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Everything about If and only if

Logical connective

In logic and related fields such as mathematics and philosophy, "if and only if" states that the truth values of two statements are equal. It is paraphrased by the biconditional, a logical connective between statements. The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional, and can be likened to the standard material conditional combined with its converse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other, though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, P if and only if Q means that P is true whenever Q is true, and the only case in which P is true is if Q is also true, whereas in the case of P if Q, there could be other scenarios where P is true and Q is false. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: If and only ifA 5-minute orientation
  2. Skim a recent paper: Interesting features finder (IFF): Another way to explore spectroscopic imaging data sets giving minor compounds and traces a chance to express themselvesInfluential work since 2022
  3. Pick up a classic book: Review of DOD's combat aircraft identification programThe most-reprinted book on the subject
  4. Read the landmark paper: The IFF proof procedure for abductive logic programmingCited 115 times
  5. Go sideways: Logical biconditionalA closely related topic
  6. Go sideways: Logical connectiveA closely related topic

📖 Definitions

Symbol ISO 639-3 language code for Ifo.

Conjunction Abbreviation of if and only if.

Conjunction Obsolete spelling of if.

🗂️ The subject at a glance

  1. Definition
  2. Usage
  3. In terms of Euler diagrams
  4. More general usage
  5. When "if" means "if and only if"

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics