Intelligent Systems 2II40 C5

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Intelligent Systems (2II40)C5

• Alexandra I. Cristea

October 2005
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Categories and Objects

• Ontologies
• Organize objects into categories
• Organize categories into taxonomic hierarchies
  (by sub-classing)
• Imply inheritance for properties over subclasses

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IV.4.B. Categories terminology

• FOL category predicate or object
• Teacher(Cristea) vs. Member(Cristea,Teachers)
• Reification category as object
• Inheritance proprieties transmitted from class
  to subclass (like in OO)
• Subset(Teachers,Staff)
• Taxonomy class-subclass relation organization
• Partition disjoint exhaustive decomposition
• E.g., Animals into Males and Females
• Composite object objects being PartOf another

• FOL category predicate or object
• Teacher(Cristea) vs. Member(Cristea,Teachers)
• Reification category as object
• Inheritance proprieties transmitted from class
  to subclass (like in OO)
• Subset(Teachers,Staff)
• Taxonomy class-subclass relation organization
• Partition disjoint exhaustive decomposition
• E.g., Animals into Males and Females
• Composite object objects being PartOf another

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Relations for objects, categories

• PartOf
• BunchOf

PartOf is a relation, like in UML. PartOf(Leg,
Body) This doesnt make sense for substances,
such as Butter, for instance. (PartOf(Butter,Butte
r) ?)
BunchOf is similar to the Bag relation in RDF. We
cannot use set here, because a set is a
different, abstract mathematical
concept. BunchOf(Apple1, Apple2, Apple3) (no
particular structure)
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Measurements for objects

• Measure function and units
• Diameter(basketball3)Inches(9.5)
• ListPrice(basketball3)(19)
• Measures are ordered!
• e1?Exercises ? e2 ?Exercises ? Wrote(Norvig, e1)
  ? Wrote(Russel, e2) ? Difficulty(e1) gt
  Difficulty(e2)

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IV.4.B.Actions, Situations Events
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Actions, Situations, Events

• How do we represent situations, results of
  actions, events? Representation of these is
  essential for knowledge-based agents!
• PL unsuitable (1 proposition at a time)
• Obvious way to solve this in FOL quantify over
  time ?t t1
• Instead of dealing w time explicitly, deal w
  situations, i.e. states resulting from executing
  actions situational calculus

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Situational calculus - ontology

• Situations Actions
• in active databases event condition action (ECA)
  rules e.g., actions Turn(Right) or Forward
  situations S0 in Result(Forward, S0)
• Fluents varying predicates/ functions
• e.g. ?Gray(Anna,S0) Gray(Anna,S50)
• Atemporal predicates/ functions
• e.g. Female(Anna)

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Reasoning about action sequences

• Result(,s) s
• Result(aseq,s) Result(seq,Result(a,s))

Projection Task Given a (sequence of) actions,
deduce its outcome
Result(seq,state) Planning Task
finding the sequence that gives the desired
effect (projection)
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IV.4.C. 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
• substitute freely a term for an equal term
• Referential opaqueness
• not possible (without changing meaning)
• Why do we need it?

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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 strings
• Modal logic FOLmodal operators
• B (belief), K (knowledge) modal context

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IV.4.D. Internet Shopping World
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Internet shopping

• The query
• RelevantOffer(page,url,query) ?
  Relevant(page,url,query) ? Offer(page)
• Prerequisite knowledge
• Amazon ? OnlineStores ? Homepage(Amazon,
  amazon.com)
• Taxonomy of product categories
• Books ? Products
• MusicRecordings ? Products
• Result
• ?lc, offer lc ? LaptopComputers ? offer
  ?ProductOffers ? ScreenSize(lc,Inches(14))
  OfferedProduct(offer,lc) ?Store(offer,GenStore)
  ?Price(offer,(449)) ?Date(offer,Today)

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IV.4.E. Reasoning System for categories
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IV.4.E. Reasoning System for categories

• Semantic networks
• graphical aid to visualize KB
• alg. to infer object prop.
• Description logics
• formal lang. to constructcombine category defs
• alg. to decide sub/superset rel. of 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
Persons
Female Persons
Male Persons
Mary
John
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Discussion Semantic Nets

• Semantic Nets concept maps, mind maps
• better resolution formalism
• Reification of links needed
• ?p,s HasSister(p,s) ? SisterOf(s,p)
• SN indexed by objects, categories
• 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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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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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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Conclusion Knowledge Reasoning

• 322-283 BC Aristotle comprehensive taxonomies,
  emphasizing classification categorization
• Still hot topic
• IEEE Standard Upper Ontology Working Group
• 2004-02-10 The OWL Web Ontology Language W3C
  Candidate Recommendation endorsed
• Example OWL airport ontology in RDF
• 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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Homework 5 - part 1

• Read the memory refreshing presentations on PL
  and FOL (last course). What are the major
  differences between these basic logics?
• Find ontologies for some subject that interests
  you give a small sample of the upper, as well
  as the lower ontology (graphically or
  hierarchically).
• Find other examples of ontological languages
  besides OIL and DAMLOIL, OWL. Give at least 2
  examples based on FOL, and 2 on XML.
• Who is Ted Nelson?

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Homework 5 part 2

• 5. Step 8,9 of the project
• STEP 8 Integration of software. Integrate
  software, check it out.
• STEP 9 Make an appointment for the interim
  presentation. Dates will be announced on the
  course site. You only need to demo your system
  and talk about any aspects you want. No
  powerpoint presentation. Time per group (1min
  setup, 10-15min presentation, 4-9 min QA). These
  presentations will not be public. Choose the
  presentation date time according to the stage
  of your project. The location will be announced
  on the course site.

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Outline

• Introduction IS
• Intelligent agents
• Search
• Knowledge and reasoning
• Planning
• Uncertainty
• Learning
• Hybrid systems

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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
• O(n!) worst case
• O((n/k)!k) if pb decomposable 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
• Open condition precondition of a step not yet
  causally linked
• Precondition achieved
• it is effect of earlier step AND
• no (possibly intervening) step undoes it
• Plan complete every precondition achieved/ closed

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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 what for?
• 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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Homework 5 part 3

• 6. 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)

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Hierarchical task network planning (HTN)

• Generalization of POP
• Higher level actions, to be decomposed into lower
  level actions
• more expressive than STRIPS
• Idea problem reduction decompose tasks into
  subtasks, handle constraints, resolve
  interactions if necessary, backtrack try other
  decompositions
• More info
• HTNpaper.pdf
• a presentation on HTN 2003-9-18-htn.ppt

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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) maxAltB ES(A) Duration(A)
• LS(Finish) ES(Finish)
• LS(A) minAltB LS(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