Propositional Logic Sentence

From GM-RKB
Jump to navigation Jump to search

A Propositional Logic Sentence is a formal logic sentence composed of propositional variables and propositional relations.



References

2009

  • (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Propositional_formula
    • In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, or a sentential formula.

      A propositional formula is constructed from simple propositions, such as "x is greater than three" or propositional variables such as P and Q, using connectives such as NOT, AND, OR, and IMPLIES; for example:

      (x = 2 AND y = 4) IMPLIES x + y = 6.

      In mathematics, a propositional formula is often more briefly referred to as a “proposition", but, more precisely, a propositional formula is not a proposition but a formal expression that denotes a proposition, a formal object under discussion, just like an expression such as "x + y" is not a value, but denotes a value. In some contexts, maintaining the distinction may be of importance.

2005

  • (Goldrei, 2005) ⇒ Derek Goldrei. (2005). “Propositional and Predicate Calculus: A mOdel of Argument." Springer.
    • QUOTE: Our formal version of statements, which we'll call formulas, is given by the following definition.
      • Definition: Formula Let [math]\displaystyle{ P }[/math] be a set of propositional variables and let [math]\displaystyle{ S }[/math] be the set of connectives {...}. A formula is a member of the set Form(P,S) of strings of symbols involves elements of P, S and brackets (and ) formed according to the following rules.
        • (i) Each propositional variable is a formula.
        • (ii) If theta and ψ are formuals, then so are::
          • ¬θ
          • (θψ)
          • (θψ)
          • (θψ)
          • (θψ)
        • (iii) All formulas arise from finitely many applications of (i) and (ii).
        • If we use a different set [math]\displaystyle{ S }[/math] of connectives, for instance just {Or, implies}, then clause (ii) is amended accordingly to cover just these symbols.
      • In many books the phrase well-formed formula is used instance of formula. These 'well-formed' emphasizes that the string has to obey special construction rules.