A proof-theoretical investigation of global intuitionistic (fuzzy) logic
نویسنده
چکیده
We perform a proof-theoretical investigation of two modal predicate logics: global intuitionistic logic GI and global intuitionistic fuzzy logic GIF. These logics were introduced by Takeuti and Titani to formulate an intuitionistic set theory and an intuitionistic fuzzy set theory together with their metatheories. Here we define analytic Gentzen style calculi for GI and GIF. Among other things, these calculi allows one to prove Herbrand’s theorem for suitable fragments of GI and GIF.
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 کاملAN ALGEBRAIC STRUCTURE FOR INTUITIONISTIC FUZZY LOGIC
In this paper we extend the notion of degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. It would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. We give the main properties of the operations defined and prove som...
متن کاملEvaluating Construction Projects by a New Group Decision-Making Model Based on Intuitionistic Fuzzy Logic Concepts
Select an appropriate project is a main key for contractors to increase their profits. In practice, in this area the uncertainty and imprecise of the involved parameters is so high. Therefore, considering fuzzy sets theory to deal with uncertainly is more appreciate. The aim of this paper is present a multi-criteria group decision-making model under an intuitionistic fuzzy set environment. Henc...
متن کاملIntuitionistic fuzzy logic for adaptive energy efficient routing in mobile ad-hoc networks
In recent years, mobile ad-hoc networks have been used widely due to advances in wireless technology. These networks are formed in any environment that is needed without a fixed infrastructure or centralized management. Mobile ad-hoc networks have some characteristics and advantages such as wireless medium access, multi-hop routing, low cost development, dynamic topology and etc. In these netwo...
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 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:
- Arch. Math. Log.
دوره 44 شماره
صفحات -
تاریخ انتشار 2005