Propositional Logic
Propositional logic, also called zeroth-order logic, is a formal system. Given the properties of a formal system, this means that the rules are entirely regular. The primary application of propositional logic is to model statements in natural language.
Domain
There are only two distinct values: true and false, denoted by T and F respectively.
Syntax
The rules for constructing expressions in propositional logic follow.
Negation
A negation is denoted by the following symbol: .
Connective
A connective is one of the following symbols: .
Atom
An atom is denoted by a string of letters without spaces. For instance:
Clause
A clause is either of the following: an atom; or a clause, followed by a connective, followed by a clause. In the second case, it must be enclosed in parentheses. A clause may be preceded by a negation. For instance:
Semantics
The rules for determining the value of expressions follow.
Atom
An atom can have one of the values T and F, but not both or neither.
Negation
If an atom a is preceded by a negation, the value of the resulting expression is represented by this table:
T | F |
F | T |
Clause
The rules for determining the value of clauses follow, where a and b are some given clauses:
T | T | T | T |
T | F | F | T |
F | T | F | T |
F | F | F | F |
Thus conclude the rules of propositional logic.