Unit Two

1
Unit Two

• Knowledge and Reasoning continued

2
Review The concept of a Knowledge Base

• A knowledge base (KB) is a set of
  representations (sentences) of facts about the
  world.
• The KB stores these representations using a set
  of sentences in a formal language
• TELL and ASK - two basic operations
• to add new knowledge to the KB
• to query what is known to the KB
• Infer - what should follow after the KB has been
  TELLed.

3
Review Implementation

• In order to do this we need to have some sort of
  language in which the KB encodes its knowledge
  and in which we can ask the KB questions.
• This is typically done with some form of Logic

4
Review What is Logic?

• A formal language
• Syntax what expressions are legal
• Semantics what legal expressions mean
• Proof system a way of manipulating syntactic
  expressions to get other syntactic expressions
  (which will tell us something new)
• Why proofs? Two kinds of inferences an agent
  might want to make
• Multiple percepts ? conclusions about the world
• Current state operator ? properties of next
  state

5
Review Types of logic
6
Review Propositional logic syntax
7
Review Propositional logic semantics
8
Truth tables for basic connectives
Tables that show truth values for all possible
inputs to a logical operator.
9
Complex Truth Tables

• We can produce truth tables for complex logical
  expressions, which show the overall value of the
  expression for all possible combinations of
  variables

10
Tautology

• The expression A v A is a tautology.
• This means it is always true, regardless of the
  value of A.
• A tautology is true under any interpretation.
• An expression which is false under any
  interpretation is contradictory.

11
Equivalence

• Two expressions are equivalent if they always
  have the same logical value under any
  interpretation
• A ? B ? B ? A
• Equivalences can be proven by examining truth
  tables.

12
Some Useful Equivalences

• A v A ? A
• A ? A ? A
• A ? (B ? C) ? (A ? B) ? C
• A v (B v C) ? (A v B) v C
• A ? (B v C) ? (A ? B) v (A ? C)
• A ? (A v B) ? A
• A v (A ? B) ? A
• A ? true ? A A ? false ? false
• A v true ? true A v false ? A

13
Standard Logical Equivalences
14
Proof methods
15
Propositional inference enumeration method
16
Enumeration Solution
17
Inference rules
18
What can we say about Wumpus?
19
Wumpus World Sentences
20
Wumpus World Sentences