Gödel Logics and Cantor-Bendixon Analysis
نویسنده
چکیده
This paper presents an analysis of Gödel logics with countable truth value sets with respect to the topological and order theoretic structure of the underlying truth value set. Gödel logics have taken an important rôle in various areas of computer science, e.g. logic programming and foundations of parallel computing. As shown in a forthcoming paper all these logics are not recursively axiomatizable. We show that certain topological properties of the truth value set can distinguish between various logics. Complete separation of a class of countable valued logics will be proven and direction for further separation results given.
منابع مشابه
Truth Values and Connectives in Some Non-Classical Logics
The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...
متن کاملOn a class of pseudocompact spaces derived from ring epimorphisms
A Tychonoff space X is called RG if the embedding of C(X) → C(Xδ) is an epimorphism of rings. Compact RG spaces are known and easily described. We study the pseudocompact RG spaces. These must be scattered of finite Cantor Bendixon degree but need not be locally compact. However, under strong hypotheses, (countable compactness, or small cardinality) these spaces must, indeed, be compact. The ma...
متن کاملGödel Logics: Foundations and Applications to Computer Science
Gödel logics are a family of many-valued logics which have recently received significant attention in Computer Science. They are one of the families of logics which have been used as a basis of fuzzy logic; they have been used to give characterizations of the stable model semantics in logic programming; and they have been put forward as candidates for a logical analysis of parallel computation....
متن کاملCompact serialization of Prolog terms (with catalan skeletons, cantor tupling and Gödel numberings)
We describe a compact serialization algorithm mapping Prolog terms to natural numbers of bit-sizes proportional to the memory representation of the terms. The algorithm is a “ no bit lost” bijection, as it associates to each Prolog term a unique natural number and each natural number corresponds to a unique syntactically well-formed term. To avoid an exponential explosion resulting from bijecti...
متن کاملCharacterization of the Axiomatizable Prenex Fragments of First-Order Gödel Logics
The prenex fragments of first-order infinite-valued Gödel logics are classified. It is shown that the prenex Gödel logics characterized by finite and by uncountable subsets of [0,1] are axiomatizable, and that the prenex fragments of all countably infinite Gödel logics are not axiomatizable.
متن کامل