Overview
Propositional logic is a simple logic that encapsulates reasoning about truth assignments. That is, each variable in the logic is meant to be assigned a truth value, either true or false, and compound formulas can be built from these atomic building blocks, using connectives such as and or or. These compound expressions can then be evaluated for their truth values, given the assignments of the underlying variables. As the underlying assignments change, so does the truth value of the compound formula.
Syntax
- A set of variables, {% x_1, x_2, ... %}, each of which is considered a formula
- Given formulas {% \phi %} and {% psi %}, the following are formulas
- {% \neg \phi %}
- {% \phi \wedge \psi %}
- {% \phi \vee \psi %}
- {% \phi \rightarrow \psi %}