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Unit – 2 – Logical Reasoning
Propositional Logic – Part-II - A Simple Knowledge Base (KB)

We have defined the semantics for propositional logic, we can construct a knowledge base for the Wumpus world
Let Pi,j be true if there is a Pit in [i, j].
Let Bi,j be true if there is a Breeze in [i, j] .
The knowledge base includes the following sentences, each one labeled for convenience:
There is no Pit in [1, 1]:

A square is Breezy if and only if there is a Pit in a neighboring square

The preceding sentences are true in all Wumpus worlds.


The knowledge base consists of sentences R1 through R5
It can also be considered as a single sentence –
The conjunction R1  R2  R3  R4  R5 –
because it asserts that all the individual sentences are true.
A Truth Table constructed for the knowledge base given in the text.
KB is true if R1 through R5 are true, (R1  R2  R3  R4  R5)
which occurs in just 3 of the 128 rows

Sound
Yes, because the inference rules themselves are sound. (This can be proven using a truth table argument).
Complete
Yes, If we allow all possible inference rules (because the rules are limited), we’re searching in a finite state space, hence complete.
If we limit/reduce inference rules, we run the risk of (sometimes) leaving out the necessary one… (hence not complete)

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