tl;dr: Propositional calculus is a branch of logic that deals with propositions, which are statements that can be either true or false.

## What is a proposition?

A proposition is a statement that is either true or false. In AI, propositions are often used as a way of representing knowledge. For example, a proposition might be used to represent the fact that a certain object is a chair.

Propositions can be combined to form more complex statements. For example, the proposition "the sky is blue" can be combined with the proposition "the sun is shining" to form the statement "the sky is blue and the sun is shining."

Propositions can also be used to represent rules or constraints. For example, the proposition "x is greater than y" can be used to represent a rule that x must be greater than y.

## What is the truth value of a proposition?

In AI, the truth value of a proposition is the degree to which the proposition is true. The higher the truth value, the more true the proposition is.

## What is the negation of a proposition?

In AI, the negation of a proposition is the logical opposite of that proposition. So, if a proposition is true, its negation is false, and vice versa. The negation of a proposition is usually symbolized by the symbol "~" (tilde).

## What is the conjunction of two propositions?

In AI, the conjunction of two propositions is a statement that is true if and only if both propositions are true. For example, the conjunction of the propositions "the sky is blue" and "the sun is shining" is the statement "the sky is blue and the sun is shining."

## What is the disjunction of two propositions?

In AI, the disjunction of two propositions is a logical operation that returns true if either of the propositions is true. It is typically used to combine two conditions that must be met in order for a certain action to be taken. For example, the disjunction of the propositions "the light is green" and "the light is yellow" would be true if either of those propositions is true.