Artificial Intelligence Lecture 10: Logical Agents and Knowledge-Based Systems - Prof. Dav, Study notes of Computer Science

A portion of cs 416 artificial intelligence lecture notes focusing on logical agents and knowledge-based systems. It includes information on logical agents, the benefits of studying them, components of a knowledge-based agent, and an example of logical reasoning using the wumpus world. The document also covers knowledge representation, logical reasoning, and model checking.

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Uploaded on 03/19/2009

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CS 416
Artificial Intelligence
Lecture 10
Logical Agents
Chapter 7
Midterm Exam
Midterm will be on Thursday, March 13th
It will cover material up until Feb 27th
Chess Article
•Garry Kasparov reflects on computerized chess
IBM should have released the contents of Deep Blue to chess
community to advance research of computation as it relates to
chess
Kudos to Deep Junior for putting information in public domain
so state of the art can advance
Deep Blue made one good move the surprised Kasparov
(though he thinks a person was in the loop)
Deep Junior made a fantastic sacrifice that reflects a new
accomplishment for computerized chess
•http://www.opinionjourn al.com/extra/?id=110003081
Logical Agents
What are we talking about, “logical?”
Aren’t search-based chess programs logical
Yes, but knowledge is used in a very specific way
Win the game
Not useful for extracting strategies or understanding other aspects
of chess
We want to develop more general-purpose
knowledge systems that support a variety of logical
analyses
Why study knowledge-based agents
Partially observable environments
combine available information (percepts) with general
knowledge to select actions
Natural Language
Language is too complex and ambiguous. Problem-solving
agents are impeded by high branching factor.
Flexibility
Knowledge can be reused for novel tasks. New knowledge
can be added to improve future performance.
Components of knowledge-based agent
•Knowledge Base
Store information
knowledge representation language
Add information (Tell)
Retrieve information (Ask)
Perform inference
derive new sentences (knowledge) from existing sentences
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pf5

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CS 416

Artificial Intelligence

Lecture 10 Logical Agents Chapter 7

Midterm Exam

  • Midterm will be on Thursday, March 13 th
  • It will cover material up until Feb 27 th

Chess Article

•Garry Kasparov reflects on computerized chess

  • IBM should have released the contents of Deep Blue to chess community to advance research of computation as it relates to chess
  • Kudos to Deep Junior for putting information in public domain so state of the art can advance
  • Deep Blue made one good move the surprised Kasparov (though he thinks a person was in the loop)
  • Deep Junior made a fantastic sacrifice that reflects a new accomplishment for computerized chess •http://www.opinionjournal.com/extra/?id=

Logical Agents

  • What are we talking about, “logical?”
    • Aren’t search-based chess programs logical
      • Yes, but knowledge is used in a very specific way
        • Win the game
        • Not useful for extracting strategies or understanding other aspects of chess
    • We want to develop more general-purpose knowledge systems that support a variety of logical analyses

Why study knowledge-based agents

  • Partially observable environments
    • combine available information (percepts) with general knowledge to select actions
  • Natural Language
    • Language is too complex and ambiguous. Problem-solving agents are impeded by high branching factor.
  • Flexibility
    • Knowledge can be reused for novel tasks. New knowledge can be added to improve future performance.

Components of knowledge-based agent

•Knowledge Base

  • Store information
    • knowledge representation language
  • Add information (Tell)
  • Retrieve information (Ask)
  • Perform inference
    • derive new sentences (knowledge) from existing sentences

The wumpus world

  • A scary world, indeed
    • A maze in a cave
    • A wumpus who will eat you
    • One arrow that can kill the wumpus
    • Pits that can entrap you (but not the wumpus for it is too large to fall in)
    • A heap of gold somewhere

But you have sensing and action

  • Sensing (each is either on or off – a single bit)
    • wumpus emits a stench in adjacent squares
    • pits cause a breeze in adjacent squares
    • gold causes glitter you see when in the square
    • walking into wall causes a bump
    • death of wumpus can be heard everywhere in world

But you have sensing and action

  • Action
    • You can turn left or right 90 degrees
    • You can move forward
    • You can shoot an arrow in your facing direction

An example

An example Our agent played well

  • Used inference to relate two different percepts observed from different locations
  • Agent is guaranteed to draw correct conclusions if percepts are correct

Logical inference

  • Entailment permitted logic
    • we inferred new knowledge from entailments
  • Model Checking
    • We enumerated all possibilities to ensure inference was complete

Inference Algorithms

  • Sound
    • only entailed sentences are inferred
    • always true
  • Complete
    • inference algorithm can derive any sentence that is entailed
    • can inference algorithm become caught in infinite loop?

Propositional (Boolean) Logic

  • Syntax of allowable sentences
    • atomic sentences
      • indivisible syntactic elements
      • one propositional symbol
      • Use uppercase letters as representation
      • True and False are predefined proposition symbols

Complex sentences

  • Formed from symbols using connectives
    • ~ (not): the negation
    • ^ (and): the conjunction
    • V (or): the disjunction
    • => (implies): the implication
    • Ù (if and only if): the biconditional

Backus-Naur Form (BNF) Propositional (Boolean) Logic

  • Semantics
    • given a particular model (situation), what are the rules that determine the truth of a sentence?
    • use a truth table to compute the value of any sentence with respect to a model by recursive evaluation

Truth table Example from wumpus

•A square is breezy only if a neighboring square has a pit

  • B1,1 Ù (P1,2 V P2,1)

•A square is breezy if a neighboring square has a pit

  • (P1,2 V P2,1) => B1,

•Former is more powerful and true to wumpus rules

A wumpus knowledge base

  • Initial conditions
    • R 1 : ~P (^) 1,1 no pit in [1,1]
  • Rules of Breezes (for a few example squares) - R 2 : B (^) 1,1 Ù (P (^) 1,2 V P (^) 2,1) - R 3 : B (^) 2,1 Ù (P (^) 1,1 V P (^) 2,1 V P (^) 3,1)
  • Percepts
    • R 4 : ~B (^) 1,
    • R 5 : B (^) 2, •We know: R 1 ^ R 2 ^ R 3 ^ R 4 ^ R 5

Inference

  • Does KB entail α (KB -> α?)
    • Is there a pit in [1,2]: P (^) 1,2?
    • Consider only what we need
      • B1,1 B2,1 P1,1 P1,2 P2,1 P2,2 P3,
      • 2^7 permutations of models to check
    • For each model, see if KB is true
    • For all KB = True, see if α is true

Inference

  • Truth table

Concepts related to entailment

•logical equivalence

  • a and b are logically equivalent if they are true in the same set of models… aÙ b •validity (or tautology)
  • a sentence that is valid in all models
  • P V ~P
  • deduction theorem: a entails b if and only if a implies b •satisfiability
  • a sentence that is true in some model
  • a entails b Ù (a ^ ~b) is unsatisfiable