In this class learned about the knowledge,knowledge based reasoning,Propositional logic,inference,inference rule,first order logic,knowledge engineering.
We humans can make conclusions from the our existing knowledge like we know that computer can compute something and it's need some input.From that we can conclude that it can give some output.
The concept of representing knowledge and drawing conclusions from it is also used in AI, and in this lecture we will explore how we can achieve this behaviour.
Now there are the agents which we know from previous class that agents are the things which can interact with the enviourment.
Knowledge based Agents
The agents which are give reasons by operating on internal representation of knowledge.
Took the example used in class:
What does “reasoning based on knowledge to draw a conclusion” mean?
Let’s start answering this with a Harry Potter example. Consider the following sentences:
If it didn’t rain, Harry visited Hagrid today.
Harry visited Hagrid or Dumbledore today, but not both.
Harry visited Dumbledore today.
Based on these three sentences, we can answer the question “did it rain today?”, even though none of the individual sentences tells us anything about whether it is raining today. Here is how we can go about it: looking at sentence 3, we know that Harry visited Dumbledore. Looking at sentence 2, we know that Harry visited either Dumbledore or Hagrid, and thus we can conclude
Harry did not visit Hagrid.
Now, looking at sentence 1, we understand that if it didn’t rain, Harry would have visited Hagrid. However, knowing sentence 4, we know that this is not the case. Therefore, we can conclude
It rained today.
To come to this conclusion, we used logic, and today’s lecture explores how AI can use logic to reach to new conclusions based on existing information.
Sentence
A sentence is an assertion about the world in a knowledge representation language. A sentence is how AI stores knowledge and uses it to infer new information.
___________ PROPOSITIONAL lOGIC
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Logic /
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\________________ fIRST oRDER lOGIC
Now Propositional logic have the following components
I try to give a diagram representation instead of a text version:
Propostional Logic
propositional logic is based on the statements told by us about the world that can be either true or false.


LOGICAL CONNECTIVES
These are the logical symbols that connect
propositional symbols in order to reason in a
more complex way about the world.

 Not (¬) inverses the truth value of the
proposition.So the example if P:"it is raining"
then ¬P means not raining.

P  false
¬P  true

P  true
¬P  false

 And(^) connects two different propositions. When
these two proposition, P and Q, are connected by
∧, the resulting proposition P ∧ Q is true only in
the case that both P and Q are true.

P  false
Q  false
p^Q  false

P  true
Q  false
p^Q  false

P  false
Q  true
p^Q  false

P  true
Q  true
p^Q  true

 Or (∨) is true as as long as either of its
arguments is true. This means that for P ∨ Q to be
true, at least one of P or Q has to be true.

P  false
Q  false
pvQ  false

P  true
Q  false
pvQ  true

P  false
Q  true
pvQ  true

P  true
Q  true
p^Q  true

It is worthwhile to mention that there are two
types of Or: an inclusive Or and an exclusive Or.
In an exclusive Or, P ∨ Q is false if P ∧ Q is
true. That is, an exclusive Or requires only one of
its arguments to be true and not both. An inclusive
Or is true if any of P, Q, or P ∧ Q is true. In the
case of Or (∨), the intention is an inclusive Or.


 Implication (→) represents a structure of “if P
then Q.” For example, if P: “It is raining” and
Q: “I’m indoors”, then P → Q means “If it is
raining, then I’m indoors.” In the case of P
implies Q (P → Q), P is called the antecedent and
Q is called the consequent.
___________________________
P  false
Q  false
P → Q  true

P  false
Q  true
P → Q  true

P  true
Q  false
P → Q  false

P  true
Q  true
P → Q  true

 Biconditional (↔) is an implication that goes both
directions. You can read it as “if and only if.” P
↔ Q is the same as P → Q and Q → P taken together.
For example, if P: “It is raining.” and Q: “I’m
indoors,” then P ↔ Q means that “If it is raining,
then I’m indoors,” and “if I’m indoors, then it is
raining.” This means that we can infer more than
we could with a simple implication. If P is false,
then Q is also false; if it is not raining, we
know that I’m also not indoors.
___________________________
P  false
Q  false
P → Q  true

P  false
Q  true
P → Q  false

P  true
Q  false
P → Q  false

P  true
Q  true
P → Q  true

Model(The model is an assignment of a truth value
to every proposition.)


Knowledge Base(KB):The knowledge base is a set
of sentences known by a knowledgebased agent. This
is knowledge that the AI is provided about the
world in the form of propositional logic sentences
that can be used to make additional inferences
about the world.
In next part we will look through the inference and model checking algorithm.
Reference:
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