منابع مشابه
On bounded functional interpretations
A unified view over well-known interpretations of intuitionistic logic, such as Gödel’s dialectica interpretation [6], Diller-Nahm interpretation [1] and Kreisel’s modified realizability [7] was achieved through a parametrised interpretation in the intuitionistic logic context [8] but also, very elegantly, in the linear logic setting (see [10], [9] and [3]). In this talk we report on work in pr...
متن کاملOn Interpretations of Bounded Arithmetic and Bounded Set Theory
In [5], Kaye and Wong proved the following result, which they considered to belong to the folklore of mathematical logic. Theorem 1 The first-order theories of Peano arithmetic and ZF with the axiom of infinity negated are bi-interpretable: that is, they are mutually interpretable with interpretations that are inverse to each other. In this note, I describe a theory of sets that is bi-interpret...
متن کاملPolynomially Bounded Matrix Interpretations
Matrix interpretations can be used to bound the derivational complexity of rewrite systems. We present a criterion that completely characterizes matrix interpretations that are polynomially bounded. It includes the method of upper triangular interpretations as a special case, and we prove that the inclusion is strict. The criterion can be expressed as a finite domain constraint system. It trans...
متن کاملHybrid Functional Interpretations
We show how different functional interpretations can be combined via a multi-modal linear logic. A concrete hybrid of Kreisel’s modified realizability and Gödel’s Dialectica is presented, and several small applications are given. We also discuss how the hybrid interpretation relates to variants of Dialectica and modified realizability with non-computational quantifiers.
متن کاملUnifying Functional Interpretations
The purpose of this article is to present a parametrised functional interpretation. Depending on the choice of the parameter relations one obtains well-known functional interpretations, such as Gödel’s Dialectica interpretation, Diller-Nahm’s variant of the Dialectica interpretation, Kohlenbach’s monotone interpretations, Kreisel’s modified realizability and Stein’s family of functional interpr...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2012
ISSN: 0168-0072
DOI: 10.1016/j.apal.2011.12.025