Higher-Order Illative Combinatory Logic
نویسندگان
چکیده
منابع مشابه
Higher-order illative combinatory logic
We show a model construction for a system of higher-order illative combinatory logic Iω, thus establishing its strong consistency. We also use a variant of this construction to provide a complete embedding of first-order intuitionistic predicate logic with second-order propositional quantifiers into the system I0 of Barendregt, Bunder and Dekkers, which gives a partial answer to a question pose...
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This work introduces the theory of illative combinatory algebras, which is closely related to systems of illative combinatory logic. We thus provide a semantic interpretation for a formal framework in which both logic and computation may be expressed in a unified manner. Systems of illative combinatory logic consist of combinatory logic extended with constants and rules of inference intended to...
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In [3] the prepositional connectives were defined in terms of the combinators K and S and the illative obs Ξ and H (ΞXY can be interpreted as “Y V holds for all V such that XV holds” and HX can be interpreted as “X is a proposition”). Given an elimination rate for Ξ and introduction rules for H and Ξ, all the standard intuitionistic propositional calculus results could be proved provided the va...
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Illative systems of combinatory logic or lambda-calculus consist of type-free combinatory logic or lambda-calculus extended with additional constants intended to represent logical notions. In fact, early systems of combinatory logic and lambda calculus (by Schönfinkel [15], Curry [4] and Church [2, 3]) were meant as very simple foundations for logic and mathematics. However, the Kleene-Rosser a...
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Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers 4 systems of illative combinatory logic that are sound for first-order propositional and predicate calculus.
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2013
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl.7803080