What is a Sub Formula and What is a Maximal Sub Formula in Propositional Logic

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The notion of a subformula is absolutely standard -- have you consulted a textbook or two? If so, which book(s), and which page(s) did you not understand?

Informally, a subformula is a part of a wff which is itself a wff. More formally the best approach is via the idea of the constructional history for a wff, with the subformulae being the wffs that appear in the history. Any decent textbook will explain this, and explain how you set out constructional histories as trees.

"Maximal subformula" is not standard jargon, so I'll comment on that. The usual way of setting things up formally is to allow any wff that appears on a construction tree of the wff $A$ to count as a subformula of $A$, including $A$ itself -- so trivially the maximal subformula of $A$, in the natural sense of the biggest one, is $A$ itself. The maximal proper subformula(e) of $A$ would be the subformula or subformulae which appear at the penultimate level of the construction tree.

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Updated on August 01, 2022

Comments

  • Pavan K
    Pavan K over 1 year

    What is a Sub formula of a Propositional Formula? Suppose I have a formula C or -C Then what are the sub formulas of this and what is the maximal sub formula of this Propositional Formula. I am a bit confused of these terms. Kindly explain.

    Thanks,

  • Peter Smith
    Peter Smith almost 10 years
    Yes "need" was too strong. I've edited.
  • Doug Spoonwood
    Doug Spoonwood almost 10 years
    I'd like to understand your view better. Why do you think the constructional history for a wff the best approach?