Propositional Logic Sentence Variable

References

http://en.wiktionary.org/wiki/propositional_variable
- 1. (logic) A variable that can either be true or false.
(Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Propositional_variable
- In mathematical logic, a propositional variable (also called a sentential variable or sentential letter) is a variable which can either be true or false. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher logics.
- Formulas in logic are typically built up recursively from some propositional variables, some number of logical connectives, and some logical quantifiers. Propositional variables are the atomic formulas of propositional logic. For example, in a given propositional logic, we might define a formula as follows:
  - Every propositional variable is a formula.
  - Given a formula X the negation ¬X is a formula.
  - Given two formulas X and Y, and a binary connective b (such as the logical conjunction ∧), then (X b Y) is a formula. (Note the parentheses.)
- In this way, all of the formulas of propositional logic are built up from propositional variables as a basic unit.

(Goldrei, 2005) ⇒ Derek Goldrei. (2005). “Propositional and Predicate Calculus: A Model of Argument." Springer.
- QUOTE: With considerations like these in mind, we shall define our formal statements as follows. First we shall specify the formal language, that is, the symbols from which strings can be formed. We shall always allow brackets - these will be needed to avoid ambiguity. We shall specify a set [math]\displaystyle{ P }[/math] of basic statements, called propositional variables. From these we can build more complex statements by joining statements together using brackets and symbols in a set [math]\displaystyle{ S }[/math] of connectives, which are going to represents ways of connecting statements to each other, like V for 'or' and other symbols mentioned earlier. ...
- QUOTE: Convention for variables We shall normally use individual lower case letters like p, q, r, s, ... and subscripted letters like p₀,p₁,p₂,...p_n,... for our propositional variables. Distinct letters or subscripts give us distinct symbols. When we don't specific the set [math]\displaystyle{ P }[/math] of propositional variables in a precise way, we shall use p,q,r and so on to represent different members of the set.