Autonomy Knowledge Representation

1
Autonomy 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

3
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
5
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)

6
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

7
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

8
Description Levels

• Knowledge level (epistemological level)
• Most abstract
• Example Taipei is in the north of I-Lan
• Logical level
• Knowledge is encoded into sentences
• Example North( Taipei, Taiwan )
• Implementation level
• Physical representation of the sentences at the
  logical level
• Important to the efficient performance of the
  agent

9
Knowledge Representation

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

10
Some Kinds of Knowledge

• Simple facts or complex relationships
• Mathematical formulas or rules for natural
  language syntax
• Associations between related concepts
• Inheritance hierarchies between classes of objects

11
Choosing Knowledge Representations

• Each type of knowledge places special
  requirements on both human comprehension and
  computer manipulation
• A good knowledge representation
• Easy to use
• Easily modified and extended

12
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

13
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

14
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

15
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

16
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

17
A Frame Example
isa
isa
isa
isa
isa
18
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

19
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
20
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

21
Entailment

• A set of sentences entails a sentence if the fact
  represented by the sentence follows the facts
  represented by the set of sentences

22
Inference Procedure

• Given a knowledge base KB, an inference procedure
  can generate new sentences that purport to be
  entailed by KB
• Given a knowledge base KB and another sentence a,
  an inference procedure can report whether or not
  a is entailed by KB
• An inference procedure that generates only
  entailed sentences is called sound or
  truth-preserving

23
Proof, Complete Procedure, and Proof Theory

• The record of operations of a sound inference
  procedure is called a proof
• An inference procedure is complete if it can find
  a proof for any sentence that is entailed
• Proof theory specifies a set of rules for
  deducing the entailments of a set of sentences

24
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

25
Some Formal Languages
26
Propositional Logic Syntax
27
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

28
Truth Tables for Connectives
29
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
• 
  

30
Models (1)

• Any world in which a sentence is true under a
  particular interpretation is called a model of
  the sentence under that interpretation
• The meaning of a sentence can be defined by means
  of set operations on sets of models
• Another view is to regard a model as a mapping
  from proposition symbols to truth and falsehood,
  and the models of a sentence are those mappings
  that make the sentence true

31
Models (2)
32
Inference Rules (1)

• The soundness of an inference can also be
  established through truth tables
• Inference rules are some inference patterns that
  occur frequently
• Inference rules can be used to make inferences
  without going through the tedious process of
  building truth tables
• The inference rule that b can be derived from a
  is denoted as

33
Inference Rules (2)

• Conjunctions and conjuncts
• Disjunctions and disjuncts

34
Inference Rules (3)

• Modus Ponens or Implication-Elimination
• And Elimination

35
Inference Rules (4)

• And-Introduction
• Or-Introduction

36
Inference Rules (5)

• Double-Negation Elimination
• Unit Resolution

37
Inference Rules (6)

• Resolution
• b cannot be both true and false, one of the
  other disjuncts must be true in one of the
  premises
• Or, equivalently, implication is transitive

38
Completeness and Complexity of Propositional
Inference

• The truth-table method of inference is complete
• For any proof involving n proposition symbols, 2n
  rows of the table is enumerated
• Complexity is O(2n)
• A more efficient inference procedure relies on
  the monotonicity

39
Monotonicity

• A logic is monotonic if when we add some new
  sentences to the knowledge base, all the
  sentences entailed by the original knowledge base
  are still entailed by the new larger knowledge
  base
• This is true regardless of the contents of the
  new knowledge base it can be irrelevant or even
  contradictory to the original knowledge base
• Propositinal logic and first-logic are monotonic
  in this sense

40
A Knowledge Base Example
41
An Inference Example
42
The Wumpus World
43
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

44
Acting and Reasoning in the Wumpus World (1)
45
Acting and Reasoning in the Wumpus World (2)
46
Acting and Reasoning in the Wumpus World (3)
47
Acting and Reasoning in the Wumpus World (4)
48
Knowledge After the Third Move
49
Propositional Knowledge Base After the Third Move
50
Finding the Wumpus
51
Propositional Agent Action

• Action rule example
• Action Query
• while(actionIterator.hasNext())
• if( kb.ask( new
• ActionQuery(t, action) )
• t
• return action

52
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

53
First-Order Logic Syntax
54
Quantifiers

• Universal quantifier
• Existential quantifier

55
Some Properties of Quantified Sentences
56
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

57
Axioms, Definitions, and Theorems

• Axioms Basic facts about a domain
• Definition Basic description of concepts in a
  domain
• Example Definition of P
• Theorem Sentences proved through axioms and
  definitions
• Independent axioms and redundant axioms

58
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?

59
Special Notations for Sets and Lists
60
Accessing First-Order Logic KB

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

61
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

62
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

63
Reflex Agent

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

64
Reflex Agent for the Wumpus World (1)

• Direct rules
• Example
• Mediated rules
• Example

65
Reflex Agent for the Wumpus World (2)

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

66
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

67
Situational Calculus
68
Representing Changes

• Relations or functions
• Examples
• Function Result
• Examples
• Effect axioms
• Examples

69
Defining Time-Varying Predicates

• Frame axioms
• Examples
• Successor-state axioms
• Example

70
Describing the Map
71
Synchronic Rules

• Causal Rules
• Examples
• Diagnostic Rules
• Examples

72
Diagnostic Rules vs. Model-Based Reasoning

• Reasoning that a square is OK
• Diagnostic rules
• Model-based reasoning

73
Action-Value System

• Example
• Great, Good, Medium, Risky, Deadly
• Recommending an action

74
Agent Exploration Policy

• Great to pick up the gold when found and climbing
  out of the cave with the gold
• Good to move to an OK square that has not been
  visited
• Medium to move to an OK square that has been
  visited
• Risky to move to a square that is not deadly, but
  is not known to be OK either
• Deadly to move to a square that is known to
  contain a pit or a live wumpus

75
Knowledge Engineering

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

76
Knowledge Engineering vs. Programming
77
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

78
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

79
A General Ontology Hierarchy