In propositional logic, a model simply fixes the truth value—true or false—for every proposition symbol.

In AI propositional logic is not categorized as the study of truth values, but it is based on relativity of truth values.

A^B and B^A should have same meaning but in natural language words and sentences may have different meanings. Say foe e.g.:

i. Radha started feeling feverish and Radha went to doctor and

ii. Radha went to the doctor and Radha stared feling feverish.

Here, sentence 1 and sentence 2 have different meanings.

In AI, propositional logic is a relationship between truth values of one statement to that of truth value of other statement.

Syntax:

i. NEGATION ¬ (not). A sentence such as ¬W1,3 is called the negation of W1,3. A literal is either a LITERAL atomic sentence (a positive literal) or a negated atomic sentence (a negative literal).

ii. ∧ (and). A sentence whose main connective is ∧, is called a CONJUNCTION junction; its parts are the conjuncts. E.g. A^B.

iii. DISJUNCTION ∨ (or). A sentence using ∨, such as is a disjunction of the disjuncts. E.g. AVB.

iv. IMPLICATION ⇒ (implies). A sentence such as A⇒B is called an implication.

v. BICONDITIONAL ⇔ (if and only if) is a biconditional.

Atomic sentences are : • True is true in every model and False is false in every model

Semantics:

The truth value of every other proposition symbol must be specified directly in the model. For example, in the model m1 given earlier, P1,2 is false. For complex sentences, we have five rules, which hold for any subsentences P and Q in any model m (here “iff” means “if and only if”):

• ¬P is true iff P is false in m.

• P ∧ Q is true iff both P and Q are true in m.

• P ∨ Q is true iff either P or Q is true in m.

• P ⇒ Q is true unless P is true and Q is false in m.

• P ⇔ Q is true iff P and Q are both true or both false in m.