A.I.- dealing with inconsistencies

1. DEALING WITH
INCONSITENCIES
~ANKIT SHARMA
M.Tech 3rd Sem
ROLL No. 312

2. 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.

3. 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).

4. 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.

5. 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.

6. 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.

7. 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 It will rain in December.
UNCERTAINITY
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.

8. 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.

9. 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.

10. 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.

11. 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.
INFERENCE TELL
ENGINE ASK TMS
Architecture of the problem
solver with TMS
KNOWLEDGE
BASE

12. Structured knowledge
PROFESSION(bob,professor)
FACULTY(bob,engineering)
.
.
MARRIED(bob,sandy)
FATHER-OF(bob,sue,joey)
OWNS(bob,house)
When the quantity of information becomes large, the maintenance of
knowledge becomes difficult. in such cases, some form of knowledge
structuring is done.

13. 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 fly
• a-kind-of color
bird tweety yellow
Has
wings fragment of associative n/w.

14. 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.

15. 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.

16. Frame syntax
• (<frame name>
(<slot1>(<facet 1><value1>…<value1>)
(<facet 2><value2>…<value2>)
.
.
(<slot2>(<facet 1><value1>…<valuem>)
.
.
.)

17. 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)))

18. Graphical Representation
• Graphs easy to store in a computer
• To be of any use must impose a formalism

19. 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

20. Thank you