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Programming with Higher-Order Logic

open access: yes, 2012
Formal systems that describe computations over syntactic structures occur frequently in computer science. Logic programming provides a natural framework for encoding and animating such systems. However, these systems often embody variable binding, a notion that must be treated carefully at a computational level.
Miller, Dale, Gopalan, Nadathur
openaire   +5 more sources

Boolean-Valued Second-Order Logic

open access: yesNotre Dame Journal of Formal Logic, 2015
In so-called full second-order logic, the second-order variables range over all subsets and relations of the domain in question. In so-called Henkin second-order logic, every model is endowed with a set of subsets and relations which will serve as the ...
Jouko Väänänen
exaly   +2 more sources

On connections and higher-order logic

Journal of Automated Reasoning, 1989
Mathematics Technical ...
openaire   +1 more source

Hauptsatz for higher order logic

Journal of Symbolic Logic, 1968
I shall prove in this paper that Gentzen's Hauptsatz is extendible to simple type theory, i.e., to the predicate logic obtained by admitting quantification over predicates of arbitrary finite type and generalizing the second order quantification rules to cover quantifiers of other types.
openaire   +1 more source

Connections and higher-order logic

1986
Theorem proving is difficult and deals with complex phenomena. The difficulties seem to be compounded when one works with higher-order logic, but the rich expressive power of Church's formulation [10] [3] of this language makes research on theorem proving in this realm very worthwhile.
openaire   +1 more source

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