Knowledge Representation

Use of logic

Artificial agents

need Knowledge and reasoning power Can combine GK with current percepts Build up KB incrementally Logic primary vehicle K always definite ( T/F)

Problem for a robot

If red light is ON or it is morning shift or supervisor absent then door is locked.

If door is locked it implies that the red light is turned ON or it is morning shift or the supervisor is absent

If load is small in size or load is light then the conveyor belt moves

If the conveyor belt is moving then it means the load has a small size or load is light

The Red light is off, the Conveyor belt is not moving and the Door is locked.

The robot wants to know if the load is heavy (not light).

Robot needs a Knowledge Base and reasoning ability

Knowledge base

Central component of a K based agent Set of sentences INFERENCE

– Deriving new info from old

Language to enable building KB

Interpretations

Language semantics defines TRUTH of each sentence w.r.t. each possible world

Similarity with CSP

Constraint solving is a form of Logical reasoning

Constraint languages: LOGICS

Wff and logical reasoning

Entailment:– Sentence follows logically from another sentence

KB |= s iff in every model in which KB is true, s is

also true

Inference algorithm

Enumerate the models Check if s is true in every model

(interpretation) for which KB is also true Backtracking search – recursively assign

values to variables Exponential complexity

definitions

Validity Tautology Deduction theorem Satisfiability inconsistancy

Reasoning patterns in Propositional logic

Inference rules

Modus Ponens And Elimination Standard logical equivalances

– De Morgan– Contra positive– Distributive laws– Associative laws

Deduction

With the knowledge base that the robot has, and what it currently perceives

(more knowledge added to the KB),

the robot wants to deduce that

the load is not light

Knowledge that robot has

If red light is ON or it is morning shift or supervisor absent then door is locked.

If door is locked it implies that the red light is turned ON or it is morning shift or the supervisor is absent

If load is small in size or load is light then the conveyor belt moves

If the conveyor belt is moving then it means the load has a small size or load is light

Observations by the robot

Red light is off Conveyor belt is not moving Door is locked

What the robot wants to establish?

The load is not light

( or in other words it is heavy)

Knowledge + Observation (K.B.)

If red light is ON or it is morning shift or supervisor absent then door is locked.

If door is locked it implies that the red light is turned ON or it is morning shift or the supervisor is absent

If load is small in size or load is light then the conveyor belt moves

If the conveyor belt is moving then it means the load has a small size or load is light

Red light is off Conveyor belt is not moving Door is locked

Propositions

P: red light is ON M: it is morning shift N: supervisor absent D: door is locked. Q: load is small in size R: load is light B: the conveyor belt is moving

Next?

Now generate wffs and start the inference process

Steps to help the robot (inferencing)

Consider a relevant rule for conveyor belt Use And-elimination Use contra-positive relation Use modus ponens Use de morgan’s law

PROOF?

PROOF: Sequence of application of Inference rules. Finding proofs is like finding solutions to search

problems. Successor function generates all possible application

of inference rules In worst case, search for proof would be as bad as

enumerating all the models Some irrelevant propositions can be ignored to

speed up search.

Monotonicity

Set of entailed sentences can only increase as info is added to KB.

Rules can be applied wherever suitable

Resolution

What about completeness? Can everything be inferred? Resolution rule forms basis for a family of

complete inference procedures.

Refutation completeness

Resolution can be used to either

CONFIRM

or

REFUTE a sentence

Artificial Intelligence

Intelligent?

What is intelligence?

computational part of the ability to achieve goals in the world