Hintikka set

In mathematical logic, a Hintikka set is a set of logical formulas whose elements satisfy the following properties:

  1. An atom or its conjugate can appear in the set but not both,
  2. If a formula in the set has a principle operator that is of "conjuctive-type", then its two operands appear in the set,
  3. If a formula in the set has a principle operator that is of "disjuntive-type", then at least one of its two operands appears in the set.

The exact meaning of "conjuctive-type" and "disjunctive-type" is defined by the method of semantic tableaux.

Hintikka sets arise when attempting to prove completeness of propositional logic using semantic tableaux. They are named after Jaakko Hintikka.

References
  • Smullyan, R. M. (1971). First-Order Logic (Second printing ed.). Springer Science & Business Media. pp. 21, 26–27. ISBN 978-3-642-86720-0. LCCN 68-13495.
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