KNOWLEDGE%20REPRESENTATION,%20REASONING%20AND%20DECLARATIVE%20PROBLEM%20SOLVING

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KNOWLEDGE REPRESENTATION, REASONING AND
DECLARATIVE PROBLEM SOLVING

• Chitta Baral
• Arizona State University
• Tempe, AZ 85287.

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Introduction

• Long term goal of this line of research
• Make programs, systems, interfaces and agents
  behave intelligently.

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What is intelligence?

• Some characteristics of intelligent entities
• - They can reason.
• - They can make decisions, and plans.
• - They can learn.
• - They can communicate
• take commands, queries, requests,
  preferences
• act, return answers, plans, decisions, control
  commands.

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Reasoning

• Reasoning can not be done in vacuum.
• We need knowledge to reason with.
• Mathematically, a reasoning task can be expressed
  as KB Conclusion.
• Questions
• In what language(s) KB and Conclusion are
  expressed?
• How is defined?

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Decision making and planning

• Need data and knowledge to make decisions and
  plans.
• Need to be able to express what a valid plan is,
  and when a decision is optimal or preferred.
• Thus, need to be able to express preferences and
  optimality criteria.

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Decision making cont.

• Questions
• How is knowledge expressed?
• How is the goal of a plan expressed?
• How are optimality criteria and preferences
  expressed?
• Given data and knowledge what are the
  options that are enumerated? (How are models
  defined?)

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Learning

• In what language do we express what is learned?
• Learning also can not be done (efficiently) in
  vacuum. Background knowledge and focus are
  important.

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Communication What vs How?

• Request for Coffee the two secretaries.
• Secretary1 Sir, there is no water in the coffee
  pot what should I do?
• Secretary2 Coffee on desk every morning the boss
  is in except in summer, when there is a glass of
  cold water,

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What vs How?

• How Exact step by step instructions.
• What A high level directive or request whose
  detailed implementation is left up to the
  intelligent entity.
• The more high level the directives and requests
  an entity can handle
• How are the high level directives expressed?
• Knowledge, and reasoning are also needed to
  handle them.

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The fundamental issue

• Need appropriate languages to be able to express
  knowledge, queries, preferences, high-level
  directives, etc.
• Recall, KB Conclusion.
• Syntax for KB and Conclusion.
• Semantics that defines .
• Semantics Enumerating the models of KB.

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Some expected properties of Knowledge Calculus!

• Must make it easier to add and revise knowledge.
• Ordering should not matter that much.
• It should be possible that KB Concl and
• KB New Knowledge \ Concl.
• (This rules out any monotonic logic, such as
  first-order predicate calculus, to be the
  language for knowledge representation.)

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Some expected properties ..cont.

• Must allow default reasoning.
• The Tweety flies example.
• Birds normally fly. Tweety is a bird. Penguins
  are birds that do not fly. Tweety flies.
• KB Tweety is a penguin Tweety does not fly.
• The airline databases. (Closed world assumption)

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Expected properties cont.

• Intuitive syntax (for the knowledge writer)
• Bird(X) gt Flies(X) is often more intuitive than
  Bird(X) V Flies(X).
• If-then form seems to be quite intuitive.
• Nesting is hard. ( ( ) ( ( ) ) )

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Expected properties cont.

• Semantics.
• Easily definable.
• If high complexity, then sound (and useful)
  approximations.
• Some structure
• Subclasses with different degrees of complexity
  and expressiveness.

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AnsProlog a possible candidate

• Syntax A collection of statements of the form
• A0 or or Ak ? B1, , Bm,
• not C1, not
  Cn.

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The Tweety example in AnsProlog

• Fly(X) ? Bird(X), not Ab(X).
• Bird(X) ? Penguin(X).
• Ab(X) ? Penguin(X).
• Bird(tweety).
• T Fly(tweety).
• T 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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Differences with

• Prolog Ordering matters in Prolog can not
  handle cycles with not.
• Logic Programming It is a class of languages and
  many different semantics are proposed for not.
• Classical Logic
• ? is not reverse implication.
• Disjunction symbol or is non-classical.
• The negation as failure symbol not is
  non-classical.
• The classical negation symbol is also used.

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Planning a DPS example.

• The planning problem.
• Actions puton(X,Y), lift, open, a.
• Fluents on(X,Y), lifted, opened, closed, f.
• States state of the world.
• Often represented by a set of fluents true in
  that state.
• A simple goal collection of fluents that need
  to be true in a state that we want the world to
  be in.

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A simple planning domain

• initially f.
• initially g.
• b causes f if g.
• a causes g.
• finally f.
• ab is a plan that achieves the goal.

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Planning in AnsProlog.

• 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).

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Planning in AnsProlog cont

• Enumerating possible plans.
• other-occurs(A,T) ?occurs(B,T), A \ B.
• occurs(A,T) ? not other-occurs(A,T).
• Eliminating models which do not encode a plan.
• ?not holds(f, plan-length1).
• All models (answer sets) encode a plan.

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Building blocks towards a knowledge calculus.

• Subclasses and their properties.
• 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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Properties 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.

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Example Prop. -- Expressibility

• Normal function-free AnsProlog Pi1P (Co-NP)
• Function-free AnsProlog Pi2 P.
• AnsProlog Pi11

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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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Applications

• Reasoning
• Reasoning with incomplete information, default
  reasonong.
• 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.

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Applications. (Cont.)

• Software Engineering Specification is the
  program. (rapid prototyping)

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Conclusion

• Representing knowledge and reasoning with it is
  of fundamental importance in building intelligent
  entities.
• AnsProlog is a good candidate for this task.
• There is now a sizable body of theoretical
  results, several interpreters, and it has been
  now used in several applications.
• This is not my individual work, but has been done
  by several researchers over the years, most of it
  in the last ten years.