Higher-order illative combinatory logic

نویسنده

  • Lukasz Czajka
چکیده

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 posed by these authors.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Completeness of two systems of illative combinatory logic for first-order propositional and predicate calculus

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.

متن کامل

Completeness of the Propositions-as-Types Interpretation of Intuitionistic Logic into Illative Combinatory Logic

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. In a preceding paper, [2], we considered 4 systems of illative combinatory logic that are sound for first order intuitionistic prepositional and predicate logic. The interpretation from ordinary logic into the illativ...

متن کامل

A Semantic Approach to Illative Combinatory Logic

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...

متن کامل

Semantic consistency proofs for systems of illative combinatory logic

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...

متن کامل

Systems of Illative Combinatory Logic Complete for First-Order Propositional and Predicate Calculus

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 systems of illative combinatory logic that are sound for first-order propositional and predicate calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • J. Symb. Log.

دوره 78  شماره 

صفحات  -

تاریخ انتشار 2013