The syntax of PL defines the allowable sentences. The Atomic sentences – The indivisible syntactic elements – consists of a single propositional symbol. Each such a symbol stands for proposition that the wumpus is in [1,3]

Complex sentences – constructed from simpler sentences using logical connectives.

$\neg$ not $\neg$ $w_{1, 3}$ is called negation of $w_{1, 3}$

$\wedge$ and $w_{1, 3}$ $\wedge$ $p_3$, 1 is called a conjunction.

V or ($w_{1,3}$ $\wedge$ $p_{3,1}$) V $w_{2,2}$ is called dis-junction.

implies ($w_{1/3}$ $\wedge$ $ p_{3,1}$) $\Rightarrow$ $\neg$ $w_{2,2}$ is called implication it is called as rules or if then statements.

$\Leftrightarrow$ (if and only if) $w_{1,3}$ $\Leftrightarrow$ $\neg$ $w_{2,2}$ is a bi directional.

BNF (Bodacious - Naur Form) grammer of sentences in propositional logic.

Syntax is completely unambiguous means ((A $\wedge$ B) $\Rightarrow$ C) you can write $A \wedge B \Rightarrow C$

The order of precedence in propositional logic is (from highest to lowest):

$ \neg, \wedge, \vee, \Rightarrow, \Leftrightarrow$

Example: $\neg \ P \ V \ Q \ \wedge \ \Rightarrow \ S \ \neq \ ((\neg \ p) \ \vee (Q \ \wedge \ R)) \Rightarrow \ S$

Semantics:

The Semantics defines the rules for determining the truth of a sentence with respect to a particular model. In PL, a model simply fixes the truth values true or false.

Example: If the sentences in KB make use of the proposition symbols $P_{1,2} , \ P_{2,2} , \ P_{3,1}$ then are possible model is,

$m_1$ = { $ P_{1,2}$ = False, $ P_{2,2} $ = False, $ P_{3,1}$ = True }

Proposition symbols = $2^3 = 8$ possible models.