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Observation:

  1. Sigma summation is iterative form of binary plus.
  2. Pi-capital product is iterative form of multiplication.
  3. Lattice supremum is iterative form binary meet.
  4. Lattice infinum is iterative form binary join.
  5. Existential and universal quatifiers are lattice supremum and infinum.
  6. Integral is summation "in the limit".

Does any quantifier have associated binary operation; for example what generalized quantifiers like "more than 5" corresponds to? Positive answer to this question would hint to binary operation corresponding to the limit quantifier -- essentially we are looking into where sequence "majority" leads to.

Likewise, what might be a binary operation corresponding to lambda abstraction? Having associated binary operation greatly facilitates intuition behind quantifier; it can be thought of as just repetitive application of binary operation.

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    @TegiriNenashi: Lambda abstraction doesn't really fit into your framework, as it operates on _terms_, not _formulae_.2012-06-14

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