predicate calculas

A language which tells us how to build up sentences in the language (i.e., syntax), and and what the sentences mean (i.e., semantics)
An inference procedure which tells us which sentences are valid inferences from other sentences

The symbols of propositional calculus are
the propositional symbols:
P, Q, R, S, …
the truth symbols:
true, false
and connectives:
?, ?, ?, ?, ?
Every propositional symbol and truth symbol is a sentence.
Examples: true, P, Q, R.
The negation of a sentence is a sentence.
Examples: ?P, ? false.
The conjunction, or and, of two sentences is a sentence.
Example: P ? ?P

The disjunction, or or, of two sentences is a sentence.
Example: P ? ?P
The implication of one sentence from another is a sentence.
Example: P ? Q
The equivalence of two sentences is a sentence.
Example: P ? Q ? R

Legal sentences are also called well-formed formulas or WFFs.
An interpretation of a set of propositions is the assignment of a truth value, either T or F to each propositional symbol.
The symbol true is always assigned T, and the symbol false is assigned F.
The truth assignment of negation, ?P, where P is any propositional symbol, is F if the assignment to P is T, and is T is the assignment to P is F.
The truth assignment of conjunction, ?, is T only when both conjuncts have truth value T; otherwise it is F.