Hintikka set

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In mathematical logic, a Hintikka set is a set of

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

Hintikka sets arise when attempting to prove completeness of propositional logic using

In a semantic tableau for propositional logic, Hintikka sets can be defined using uniform notation for propositional tableaux. The elements of a propositional Hintikka set S satisfy the following conditions:^[1]

1. No variable and its conjugate are both in S,
2. For any ${\displaystyle \alpha }$ in S, its components ${\displaystyle \alpha _{1},\alpha _{2}}$ are both in S,
3. For any ${\displaystyle \beta }$ in S, at least one of its components ${\displaystyle \beta _{1},\beta _{2}}$ are in S.

If a set S is a Hintikka set, then S is

References