Second-Order Quantifier Elimination on Relational Monadic Formulas - A Basic Method and Some Less Expected Applications
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Early Steps of Second-Order Quantifier Elimination beyond the Monadic Case: The Correspondence between Heinrich Behmann and Wilhelm Ackermann 1928-1934 (Abstract)
This presentation focuses on the span between two early seminal papers on second-order quantifier elimination on the basis of first-order logic: Heinrich Behmann’s Habilitation thesis Beiträge zur Algebra der Logik, insbesondere zum Entscheidungsproblem (Contributions to the algebra of logic, in particular to the decision problem), published in 1922 as [4], and Wilhelm Ackermann’s Untersuchunge...
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For relational monadic formulas (the Löwenheim class) second-order quantifier elimination, which is closely related to computation of uniform interpolants, projection and forgetting – operations that currently receive much attention in knowledge processing – always succeeds. The decidability proof for this class by Heinrich Behmann from 1922 explicitly proceeds by elimination with equivalence p...
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Finding solution values for unknowns in Boolean equations was, along with second-order quantifier elimination, a principal reasoning mode in the Algebra of Logic of the 19th century. Schröder [19] investigated it as Auflösungsproblem (solution problem). It is closely related to the modern notion of Boolean unification. For a given formula that contains unknowns formulas are sought such that aft...
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