The logical formalism of a language is useful because it immediately suggests a powerful way of deriving new knowledge from old using mathematical deduction.
In this formalism, we can conclude that a new statement is true by proving that it follows from the statements that are already known.
Proposition
A proposition is a statement, or a simple declarative sentence.
For example, “the book is expensive” is a proposition.
A proposition can be either true or false.
Propositional logic
Logical constants: true, false
Propositional symbols: P, Q, S,… (atomic sentences)
Propositions are combined by connectives:
Propositional logic is a simple language useful for showing key ideas and definitions.
User defines a set of propositional symbols, like P and Q.
User defines the semantics of each propositional symbol:
P means “It is hot”
Q means “It is humid”
R means “It is raining”
A sentence (well-formed formula) is defined as follows:
Real world facts can be represented by well-formed formulas (wffs) in propositional logic.
