Ackermann's implication for typefree logic (Q2720395)
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scientific article; zbMATH DE number 1611139
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Ackermann's implication for typefree logic |
scientific article; zbMATH DE number 1611139 |
Statements
11 March 2002
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Ackermann's implication
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type-free logics
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implicative logic
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substructural logic
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positive Ackermann lattice
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partial logic
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positive fragment
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algebraic semantics
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Ackermann's implication for typefree logic (English)
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The implication in Ackermann's system of partial logic has a deductive interpretation, viz. \( A \to B\) means that \(B\) is derivable from \(A\). The paper studies the positive fragment of Ackermann's logic and gives a Hilbert-style and a natural deduction formulations for it. Then it is characterized by a hierarchy of deductive systems. Finally, the paper introduces a new algebraic semantics for the positive fragment of Ackermann's system in terms of so-called `positive Ackermann's lattices', and establishes a completeness result with respect to this semantics.
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