CS621: Artificial Intelligence

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CS621: Artificial Intelligence. Pushpak Bhattacharyya CSE Dept., IIT Bombay Lecture 34– Predicate Calculus and Himalayan Club example (lectures 32 and 33 were on HMM+Viterbi combined AI and NLP). Resolution - Refutation. man(x) → mortal(x) Convert to clausal form

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## CS621: Artificial Intelligence

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### CS621: Artificial Intelligence

Pushpak BhattacharyyaCSE Dept., IIT Bombay

Lecture 34– Predicate Calculus and Himalayan Club example

(lectures 32 and 33 were on HMM+Viterbi combined AI and NLP)

Resolution - Refutation
• man(x) → mortal(x)
• Convert to clausal form
• ~man(shakespeare) mortal(x)
• Clauses in the knowledge base
• ~man(shakespeare) mortal(x)
• man(shakespeare)
• mortal(shakespeare)
Resolution – Refutation contd
• Negate the goal
• ~man(shakespeare)
• Get a pair of resolvents
Search in resolution
• Heuristics for Resolution Search
• Goal Supported Strategy
• Set of support strategy
• Always one of the resolvents is the most recently produced resolute
Inferencing in Predicate Calculus
• Forward chaining
• Given P, , to infer Q
• P, match L.H.S of
• Assert Q from R.H.S
• Backward chaining
• Q, Match R.H.S of
• assert P
• Check if P exists
• Resolution – Refutation
• Negate goal
• Convert all pieces of knowledge into clausal form (disjunction of literals)
• See if contradiction indicated by null clause can be derived
P
• converted to

Draw the resolution tree (actually an inverted tree). Every node is a clausal form and branches are intermediate inference steps.

Terminology
• Pair of clauses being resolved is called the Resolvents. The resulting clause is called the Resolute.
• Choosing the correct pair of resolvents is a matter of search.
Predicate Calculus
• Introduction through an example (Zohar Manna, 1974):
• Problem: A, B and C belong to the Himalayan club. Every member in the club is either a mountain climber or a skier or both. A likes whatever B dislikes and dislikes whatever B likes. A likes rain and snow. No mountain climber likes rain. Every skier likes snow. Is there a member who is a mountain climber and not a skier?
• Given knowledge has:
• Facts
• Rules
Predicate Calculus: Example contd.
• Let mc denote mountain climber and sk denotes skier. Knowledge representation in the given problem is as follows:
• member(A)
• member(B)
• member(C)
• ∀x[member(x) → (mc(x) ∨ sk(x))]
• ∀x[mc(x) → ~like(x,rain)]
• ∀x[sk(x) → like(x, snow)]
• ∀x[like(B, x) → ~like(A, x)]
• ∀x[~like(B, x) → like(A, x)]
• like(A, rain)
• like(A, snow)
• Question: ∃x[member(x) ∧ mc(x) ∧ ~sk(x)]
• We have to infer the 11th expression from the given 10.
• Done through Resolution Refutation.
Club example: Inferencing
• member(A)
• member(B)
• member(C)
• Can be written as

member(A)

• member(B)
• member(C)
• Now standardize the variables apart which results in the following

10

7

12

5

4

13

14

2

11

15

16

13

2

17

Assignment
• Prove the inferencing in the Himalayan club example with different starting points, producing different resolution trees.
• Think of a Prolog implementation of the problem
• Prolog Reference (Prolog by Chockshin & Melish)

### Problem-2

From predicate calculus

A “department” environment
• Dr. X is the HoD of CSE
• Y and Z work in CSE
• Dr. P is the HoD of ME
• Q and R work in ME
• Y is married to Q
• By Institute policy staffs of the same department cannot marry
• All married staff of CSE are insured by LIC
• HoD is the boss of all staff in the department
Diagrammatic representation

CSE

ME

Dr. P

Dr. X

Z

Y

R

Q

married

Questions on “department”
• Who works in CSE?
• Is there a married person in ME?
• Is there somebody insured by LIC?

### Text Knowledge Representation

past tense

bought

time

agent

object

student

June

computer

the: definite

in: modifier

a: indefinite

modifier

new

A Semantic Graph

The student bought a new computer in June.

UNL representation

Representation of Knowledge

UNL: a United Nations project

Dave, Parikh and Bhattacharyya, Journal of Machine Translation, 2002

• Started in 1996
• 10 year program
• 15 research groups across continents
• First goal: generators
• Next goal: analysers (needs solving various ambiguity problems)
• Current active language groups
• UNL_French (GETA-CLIPS, IMAG)
• UNL_Hindi (IIT Bombay with additional work on UNL_English)
• UNL_Italian (Univ. of Pisa)
• UNL_Portugese (Univ of Sao Paolo, Brazil)
• UNL_Russian (Institute of Linguistics, Moscow)
Knowledge Representation

UNL Graph - relations

agt

obj

Ram

newspaper

Knowledge Representation

UNL Graph - UWs

obj

agt

newspaper(icl>print_media)

Ram(iof>person)

Knowledge Representation

UNL graph - attributes

@entry

@present

@progress

obj

agt

@def

newspaper(icl>print_media)

Ram(iof>person)

go(icl>move)

@ entry @ past

agt

plt

boy(icl>person)

@ entry

school(icl>institution)

here

agt

plc

:01

work(icl>do)

The boy who works here went to school

Another Example

What do these examples show?
• Logic systematizes the reasoning process
• Helps identify what is mechanical/routine/automatable
• Brings to light the steps that only human intelligence can perform
• These are especially of foundational and structural nature (e.g., deciding what propositions to start with)
• Algorithmizing reasoning is not trivial