Defining implication relation for classical logic
نویسنده
چکیده
Classical logic is unfortunately defective with its problematic definition of implication relation, the “material implication”. This work presents a corrected definition of implication relation to replace material implication in classical logic. Common “paradoxes” of material implication are avoided while simplicity and usefulness of the system are reserved with this definition of implication relation.
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 کاملStructured Sequent Calculi for Combining Intuitionistic and Classical First-Order Logic
We define a sound and complete logic, called FO⊃, which extends classical first-order predicate logic with intuitionistic implication. As expected, to allow the interpretation of intuitionistic implication, the semantics of FO⊃ is based on structures over a partially ordered set of worlds. In these structures, classical quantifiers and connectives (in particular, implication) are interpreted wi...
متن کاملROBUSTNESS OF THE TRIPLE IMPLICATION INFERENCE METHOD BASED ON THE WEIGHTED LOGIC METRIC
This paper focuses on the robustness problem of full implication triple implication inference method for fuzzy reasoning. First of all, based on strong regular implication, the weighted logic metric for measuring distance between two fuzzy sets is proposed. Besides, under this metric, some robustness results of the triple implication method are obtained, which demonstrates that the triple impli...
متن کاملBrief study of the relation between AGM postulates (-7) and (+7) under non-classical logics
This paper studies the implication relations between the AGM postulates ( 7) and (+̇7) under non-classical logics, namely intuitionistic logic, paraconsistent logic, G3 and G3'. In order to do so, some theorems on the implication relations between such postulates are drawn for logics with a special set of axioms. These are later used to deduce similar results under the four logics of interest. T...
متن کاملA hierarchy of implicational (semilinear) logics: the propositional case
In Abstract Algebraic Logic the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this kind of process one considers the Leibniz relation of indiscernible, i.e. logically equivalent, formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: ...
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:
- CoRR
دوره abs/1312.7832 شماره
صفحات -
تاریخ انتشار 2013