DEALING WITH

INCONSITENCIES~ANKIT SHARMA

M.Tech 3rd Sem

ROLL No. 312

LOGIC-a brief intro

• Logic is used to represent textual information in a formal way in

order to give the information a precise meaning and to remove

ambiguity.

• For example, we might want to express that every day when it

rains, the streets are wet.

• In first-order logic (FOL) we might express the fact that it is

raining at a specific day using a predicate rain with an

argument representing the date when it is raining, e.g., the fact

that it is raining on August, 24th, 2009 might be expressed with

the following predicate rain(24082009).

• So we conclude:

∀X : rain(X) → streets wet(X)

if we know that rain(24082009) because we observed the rain at the given date,

then we infer streets wet(24082009), which is not known before. Hence, logical reasoning can

be used to derive new facts.

Certainty factor• The Door Bell Problem

• The door bell rang at 12 O’clock in midnight.

• -was someone at the door?

• -did Mohan wake up?

• -Proposition 1: atdoor(x) doorbell.

• -Proposition 2: doorbell wake(Mohan).

Reasoning about Door Bell

Given doorbell can we say

at doorbell(x), because atDoor(x) doorbell.

Abductive reasoning.

But no, the doorbell might start ringing due to

other reasons:-

-short circuit.

-wind.

-animals.

Cnt….

• Given doorbell, can we say

• Wake(Mohan), because doorbell wake(Mohan).

• Deductive reasoning.

• yes, only if proposition 2 is always true.

• However in general Mohan may not wakeup even if

the bell rings.

Cnt…

• Therefore, we cannot answer either of the

questions with certainty.

• Proposition 1 is incomplete so modifying it as

• Atdoor(x)v shortcircuit v wind…….. Doorbell.

• Doesn't help because the list of possible causes

on the left is huge(infinite may be).

• Proposition is often true but not a tautology.

Any way out?

• However, problems like that of the doorbell are

very common in real life.

• In A.I we often need to reason under such

circumstances.

• We solve it by proper modeling of uncertainty

• & impreciseness and developing appropriate

reasoning techniques.

IMPRECISENESS

Often rarely sometimes.

e.g. boy is very tall.

UNCERTAINITY

It will rain in December.

Non monotonic reasoning

• In first order logic, adding new axioms increases

the amount of knowledge base. Therefore set of

facts and inferences in such systems can grow

larger, they cannot be reduced i.e. they increase

monotonically.

• But Nonmonotonic reasoning means adding new

facts to the database will contradict and invalidate

the old knowledge.

example

• We first state that all birds can fly and that one bird is named Tweety.

• ∀X : bird(X) → fly(X)

• bird(tweety)

• From this two pieces of knowledge we can derive that Tweety can fly, i.e.,

• bird(tweety) ∀X : bird(X) → fly(X)

• fly(tweety)

• If we add another fact like Tom is also a bird bird(Tom), then we can also derive that

Tom is also able to fly. Hence, more knowledge allows us to derive more new rules

and facts. As a consequence we conclude that classical reasoning (in FOL) is

monotonic.

• The situation changes if we add new knowledge like penguins cannot fly and that

Tweety is a penguin.

• ∀X : penguin(X) → ￢fly(X)

• penguin(tweety)

• In this case we derive a contradiction from which we can derive everything.

Truth maintenance systems

• Necessary when changes in the fact-base lead

to inconsistency / incorrectness among the facts

non-monotonic reasoning

• A Truth Maintenance System tries to adjust the

Knowledge Base or Fact Base upon changes to

keep it consistent and correct.

• A TMS uses dependencies among facts to keep

track of conclusions and allow revision /

retraction of facts and conclusions.

Dependency…….example• Suppose the knowledge base KB contained only the propositions P, P →Q. From this IE would right

fully conclude Q and this conclusion to the KB. Later if it was learned that if P was inappropriate, it

would be added to the KB resulting in an contradiction. Consequenlty it woluld be necessary to

remove P to eliminate the inconsistency. But with the P now removed, Q is no longer a justified

belief. It should be removed . This type of job is done by TMS.

• Actually the TMS does not discard the conclusions like Q as suggested. That could be wasteful since

p became again valid. so again we have to re-derive it .instead TMS maintains a dependency

records for all such conclusions. The records determine which se of beliefs are current (which are to

be used by IE). Thus Q would be removed from the current belief set and not deleted.

TMS

KNOWLEDGE

BASE

INFERENCE TELL

ENGINE ASK

Architecture of the problem

solver with TMS

Structured knowledge

When the quantity of information becomes large, the maintenance of

knowledge becomes difficult. in such cases, some form of knowledge

structuring is done.

PROFESSION(bob,professor)

FACULTY(bob,engineering)

.

.

MARRIED(bob,sandy)

FATHER-OF(bob,sue,joey)

OWNS(bob,house)

ASSOCIATIVE NETWORKS

• Network representations provides a means of structuring and

exhibiting the structure in knowledge.

• Network representations give a pictorial presentation of objects ,

their attributes and their relationships that exist between them and

other entities.

Can

• a-kind-of color

Has

fragment of associative n/w.

bird

wings

fly

yellowtweety

Understanding Frames

• Frames were first introduced by Marvin minsky as

a data structure to represent a mental model of a

stereotypical situation such as driving a car,

attending a meeting or eating in a restaurant.

• Knowledge about an object or event is stored

together in memory as a unit, then when a new

frame is encountered, an appropriate frame is

selected from memory for use in reasoning about

the situation.

Understanding Frames – Facts

Frames are record-like structures that have slots & slot-

values for an entity

Using frames, the knowledge about an object/event can be

stored together in the KB as a unit

A slot in a frame

specify a characteristic of the entity which the frame

represents

Contains information as attribute-value pairs, default

values etc.

Frame syntax

• (<frame name>

(<slot1>(<facet 1><value1>…<value1>)

(<facet 2><value2>…<value2>)

.

.

(<slot2>(<facet 1><value1>…<valuem>)

.

.

. )

Understanding Frames - Examples

1. An example frame:

• (Tweety

• (SPECIES (VALUE bird))

• (COLOR (VALUE yellow))

• (ACTIVITY (VALUE fly)))

2. Employee Details

• ( Ruchi Sharma

• (PROFESSION (VALUE Tutor))

• (EMPID (VALUE 376074))

• (SUBJECT (VALUE Computers)))

Graphical Representation

• Graphs easy to store in a computer

• To be of any use must impose a formalism

Conceptual Graphs

• Semantic network where each graph represents a single proposition

• Concept nodes can be– Concrete (visualisable) such as restaurant, my dog Spot

– Abstract (not easily visualisable) such as anger

• Edges do not have labels– Instead, conceptual relation nodes

– Easy to represent relations between multiple objects

Thank you