Truth in Applicative Theories
نویسنده
چکیده
We give a survey on truth theories for applicative theories. It comprises Frege structures, Universes for Frege structures, and a theory of supervaluation. We present the proof-theoretic results for these theories and show their syntactical expressive power. In particular, we present as a novelty a syntactical interpretation of ID1 in a applicative truth theory based on supervaluation.
منابع مشابه
Weak applicative theories , truth , and computational complexity
The aim of our thesis is the design of applicative theories on words of strength below Primitive Recursive Arithmetic to give implicit characterisations of complexity classes in the style of Strahm’s [79]. In more detail, we analyse the effect of adding second-order notions as types or truth to an applicative base theory, and obtain theories of great expressive power, but still polynomial stren...
متن کاملFrege Structures for Partial Applicative Theories
Due to strictness problems, usually the syntactical definition of Frege structures is conceived as a truth theory for total applicative theories. To investigate Frege structures in a partial framework we can follow two ways. First, simply by ignoring undefinedness in the truth definition. Second, by introducing of a certain notion of pointer. Both approaches are compatible with the traditional ...
متن کاملA feasible theory of truth over combinatory algebra
We define an applicative theory of truth TPT which proves totality exactly for the polynomial time computable functions. TPT has natural and simple axioms since nearly all its truth axioms are standard for truth theories over an applicative framework. The only exception is the axiom dealing with the word predicate. The truth predicate can only reflect elementhood in the words for terms that hav...
متن کاملApplicative Abstract Categorial Grammars
We present the grammar/semantic formalism of Applicative Abstract Categorial Grammars (AACG), based on the recent techniques from functional programming: applicative functors, staged languages and typed final language embeddings. AACG is a generalization of Abstract Categorial Grammars (ACG), retaining the benefits of ACG as a grammar formalism and making it possible and convenient to express a...
متن کاملA new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is Π1-equivalent to KP
We introduce a version of operational set theory, OST, without a choice operation, which has a machinery for ∆0 separation based on truth functions and the separation operator, and a new kind of applicative set theory, so-called weak explicit set theory WEST, based on Gödel operations. We show that both the theories and Kripke-Platek set theory KP with infinity are pairwise Π1 equivalent. We al...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Studia Logica
دوره 68 شماره
صفحات -
تاریخ انتشار 2001