Lecture-9

# Lecture-9 - Artificial Intelligence CS 165A 165A Tuesday...

This preview shows pages 1–12. Sign up to view the full content.

Artificial Intelligence S 165A CS 165A Tuesday Feb 2, 2011 irst order logic (Ch 8) First order logic (Ch. 8) 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Notes • HW#3 is out, which will be due next Tuesday o reduce the workload HW #3 only has two questions To reduce the workload, HW #3 only has two questions • Midterm Exam, 10 Feb, 2011, one hour exam – Basic Concept p – Search – MiniMax Method/alpha-beta pruning ropositional Logic – Propositional Logic 2
Relationship: Entail, Infer, Imply • A knowledge base (KB) entails sentences KB •A n inference procedure i can derive from KB KB Implication: P Q P Q β iff the sentence   β is valid 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Important Inference Rules for Propositional Logic 4
The Wumpus World 5 How to describe it using Propositional Logic?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Your Answer • Pxy: true if Pit is at x, y xy trueifa mpus at y Wxy: true if a Wumpus is at x,y • Bxy: true if the agent perceives a breeze at x, y xy true if the agent perceives a stench at x y Sxy: true if the agent perceives a stench at x, y 1: 1 1 R1: P1,1 • R2: B1,1 (P1,2 P2,1) ? R? • R4: B1,1 5: B2 1 R5: B2,1 • R6: ( P1,2) ( P2,1) 6
Propositional logic • “All men are mortal” “ om a man” Tom is a man • What can you infer? – Men => Mortal? – Tom => Man? – Tom => Mortal? 7

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Propositional logic vs. FOL • Propositional logic: P stands for “All men are mortal” Q stands for “Tom is a man” – What can you infer from P and Q? othing! Nothing! • First-order logic: x Man( x ) Mortal( x ) Tom ) hat can you infer from these? – What can you infer from these? Can infer Tom ) 8
First-Order Logic (FOL) A method of analysis or calculation using a special symbolic notation • Also known as First-Order Predicate Calculus –P r o positional logic is also known as Propositional Calculus • An extension to propositional logic in which quantifiers can bind variables in sentences – Universal quantifier ( ) xistential quantifier ( – Existential quantifier ( ) – Variables: x, y, z, a, joe, table… • Examples x Beautiful( x ) t i f l 9 x Beautiful( x )

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
First-Order Logic (cont.) • FOL can express anything that can be programmed is by far the most studied and best understood logic in It is by far the most studied and best understood logic in use • It does have limits, however – Quantifiers ( and ) can only be applied to objects, not to functions or predicates annot write om) = good Cannot write P P (mom) good This is why it’s called first-order – This limits its expressiveness • Let’s look at the syntax of first-order logic – I.e., what logical expressions can you legally construct? 10
FOL Syntax • Symbols –O b ject symbols (constants): P, Q, Fred, Desk, True, False, … These refer to things Predicate symbols: Heavy, Smart, Mother, … hese are ue or false statements out objects: Smart( ck These are true or false statements about objects: Smart( rock ) Function symbols: Cosine, IQ, MotherOf, … These return objects, exposing

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/22/2011 for the course CS 165A taught by Professor Su during the Spring '11 term at UCSB.

### Page1 / 45

Lecture-9 - Artificial Intelligence CS 165A 165A Tuesday...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online