propositional variable

A propositional variable can stand on its own as an atomic formula.

Each propositional variable is, on its own, a formula.

Such a formula can be made either true or false based on the values assigned to its propositional variables.

The satisfaction relation is uniquely determined by its value on propositional variables.

Keep repeating this until all dependencies on propositional variables have been eliminated.

Assigning values for propositional variables is referred to as valuation.

The interpretation of a propositional variable is one of the two truth values true and false.

In this context, a valuation begins with an assignment of a truth value to each propositional variable.

If is a propositional variable, then is a formula.

We define a truth assignment as a function that maps propositional variables to true or false.

Their definition begins with the arbitrary choice of a set V of propositional variables.

For a language with n distinct propositional variables there are 2 distinct possible interpretations.

Propositional variables are represented as nullary predicates in first order logic.

If a propositional variable occurs with only one polarity in the formula, it is called pure.

Every variable can be conceived as a propositional variable.

The simplest type of propositional formula is a propositional variable.

The alpha set is a finite set of elements called proposition symbols or propositional variables.

Some authors also admit propositional variables in first-order logic, which must then also be interpreted.

A modal sentence is a modal formula that contains no propositional variables.

Propositional variables are the atomic formulas of propositional logic.

Propositional variables become variables in the Boolean domain.

In propositional calculus a literal is simply a propositional variable or its negation.

The not operator can only be used as part of a literal, which means that it can only precede a propositional variable.

There are 8 possible valuations for the propositional variables A, B, C, represented by the first three columns of the following table.

The rules allow one to transpose propositional variables within logical expressions in logical proofs.