Lecture-9

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

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

View Full Document Right Arrow Icon
Artificial Intelligence S 165A CS 165A Tuesday Feb 2, 2011 irst order logic (Ch 8) First order logic (Ch. 8) 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
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
Background image of page 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
Background image of page 3

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

View Full DocumentRight Arrow Icon
Important Inference Rules for Propositional Logic 4
Background image of page 4
The Wumpus World 5 How to describe it using Propositional Logic?
Background image of page 5

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

View Full DocumentRight Arrow Icon
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
Background image of page 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
Background image of page 7

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

View Full DocumentRight Arrow Icon
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
Background image of page 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 )
Background image of page 9

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

View Full DocumentRight Arrow Icon
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
Background image of page 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
Background image of page 11

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

View Full DocumentRight Arrow Icon
Image of page 12
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 Right Arrow Icon
Ask a homework question - tutors are online