University
• Tempe, AZ 85287
• chitta_at_asu.edu
• http//www.public.asu.edu/cbaral

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QUERIES

• Prediction, explanation, planning, cause,
  counterfactual, etc.

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Queries and Answers

• Answering queries with respect to databases
  various query languages
• Relational databases SQL3
• Object-Oriented Databases OQL
• Web databases, XML Databases XML-QL
• Prolog queries
• Natural language queries
• Often translated to one of the above
• Complex Queries!
• Need knowledge beyond that is present in the
  given data (or text) to answer.
• Many can not be expressed in classical logics and
  standard database query languages

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Complex Query example predictive query

• Text/Data John is at home in Boston and has not
  bought a ticket to Paris yet.
• Query
• What happens if John tries to fly to Paris?
• What happens if John buys a ticket to Paris and
  then tries to fly to Paris?
• Missing knowledge
• When can one fly? What is the result of flying?

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Complex Query example explanation query

• Text/Data On Dec 10th John is at home in Boston
  and has not bought a ticket to Paris yet. On Dec
  11th he is in Paris.
• Query
• Explain what might have happened in between.
• Bought a ticket gone to the airport taken a
  flight to Paris.

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Complex Query Example planning query

• Text/Data On Dec 10th John is at home in Boston
  and has not bought a ticket to Paris yet.
• Query What does John need to do to be in Paris
  on Dec 11th.
• He needs to buy the ticket get to the airport
  fly to Paris.

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Complex Query ExampleCounterfactual Query

• Text/Data On Dec 10th John is at home in Boston.
  He made a plan to get to Paris by Dec 11th. He
  then bought a ticket. But on his way to the
  airport he got stuck in the traffic. He did not
  make it to the flight.
• Query What if John had not gotten stuck in the
  traffic?

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Complex Query Example query about narratives

• Text/Data John, who always carries his laptop
  with him, took a flight from Boston to Paris on
  the morning of Dec 11th.
• Queries
• Where is John on the evening of Dec 11th?
• In which city is Johns laptop that evening?

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Complex Query Example Causal queries

• Text/Data On Dec 10th John is at home in Boston.
  He made a plan to get to Paris by Dec 11th. He
  then bought a ticket. But on his way to the
  airport he got stuck in the traffic. He reached
  the airport late and his flight had left.
• Queries
• What are the causes of John missing the flight?

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Our approach to answer such queries

• Develop various knowledge modules in an
  appropriate knowledge representation and
  reasoning language.
• Travel module (includes flying, driving)
• Geography Module
• Time module
• Reasoning about actions module
• Planning module
• Explanation module
• Counterfactual module
• Cause finding module

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Knowledge Representation and Reasoning

• AnsProlog

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What properties should an appropriate KR R
language have

• Should be non-monotonic. So that the system can
  revise its earlier conclusion in light of new
  information.
• Should have the ability to represent normative
  statements, exceptions, and default statements,
  and should be able to reason with them.
• Should be expressive enough to express and answer
  problem solving queries such as planning queries,
  counterfactual queries, explanation queries and
  diagnostic queries.
• Should have a simple and intuitive syntax so that
  domain experts (who may be non-computer
  scientists) can express knowledge using it.
• Should have enough existing research (or building
  block results) about this language so that one
  does not have to start from scratch.
• Should have interpreters or implementation of the
  language so that one can indeed represent and
  reason in this language. (I.e., it should not be
  just a theoretical language.)
• Should have existing applications that have been
  built on this language so as to demonstrate the
  feasibility that applications can be indeed built
  using this language.

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AnsProlog a suitable knowledge representation
and reasoning language

• AnsProlog Programming in logic with answer sets
• Syntax Set of statements of the form
• A0 or or Ak ? B1, , Bm, not C1,
  not Cn.
• Intuitive meaning of the above statement
• If B1, , Bm is known to be true and C1, , Cn
  can be assumed to be false then at least one of
  A0 ,, Ak must be true.
• Semantics
• A set of atoms A is an answer set of a program P
  if A is the minimal model of the program PA
  obtained by using A to remove all literals of the
  form not C.
• If C is in A then remove that rule and if C is
  not in A then remove not C from that rules body
• a ? not b b ? not a a a ?

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AnsProlog Program example illustrating
non-monotonicity

• T1 fly(X) ? bird(X), not ab(X).
• T2 bird(X) ? penguin(X).
• T3 ab(X) ? penguin(X).
• T4 bird(tweety).
• T1, T2, T3, T4 fly(tweety).
• T1, T2,T3, T4, penguin(tweety)
• fly(tweety).

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Transitive Closure in AnsProlog

• ancestor(X,Y) ? ancestor(X,Z), parent(Z,Y).
• ancestor(X,Y) ? parent(X,Y).
• parent(a,b).
• parent(b,c).
• parent(c,d).
• parent(e,f).

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Planning using AnsProlog

• initially f. initially g. b causes f
  if g. a causes g. finally f.
• ab is a plan that achieves the goal.
• Planning All answer sets encode a plan.
• Describing the initial state. holds(f,
  1). holds(g, 1).
• Describing effect of actions.
• holds(f,T1) ?occurs(b,T), holds(g,T).
• holds(g,T1) ?occurs(a,T).
• Describing what does not change.
• holds(f,T1) ?holds(f,T), not
  holds(f,T1).
• holds(f,T1) ?holds(f,T), not
  holds(f,T1).
• Enumerating possible plans.
• other-occurs(A,T) ?occurs(B,T), A \ B.
• occurs(A,T) ? not other-occurs(A,T).
• Eliminating answer sets which do not encode a
  plan.

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AnsProlog vs Prolog

• Differences
• Prolog is sensitive to ordering of rules and
  ordering of literals in the body of rules.
• Inappropriate ordering leads to infinite loops.
  (Thus Prolog is not declarative hence not a
  knowledge representation language)
• Prolog stumbles with recursion through negation
• No disjunction in the head (less power)
• Similarities For certain subclasses of AnsProlog
  Prolog can be thought of as a top-down engine.

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AnsProlog vs other KR R languages

• AnsProlog has a simple syntax and semantics
• Syntax has structure that allows defining
  sub-classes
• More expressive than propositional and
  first-order logic propositional AnsProlog is as
  expressive as default logic. Yet much simpler.
• It has the largest body of support structure
  (theoretical results as well as implementations)
  among the various knowledge representation
  languages
• Description logic comes close. But its focus is
  very narrow, namely representing and reasoning
  about ontologies.

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Building blocks for AnsProlog

• Syntactic subclasses
• Definite, normal, extended, disjunctive.
• Acyclic, signed, stratified, call-consistent,
  order-consistent.
• Properties
• Existence of consistent answer sets.
• Existence of unique answer sets.
• Complexity of entailment.
• Expressibility of the entailment relation.
• Relation between the literals in an answer set
  and the program

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Building blocks for AnsProlog- cont.

• Transforming programs.
• Equivalence of programs.
• Formal relation with other languages. (classical
  logic, default logic, etc.)
• Splitting programs modular analysis, and
  computation of answer sets.
• Systematic building of programs from components
  program composition.
• Compilation to propositional logic

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Examples of specific properties

• Expressibility
• Function-free AnsProlog without disjunctions P1P
  (Co-NP)
• Function-free AnsProlog P2 P.
• AnsProlog P11
• Relation between literals in an answer set and
  the program.
• If f is in an answer set A of a program P,
  then there must be a rule in P such that
• If an answer set A of a program P satisfies the
  body of a rule r of P then, the head of that
  rule

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Some existing AnsProlog applications

• Reasoning
• Reasoning with incomplete information, default
  reasoning.
• Reasoning with preferences and priorities,
  inheritance hierarchies.
• Declarative problem solving
• Planning, job-shop scheduling, tournament
  scheduling.
• Abductive reasoning, explanation generations,
  diagnosis.
• Combinatorial graph problems.
• Combinatorial optimizations, combinatorial
  auctions.
• Product configuration.
• Software Engineering Specification is the
  program. (rapid prototyping)

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Illustration of Complex Query Answering

• John flying to Baghdad to meet Bob example.

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The extracted text and the queries

• Extracted Text
• John spent Dec 10 in Paris and took a plane to
  Baghdad the next morning. He was planning to meet
  Bob who was waiting for him there.
• Queries
• Q1 Was John in the Middle East in mid-December?
• Q2 If so, did he meet Bob in the Middle East in
  mid-December?

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Required background and common-sense knowledge

• Knowledge about geographical objects and their
  hierarchy. (M1)
• Baghdad is a city in Iraq. Iraq is a country in
  the middle east region.
• A city in a country in a region is a city in that
  region.
• Knowledge about travel events. (M2)
• If someone is in a city then she is in the
  country where the city is in and so on.
• Executability conditions and effect of travel
  events
• Inertia
• Duration of flying
• Knowledge about time units. (M3)
• Relation between various time granularities
• Knowledge about planned events, meeting events.
  (M4)
• People normally follow through their plans
• Executability condition of meeting events

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M1 The geography Module

• List of places
• is(baghdad,city).
• is(iraq,country).
• ...
• Relation between places
• in(baghdad, iraq).
• in(iraq,middle_east).
• in(paris,france).
• in(france,western_europe).
• in(western_europe,europe).
• ...
• Transitive closure
• in(P1,P3) ? in(P1,P2), in(P2,P3).
• Completeness assumption about in
• -in(P1,P2) ? not in(P1,P2)

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M2 The traveling module

• Based on theory of dynamic systems
• Views world as a transition diagram
• States are labeled by fluents
• Arcs labeled by actions
• Various types of traveling events
• instance_of(fly,travel).
• instance_of(drive,travel).
• Generic description of John flying to Baghdad
• event(a1).
• type(a1,fly).
• actor(a1,john).
• destination(a1,baghdad).
• Actual event is recorded as
• occurs(a1,i)

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M2 The traveling module (cont.)

• Representation of transition Diagram
• State Constraints
• loc(P2,X,T) ? loc(P1,X,T), in(P2,P1).
• disjoint(P1,P2) ? -in(P1,P2), -in(P2,P1),
  neq(P1,P2).
• -loc(P2,X,T) ? loc(P1,X,T),disjoint(P1,P2).
• Causal Laws
• loc(P,X,T1) ? occurs(E,T),
  type(E,travel), actor(E,X),
  destination(E,P), -interference(E,T).
• -interference(E,T) ? not interference(E,T).
• Executability Conditions
• -occurs(E,T) ? cond(T).
• Inertia Rules (frame axioms)
• loc(P,X,T1) ? loc(P,X,T), not -loc(P,X,T1).
• -loc(P,X,T1) ? -loc(P,X,T), not loc(P,X,T1).

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Reasoning with M1 and M2

• Given
• loc(paris,john,0).
• loc(baghdad,bob,0).
• occurs(a1,0).
• And with M1 and M2 AnsProlog can conclude
• loc(baghdad,john,1), loc(baghdad,bob,1),
• loc(middle_east,john,1), -loc(paris,john,1)

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M3 Time and durations

• Duration of actions (additional ones needed for
  month etc.)
• time(T1,day,D) ? occurs(E,T), type(E,fly),
• time(T,day,D), not -time(T1,day,D).
• Basic measuring units
• day(1..31). month(1..12). part(start). part(end).
  part(middle).
• Rules translating between one granularity to
  another
• time(T,part,middle) ? time(T,d,D), 10 lt
  D lt 20.
• time(T,season,summer) ? time(T,month,M), 5 lt M
  lt 9.
• Missing elements from the module
• next(date(10,12,03),date(11,12,03)).
• next(date(31,12,03),date(1,1,04)).

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Reasoning with M1, M2 and M3

• Given information about Johns flight
• loc(paris,john,0).
• loc(baghdad,bob,0).
• occurs(a1,0).
• time(0,day,11).
• time(0,month,12).
• The query Q1
• ? loc(middle_east,john,T), time(T,month,12),
  time(T,part,middle).
• AnsProlog gives the correct answer yes with T
  1.

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M4 planning to meet and meeting

• Describing the event meet
• event(a2). type(a2,meet).
• actor(a2,john). actor(a2,bob).
• place(a2,baghdad).
• Executability conditions of the meeting event
• -occurs(E,T) ? type(E,meet), actor(E,X),
  place(E,P), -loc(P,X,T).
• Planned meeting planned(a2,1).
• Planned actions and their occurrence People
  normally follow their plans
• occurs(E,T) ? planned(E,T), not -occurs(E).
• People persist with their plans until it happens
• planned(E,T1) ? planned(E,T), -occurs(E,T).
• Second query
• ? occurs(E,T), type(E,meet), actor(E,john),
  actor(E,bob), loc(middle_east,john,T),
  time(T,month,12), time(T,part,middle).
• Answer Yes.

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Conclusion

• Answering complex queries need a lot of knowledge
  and reasoning rules that are not present in the
  text or data.
• These reasoning rules and knowledge need to be
  encoded as modules in an appropriate knowledge
  representation and reasoning language.

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Ongoing and Future Work

• Further development of Modules (examples)
• Travel duration
• Time period representation issues (eg. time
  zones)
• Dealing with the case when a planned event fails
• Further development of the AnsProlog language
• Not good when dealing with time or similar
  features that result in large instantiations.
• Taking advantage of Prolog execution engine when
  necessary
• Necessity of set notations, aggregates etc.

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Acknowledgements

• Steve Maiorano, Jean-Michel Pomarede
• Ryan Weddle, Jicheng Zhao, Saadat Anwar, Luis
  Tari (all from ASU), Greg Gelfond (from Texas
  Tech University)