Knowledge Representation I

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Knowledge Representation I
Gerstner Laboratory for Intelligent Decision
Making and Control

• Michal Pechoucek

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Knowledge Representation Hypothesis

• Knowledge representation is an essential problem
  of symbolic-based artificial intelligence
• Knowledge Representation Hypothesis (Smith)
• Any mechanically embodied intelligent process
  will comprise of structural ingredients, that
• will represent the propositional account of
  knowledge the overall process exhibits
• independently of such a formal semantics will
  play formal and causal role in performing the
  behavior that manifests the knowledge

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Knowledge Representation

• In symbolic functionalism we represent
  intelligence via manipulation of our beliefs
  about the surrounding world and knowledge we
  know.
• Therefore we have to address two fundamental
  issues
• how to represent knowledge
• how to implement the process of reasoning
• State space is a space of possible courses of
  inference when combining
• actual beliefs about current world
• general knowledge
• rules of inference

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The Knowledge Level

• Three levels of the Knowledge-based System
  conceptualization
• system engineering level physical realization
  of the system
• symbol level symbol system (program )
  specification
• knowledge level knowledge (to be represented)
  specification
• Knowledge Level Hypothesis
• There is a distinct computer level lying
  immediately above the program (symbol level),
  which is characterized by knowledge as the medium
  and principle of rationality as the law of
  behavior.

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AI research Software Engineering
Intelligent Behaviour
Requirements Specification
Functional Specification
Knowledge Level
System Implementation
Symbol Level
System Level
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What is Knowledge?

• data primitive verifiable facts, of any
  representation. Data reflects current world,often
  voluminous frequently changing.
• information interpreted data
• knowledge relation among sets of data
  (information), that is very often used for
  further information deduction. Knowledge is
  (unlike data) general. Knowledge contain
  information about behavior of abstract models of
  the world.
• Knowledge Classification
• according to source empirical, theoretical
• according to orientation domain, heuristic,
  inference
• according to type declarative, procedural

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Knowledge Representation Schemas

• Logic based representation first order
  predicate logic, Prolog
• Procedural representation rules, production
  system
• Network representation semantic networks,
  conceptual graphs
• Structural representation scripts, frames,
  objects

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Mathematical Logic

• Propositional Logic
• syntactical primitives ?, ?, ?, ?, symbols,
  true, false
• rule of inference de morgan rule, modus ponens,
  
• semantic interpretation
• rains ? blows-wind ? sun-will-shine
• First Order Predicate Logic
• enriched by variables, predicates, functions
• quantifiers ?, ?
• friends(father(david),father(andrew))
• ? Y friends(Y, petr)
• ? X likes(X,ice_cream)
• ? X ? Y ? Z parent(X,Y) ? parent(X,Z) ?
  siblings(Y,Z)

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Mathematical Logic cont

• inference representation proof system
• rules of inference example modus ponens
• if p is true and p ? q is true, than mp infers q
  to be true
• ? X(man(X) ? mortal(X))
• man(socrates)
• (man(socrates) ? mortal(socrates))
• mortal(socrates)
• rules of inference can be
• sound if all conclusions the rule infers
  logically follows
• complete if it infers all conclusions that
  logically follows
• modus ponens is sound but not complete

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Mathematical Logic cont

• inference representation resolution theorem
  proving
• transform the knowledge system into clausal
  normal form (conjunction of disjunction of
  literals)
• add negation of what has to be proved
• keep resolve new disjuncts unless you produce an
  empty set
• dog(X) ? animal(X) ? ? dog(X) ? animal(X)
• (?dog(X) ? animal(X)) ? (?animal(Y) ? die(Y))
  ?(dog(fido)))
• (?die(fido) 4
• -----------------------
• (?dog(Y) ? die(Y)) 12
• (die(fido)) 123
• ? 1234

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2
1
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Logic Based Financial Advisor

• savings(inadequate) ? investment(savings)
• savings(adequate) ? income(adequate) ?
  investment(stocks)
• savings(adequate) ? income(inadequate) ?
  investment(combined)
• ? X saved(X) ? ? Y dependents(Y)?
  greater(X,5000Y) ? savings(adequate)
• ? X saved(X) ? ? Y dependents(Y)? ? greater(X,
  5000Y) ? savings(inadequate)
• ? X earnings(X,steady) ? ? Y dependents(Y)?
  greater(X,(15000(4000X)) ? income(adequate)
• ? X earnings(X,steady) ? ? Y dependents(Y)? ?
  greater(X,(15000(4000X)) ? income(inadequate)
• ? X earnings(X,unsteady) ? income(inadequate)
• saved(22000)
• earnings(25000,steady)
• dependents(3)

prolog code example
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Production System

• procedural representation of knowledge
• in the form of if then rules
• inference mechanism is firing the rules
• subject of Expert System lecture
• jug problem example
• if small0 then
• small3
• if big0 and small3 then
• big5 and small 0

5l
3l
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Conceptual Graphs

• network knowledge representation schema
• rooted in association theory of meaning
• very much used in the problem of natural language
  processing
• Conceptual Graph is complete bipartite oriented
  graph, where each node is either a concept or a
  relation between two concepts, there is one or
  two edges each going to concepts, and each
  concept may represent another conceptual graph

dog
brown
colour
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Conceptual Graphs

• A monkey scratches its ear with a pawn

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Conceptual Graphs

• each concept has got its type and an instance
• general concept a concept with a wildcard
  instance
• specific concept a concept with a concrete
  instance
• there exsists a hierarchy of types subtype
• concept w is specialisation of concept v
  iftype(v)gttype(w) or instance(w)type(v)

dogX
brown
colour
dogEmma
brown
colour
animal
dog
cat
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Conceptual Graphs

• canonic conceptual graph is sensible
  representation of knowledge that can be but does
  not necessary need to be true
• canonic formation rules formalise rules of
  inference between two graph for while preserving
  canonicity
• copy identical cloning of a graph
• restriction substituting a concept in a graph
  with its specialisation
• join joining two graphs via shared concept
• simplification deleting identical relations

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Restriction of Concepts
person
eat
agent
object
pie
pie
pie
pie
pie
pie
pie
person
girl
eat
agent
object
pie
pie
pie
pie
pie
pie
pie
personSue
eat
agent
object
pie
pie
pie
pie
pie
pie
pie
girlSue
eat
agent
object
pie
pie
pie
pie
pie
pie
pie
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Joining Concepts
person
eat
agent
object
pie
pie
pie
pie
pie
pie
pie
girlSue
person
eat
agent
manner
pie
pie
pie
pie
pie
pie
fast
girlSue
agent
object
pie
pie
pie
pie
pie
pie
pie
eat
person
manner
fast
agent
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Simplification of Concepts
agent
object
pie
pie
pie
pie
pie
pie
pie
person
eat
manner
fast
agent
object
pie
pie
pie
pie
pie
pie
pie
person
eat
agent
manner
fast
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Conceptual Graphs

• FOPL transformation to CG
• for each node ? predicate
• general concept ? variable, specific concept ?
  atom typeinstance ? type(instance)
• relation ? n-ary predicat relation(in1, in2, ,
  inn) with arguments conncecting neighbouring
  concepts
• CG is existencionally quantified conjunction of
  these predicates
• ? X (dog(emma) ? color(emma,X) ? brown(X))

dogEmma
brown
colour
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Frames

• instance of structured representation (schemes)
• static data-structure representing stereotyped
  situation
• predecessor of object-oriented systems

• default slots
• daemons procedural attachment (infoseek)

hotel chair special ofchair legsfour usesitting
hotel room special ofroom locationhotel contains
hotel chair hotel phone hotel
bed
hotel phone special ofphone use calling
room service billing through room
hotel bed superclassbed usesleeping sizeking pa
rtmattress frame
mattress superclasscushion firmnessfirm
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Scripts

• Schanks formalisation of stereotyped sequence of
  events in a particular context
• knowledge base representation in terms of the
  situations that the system is supposed to
  understand
• a restaurant script

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Modal Logic

• While propositional logic will allow us to make
  statements about object it does not allow us to
  make statements about the statements
• John is at home
• I know that John is at home
• Modal logic augments predicate calculus with
• L operator saying that the statement is necessary
  true
• M operator saying that the statement is possibly
  true
• L(location(John, home))

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Modal Logic Semantics

• L operator
• necessary true, agent knows, true in all times,
  obligatory
• M operator
• possible true, agent beliefs, true sometimes,
  permissible
• Possible Worlds Semantics
• the logical true is different in different worlds
• the worlds are mutually accessible via
  accessibility relation
• L(?) is true in w if ? is true in all wi
  accessible from w
• M (?) is true in w if ? is true in at least one
  wi accessible from w

card playing example
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Temporal Logic

• Linear with explicit time representation
• now(?), true_in(?,t), occurs(?,i), (t1 lt t2),
  start(I,t), end(I,t)
• Linear without time representation
• ??f, X? P? F? (F? ? true??) (G? ? ?F??).
• Branching time logic
• represents all possible courses of action,
  branches in future
• E?, A? - E? ? ?A??
• example
• in t0 EFx is true
• in t0 AF(x ? y) is true

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Temporal Logic Limitations

• Duration of actions
• different speed of action at different situations
• Effects occurrence (do not need to be immediate)
• Concurrency, Parallel Computation (different
  formalisms)
• Qualification Problem
• how to make sound inference about the future
  without considering everything in the past
• Ramification Problem
• how to formalise everything that changes after an
  action occurs
• Frame Problem
• how to formalise what does not change after an
  action