Propositional Logic Grammar

A Propositional Logic Grammar is a Logic Grammar that can generate Propositional Logic Sentences.

• AKA: Propositional Logic Calculus, Propositional Logic Formal Grammar.
• Context:
  • It can be a PartOf a Propositional Logic System.
• Example(s):
  • Propositional Logic Grammar #1
    • WFF ∈ {Logic Term, Logic Compound}
    • Logic Atom ∈ {True, False, Variable}.
    • Logic Variable ∈ {V₁, V₂, … } (Countable Set)
    • WFF ∈ ¬ WFF | (WFF ∧ WFF) | (WFF ∨ WFF) | (WFF → WFF) | (WFF ↔ WFF)
• See: Propositional Logic Operation Set.

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References

2011

• http://www.iep.utm.edu/prop-log/#H3
  • QUOTE: A well-formed formula (hereafter abbrevated as wff) of PL is defined recursively as follows:
    • Any statement letter is a well-formed formula.
    • If α is a well-formed formula, then so is '¬α'.
    • If α and β are well-formed formulas, then so is '(α & β)'.
    • If α and β are well-formed formulas, then so is '(α v β)'.
    • If α and β are well-formed formulas, then so is '(α → β)'.
    • If α and β are well-formed formulas, then so is '(α ↔ β)'.
    • Nothing that cannot be constructed by successive steps of (1)-(6) is a well-formed formula.

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