Intelligent Systems 2II40 C5

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Intelligent Systems (2II40)C5

• Alexandra I. Cristea

October 2003
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Outline

• IV. Knowledge reasoning (finish)
• V. Planning

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Knowledge and reasoning

• IV.1. Generalities on logics
• IV.2. Propositional logic short visit
• IV.3. First-order logic (FOL) short visit
• IV.4. Knowledge-based agents
• IV.5. Knowledge representation
• Ontological engineering
• Categories and objects
• Actions, situations and events
• Mental events and mental objects
• Internet shopping world
• Reasoning systems for categories
• Semantic networks
• Description logic

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IV.4.D. Mental Events and Mental Objects
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Mental events objects - ontology

• Knowledge vs. Belief, e.g.,
• Knows(agent, BlueCoatPoliceman)
• KnowsWhether(agent, not(BlueCoatPoliceman))
• KnowsWhat(agent,Job(BlueCoat),String)
• Believes(agent, KnowsWhat(Policeman,
  WayTo(Bucharest), ListStrings))

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Referential opaqueness for beliefs

• Referential transparency to be able to
  substitute freely a term for an equal term
• Referential opaqueness a term cannot be
  substituted for an equal term (without changing
  the meaning)
• Why?

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Example need of referential opaqueness

• (SupermanClark)
• (Believes(Lois, Flies(Superman)) ? Believes(Lois,
  Flies(Clark))
• Which is false, so FOL is inadequate answers
• Syntactic theory
• mental objects represented as strings, as on
  slide w. knowledge vs. beliefs
• Modal logic FOLmodal operators
• B (belief), K (knowledge) modal context
  substitution limitation

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IV.4.F. Reasoning System for categories
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IV.4.F. Reasoning System for categories

• Semantic networks
• Graphical aid for visualizing a knowledge base
• Algorithms for inferring object proprieties
  (based on category membership)
• Description logics
• Formal language for constructing combining
  category defs
• Algorithms for deciding sub-/super-set
  relationships between categories

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Semantic networks

• Represent
• Objects
• Categories of objects
• Relationships between objects
• Objective like FOL
• to say (easily) things about objects

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Simple Semantic Net Example
Mammals
SubsetOf
Legs
HasMother
Persons
2
SubsetOf
Female Persons
Male Persons
SubsetOf
MemberOf
MemberOf
SisterOf
Legs
Mary
John
1
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Discussion Semantic Nets

• Semantic Nets related to concept maps, mind maps
  but come usually with a better formalism for
  resolution.
• Reification of links needed for
• ?p,s HasSister(p,s) ? SisterOf(s,p)
• because semantic nets indexed by objects,
  categories, links from them
• (FOL indexed by first argument of predicate)

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Pros Cons Semantic nets

• Drawbacks
• only binary relations
• FOL but No negation, disjunction, nested
  functions, existential quantification
• Advantages
• Visual aid, easy queries
• Default values allowed to be overridden

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Description Logics

• Objective unlike FOL to describe definitions and
  properties of categories, e.g.
• Subsumption (category is subset of other?)
• Classification (object belongs to category?)
• /- Consistency (membership criteria
  logically satisfiable?)
• Allows logical operations on predicates
• And(,,) All()AtLeast()AtMost()

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The ontology spectrum
Strong semantic
Modal Logic First Order Logic
Is
disjoint subclass w. transitivity
property
Local Domain Theory
Description Logic DAMLOIL,OWL UML
Conceptual Model
Is subclass of
RDF/S XTM Extended ER
Thesaurus
Has narrower meaning than
ER
Schema
Taxonomy
Is subclassification of
Relational Model
Weak semantic
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RDF, XML

• Resource Description Framework (RDF) recommended
  by the World Wide Web Consortium (W3C), to model
  meta-data about the resources of the web.
• RDF can be written in XML
• The eXtended Markup Language (XML) is accepted as
  THE emerging standard for data interchange on the
  Web.
• XML allows authors to create their own markup
  (e.g. ltAUTHORgt), which seems to carry some
  semantics. However, from a computational
  perspective tags like ltAUTHORgt carries as much
  semantics as a tag like ltH1gt
• What is needed??

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DAMLOIL

• The DARPA Agent Markup Language (DAML) (start
  August 2000) language tools to facilitate the
  concept of the Semantic Web.
• Example DAML beer ontology in RDF
• The Ontology Inference Layer OIL is a proposal
  for a web-based representation inference layer
  for ontologies, combining
• modelling primitives from frame-based languages
• with the formal semantics and reasoning services
  provided by description logics.

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Conclusion Knowledge Reasoning

• 322-283 BC Aristotle comprehensive taxonomies,
  emphasizing classification categorization
• Still hot topic
• IEEE Standard Upper Ontology Working Group
• 2003-08-19 The OWL Web Ontology Language is now
  a W3C Candidate Recommendation.
• RDF, XML
• Semantic Web (Tim Berners-Lee 2001
• DARPA Agent Markup Language (DAML)
• Ontology Inference Layer OIL
• However e.g., Ted Nelson is against this
  (hierarchical) movement!

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V. Planning
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V. Planning

• V.1. Planning generalities
• V.1.A. Search vs. Planning
• V.1.B. STRIPS operators
• V.2.C. Partial Order Planning
• V.2. Planning in the real world
• V.2.A. Conditional Planning
• V.2.B. Monitoring and Replanning
• V.2.C. Continuous Planning
• V.2.D. Multi-agent planning

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V.1. Planning generalities

• V.1.A. Search vs. Planning
• V.1.B. STRIPS operators
• V.2.C. Partial Order Planning

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V.1.A. Search vs. Planning
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Search vs. Planning Ex.

• Task get milk, bananas, and a cordless drill
• Standard search

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Problem decomposition

• Deliver n packages worst case
• O(n!)
• O((n/k)!k) if problem can be decomposed in k
  equal parts
• Most problems partially decomposable

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V.1.B. STRIPS operators
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STRIPS (71)

• Restricted language ? efficient algorithm
• Represents states, goals and actions
• State Literals ground and function-free
• not allowed At(x,y) At(Father(Fred),Sydney)
• Goal partially specified state conjunction of
  positive ground literals
• e.g., Rich ? Famous ? At(P2,Tahiti)
• Action precondition effect
• Precondition conjunction of positive literals
• Effect conjunction of literals
• e.g.,
• ACTION Buy(x)
• PRECONDITION At(p), Sells(p,x)
• EFFECT Have(x)
• Close world assumption!
• However many details omitted

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V.2.C. Partial Order Planning (POP)
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POP

• Least commitment strategy
• Obvious, important decisions first
• POP partially ordered collection of steps, w.
• Start step (initial state effect)
• Finish step (goal description precondition)
• Causal links (outcome one step precond. other)
• Temporal ordering
• Plan complete every precondition achieved
• Precondition achieved
• it is effect of earlier step AND
• no (possibly intervening) step undoes it
• Open condition precondition of a step not yet
  causally linked

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Planning process

• Operators on partial plans
• Add a link from existing action to open condition
• Add a step to fulfill open condition
• Order one step (w. rsp. to another to remove
  possible conflicts)
• Incomplete/ vague plans ??
• ? complete, correct plans
• ( backtrack if open condition unachievable or
  conflict unsolvable)

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POP algorithm
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POP alg. cont.
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Clobbering

• Clobbering is a step that potentially destroys
  the condition achieved by a causal link.
• E.g., Go(Home) clobbers At(Supermarket)
• Solution promotion or demotion

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Clobbering promotion/ demotion

• Demotion put before
• Go(Supermarket)
• Promotion put after
• Buy(Milk)

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Example POP
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Example POP
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Example POP
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POP proprieties

• sound, complete systematic (no repetitions)
• Nondeterministic backtracks at choice point of
  failure
• Choice Sadd to achieve Sneed
• Choice demotion/ promotion clobberer
• Extensions disjunction, universals, negation,
  conditionals
• Efficient w. good heuristic
• Good for pbs. w. loosely related sub-goals

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Ex. blocks world
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Ex. blocks world - cont.

• ACTION PutOn(x,y)
• PRECONDITION Clear(x), On(x,z), Clear(y)
• EFFECT On(x,y),Clear(y),On(x,z), Clear(z)
• ACTION PutOnTable(x)
• PRECONDITION Clear(x), On(x,z)
• EFFECT On(x,Table), On(x,z), Clear(z)

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Ex. blocks world - cont.
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Ex. blocks world - cont.
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Ex. blocks world - cont.
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Ex. blocks world - cont.
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Hierarchical task network planning (HTN)

• Generalization of POP
• Higher level actions, to be decomposed into lower
  level actions
• Preconditions of high-level actions are
  intersection of external preconditions of the
  decompositions.
• Effects of high-level actions are intersection of
  external effects of the decompositions.

Counter-intuitive!!
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V.2. Planning in the real world
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Time, schedules, resources

• Critical Path Method (CPM)
• Path a linearly ordered sequence of actions
  beginning w. Start and ending w. Finish.
• Critical path path with longest duration.
• ES(action) earliest possible start time of
  action
• LS(action) latest possible start time of action
• Slack LS-ES

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Computing CPM

• ES(start)0
• ES(B)maxAltBES(A) Duration(A)
• LS(Finish)ES(Finish)
• LS(A)minAltBLS(B) - Duration(A)
• Time complexity O(Nb),
• Where N- number of actions, b- max branching
  factor into or out of an action

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V.2. Planning in the real world

• V.2.A. Conditional Planning
• V.2.B. Monitoring and Replanning
• V.2.C. Continuous Planning
• V.2.D. Multi-agent planning

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V.2. Real world planning
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Things do go wrong

• Incomplete info
• Unknown preconditions Intact(Spare)?
• Disjunctive effects Inflate(x) causes
• Inflated(x) ? SlowHiss(x) ? Burst(x) ?
  BrokenPump(x)
• Incorrect info
• Current state incorrect, e.g., spare NOT intact
• Missing/incorrect postconditions in operators
• Qualification problem it is impossible to list
  all required preconditions and possible outcomes
  of actions.

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Solutions

• Sensorless planning a plan that works regardless
  of state or outcome
• may not exist
• Conditional planning plan to obtain info plan
  for every possible situation
• expensive (plans for unlikely cases as well)
• Monitoring/repairing assume normal states,
  outcomes check progress during execution, replan
  if necessary
• unanticipated outcomes may lead to failure
• Best a combination of above

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Sensorless planningPlanning with Beliefs
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V.2.A.Conditional Planning

• World non-deterministic, or partially observable
  ? percepts provide info to split the belief state

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Conditional planning examples
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Murphy x 2
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Search Algorithm AND-OR graph

• function AND-OR-GRAPH-SEARCH(problem) returns a
  conditional plan, or failure
• OR-SEARCH(INITIAL-STATEproblem, problem, )
• function OR-SEARCH(state, problem, path) returns
  a conditional plan, or failure
• if GOAL-TESTproblem(state) then return the
  empty plan
• if state is on path then return failure
• for each action, state_set, in
  SUCCESSORSproblem(state) do
• plan ??AND-SEARCH(state_set,problem,statepa
  th)
• if plan ?? failure then return actionplan
  
• return failure
• function AND-SEARCH(state_set, problem, path)
  returns a conditional plan, or failure
• for each si in state_set do
• plani ? OR-SEARCH(si,problem,path)
• if plan failure then return failure
• return if s1 then plan1 else if s2 then plan2
  else if sn-1 then plann-1 else plann

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Murphy x 3
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V.2.B. Monitoring and Replanning

• Failure preconditions of remaining plan not met
• Preconditions of remaining plan
• All preconditions of remaining steps not achieved
  by remaining steps
• All causal links crossing current time point
• On failure, resume POP to achieve open conditions
  from current state
• Performs action monitoring plan
  monitoring

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Other ex. of emergent behaviour
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Other ex. of emergent behaviour

• Loop until success until behavior emerges

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Multi-agent planning

• Cooperation joint goals plans
• Problems
• wrong plan might be selected
• Synchronization
• Communication
• Interesting examples boids (separation,
  cohesion, alignment)
• Competition
• success/ failure vs. minimization of cost
• Plan recognition (for both) hot research area

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Summary planning

• There is much more going on in planning, we
  barely touched the surface
• HTN are used in practice a lot, although it is
  undecidable in the general case
• Conditional plans can be combined with info
  gathering from sensing actions when info is
  missing
• In non-fully observable environments, sensorless
  planning can, in principle, still lead to desired
  outcome
• All the planning methods can be applied as
  searches within belief states trees
• Execution monitoring can detect violations of
  preconditions and inform the replanning agent
• Boids were the bases of the penguins in Batman
  returns
• Plan recognition used for utterance detection in
  speech recognition

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Homework 5

• The monkey-and-bananas problem is faced by a
  monkey in a lab with some bananas hanging out of
  reach from the ceiling.
• A box is available that will enable the monkey to
  reach the bananas if he climbs on it.
• Initially, the monkey is at A, the bananas at B,
  and the box at C. The monkey and box have the
  same height Low, but if the monkey climbs on the
  box it will have height High, the same as the
  bananas.
• The actions available for the monkey include Go
  from one place to another, Push an object from
  one place to another, ClimbUp onto or ClimbDown
  from an object, and Grasp or UnGrasp an object.
  Grasping results in holding the object if the
  monkey and object are in the same place at the
  same height.
• Write down the initial state description.
• Write down STRIPS-style definitions of the six
  actions.
• Suppose the monkey wants to fool the scientists,
  who are off to tea, by grabbing the bananas, but
  leaving the box in its original place. Write this
  as a general goal (i.e., not assuming that the
  box is necessarily at C) in the language of
  situation calculus. Can this goal be solved by a
  STRIPS-style system? (Hint check also comments
  on STRIPS slide and POP)
• 4. Continue till step 6 with your project.