Knowledge Representation

1
Knowledge Representation

• Shyh-Kang Jeng
• Department of Electrical Engineering/
• Graduate Institute of Communication Engineering
• National Taiwan University

2
References

• J. P. Bigus and J. Bigus, Constructing
  Intelligent Agents with Java, Wiley Computer
  Publishing, 1998
• S. Russell and P. Norvig, Artificial
  Intelligence A Modern Approach, Englewood
  Cliffs, NJ Prentice Hall, 1995

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Goal-Based Agents
Sensors
Environment
State
Environment Model
Options
Decision Maker
Goals
Agent
Effectors
4
Knowledge-Based Agents
Sensors
Environment
Knowledge Base Management System
Knowledge Base
Agent
Effectors
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General Knowledge-Based Agent (1)

• class KBAgent
• KnowledgeBase kb
• KBMS kbms
• counter t // indicating time
• public KBAgent()
• kb new KnowledgeBase()
• kbms new KBMS( kb )
• t 0

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General Knowledge-Based Agent (2)

• public Action run(Percept percept)
• kbms.tell(new
• PerceptSentence(percept, t))
• Action action kbms.ask( new
• ActionQuery(t) )
• kbms.tell( new
• ActionSentence(action,t) )
• t return action

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Knowledge Base

• A set of representation of facts about the world
• Each individual representation is a sentence
• Sentences are expressed in a knowledge
  representation language
• Knowledge representation languages are composed
  of symbols
• Representation and reasoning support the
  operation of a knowledge-based agent, accessed
  through a knowledge base management system (KBMS)

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Knowledge Representation

• Natural language
• Most easily understood for people
• Not the best for computers because of ambiguity
• Formal logic was the first representation
  language

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Procedural Representation

• Encodes facts and defines sequence as well as the
  control structure of operations for using and
  manipulating those facts
• Example FORTRAN programs
• hardcoded logic
• Not considered to be part of AI per se
• Few AI programs exist which do not contain some
  amount of procedural control code

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Declarative Representation

• Simply states facts, rules, and relationships
• Separate the knowledge and the manipulation of
  the knowledge
• Still needs to be processed by some procedural
  code
• More easily modified
• Allows for optimization and reuse inferencing
  procedures

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Relational Representation

• Knowledge is stored in a table and manipulated
  through relational calculus
• Information of an item is represented by tuples
  or records
• Each tuple contains a set of fields or columns
  defining specific attributes and values of the
  item
• Flexible but not good at representing complex
  relationships between concepts or objects in the
  real world

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Hierarchical Representation

• Represents relationships and shared attributes
  between kinds or classes of objects
• Use categories or types to give structure to the
  world by grouping similar objects together
• Allows for compact representation
• Allows reasoning algorithms to process at
  different levels of abstraction or granularity

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Frames

• As a collection of attributes which defines the
  state of an object and its relationship to other
  frames
• Also called slot-and-filler data representations
• Slots are the data values
• Fillers are attached procedures which are called
  before, during, or after the slots value is
  changed
• Often linked to a hierarchy

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A Frame Example
isa
isa
isa
isa
isa
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Semantic Nets

• Defines the meaning of a concept by its
  relationships to other concepts
• Uses a graph data structure, where nodes hold
  concepts and links show the relationships
• Both frames and semantic nets can be transformed
  to predicate logic

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A Semantic Net Example
has-part
Vehicle
Wheels
has-part
isa
has-part
Motor
Doors
Automobile
num-wheels
isa
size
4
Sports Car
Small
num-doors
2
instance
Corvette
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Knowledge Representation Language

• Syntax
• describes the possible configurations that
  constitute sentences
• Semantics
• determines the facts in the world to which the
  sentences refer
• Logic
• A language with the syntax and semantics defined
  precisely

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Logics

• A logic consists of
• A formal system for describing states of affairs,
  consisting of the syntax and the semantics of the
  language
• A proof theory
• The ontological commitments of a logic have to do
  with the nature of reality in the related world
• The epistemological commitments of a logic have
  to do with states of knowledge an agent can have

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Propositional Logic Syntax
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Propositional Logic Semantics

• Defined by specifying the interpretation of the
  symbols and constants, and specifying the
  meanings of the logical connectives
• A complex sentence has a meaning derived from the
  meaning of its parts
• Each connective can be thought of as a function
  and defined by truth tables

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Truth Tables for Connectives
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Test for Valid Sentences

• A valid sentence is true for every possible
  combination of truth values for the propositional
  symbols in the sentence
• Truth table can be used to test for valid
  sentences
• This can be used to determine if the conclusion
  (consequent) is true given some premises
  (antecedent). Just test if the following sentence
  is valid
• 
  

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First-Order Logic Syntax
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Quantifiers

• Universal quantifier
• Existential quantifier

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Some Properties of Quantified Sentences
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First-Order Logic vs.Higher-Order Logic

• In first-order logic one can quantify over
  objects but not over relations or functions on
  those objects
• Higher-order logic allows us to quantify over
  relations and functions as well as over objects
• Example

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Accessing First-Order Logic KB

• Assertions
• Example
• Queries or goals
• Example
• Substitution or binding list
• Example

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Sets and Lists

• Sets
• Constant EmptySet
• Predicates Set, Member, Subset
• Functions Intersection, Union, Adjoint
• Lists
• Constant Nil
• Functions Cons, Append, First, Rest
• Predicates Find, Member, List?

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Special Notations for Sets and Lists
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The Wumpus World
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Agent in the Wumpus World

• The agent starts in the lower left corner labeled
  1,1, facing to the right
• Goal Find the gold, return to 1,1 and climb
  out of the cave as soon as possible
• Actions Forward, Turn(Right), Turn(Left), Grab,
  Release, Shoot, Climb
• Percepts Stench, Breeze, Glitter, Bump, Scream

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Acting and Reasoning in the Wumpus World (1)
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Acting and Reasoning in the Wumpus World (2)
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Acting and Reasoning in the Wumpus World (3)
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Acting and Reasoning in the Wumpus World (4)
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Knowledge After the Third Move
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Propositional Knowledge Base After the Third Move
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Finding the Wumpus
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Problems with Propositional Agent

• Too many propositions to handle
• Example 64 propositions for the rule dont
  forward if the wumpus is in front of you
• Dealing with change over time
• Example

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Reflex Agent

• Action run(Percept percept)
• state
• interprete(percept)
• rule
• kbms.ruleMatch(state)
• action rule.Action()

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Reflex Agent for the Wumpus World (1)

• Direct rules
• Example
• Mediated rules
• Example

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Reflex Agent for the Wumpus World (2)

• Limitations
• Unable to know the states
• Example Not knowing when to climb
• Unable to avoid infinity loop

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Model-Based Agent

• Maintain an internal model of the world
• Any system that makes decisions on the basis of
  past percepts can be rewritten to use instead a
  set of sentences about the current world state
• Example My keys are in my pocket
• Diachronic rules
• Rules describing the way in which the world
  changes or does not change

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Knowledge Engineering

• Knowledge engineering
• Process of building knowledge base
• Knowledge engineer
• Knowledge acquisition
• Prior to, or interleaved with, the process of
  creating formal representations

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Knowledge Engineering vs. Programming
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Knowledge Engineering Methodology

• Ontological engineering
• Decide what to talk about
• Decide on a vocabulary of predicates, functions,
  and constants (ontology of the domain)
• Encode general knowledge about the domain
• Encode a description of the specific problem
  instance
• Pose queries to the inference procedure and get
  answers

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General Ontology

• Ontology
• Particular theory of the nature of being or
  existence
• General ontology
• Applicable in more or less any special-purpose
  domain, with the addition of domain-specific
  axioms
• Examples Categories, measures, composite
  objects, time, space, change, events, processes,
  physical objects, substances, mental objects,
  beliefs

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A General Ontology Hierarchy