A first approach to the Deduction-Detachment Theorem in logics preserving degrees of truth

نویسنده

  • Félix Bou
چکیده

This paper studies the DeductionDetachment Theorem (DDT) in the realm of logics associated with bounded, commutative and integral residuated lattices whose consequence relation preserves degrees of truth (strictly speaking, it preserves the lower bounds of truth values of the premises). It is given some necessary conditions that must enjoy the varieties with a logic having the DDT. In two particular cases these conditions are indeed sufficient to characterize the DDT. In the paper it is also considered the case where the Delta operator is added to the language, and the case of a kind of local version of the DDT.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

EQ-logics with delta connective

In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...

متن کامل

Deduction-detachment theorem in hidden k-logics

Modern software systems usually deal with several sorts (types) of data elements simultaneously. Some of these sorts, like integers, booleans, and so on, can be seen as having an immediate, direct nature and therefore are called visible, and they are contrasted with the others, like types of objects (in OO sense), which are called hidden sorts. A language used to specify such software system ha...

متن کامل

T-norm based fuzzy logics preserving degrees of truth

T-norm based fuzzy logics are usually considered as truth preserving, that is, taking 1 as the only truth value to be preserved in inferences. In this paper we study t-norm based fuzzy logics preserving degrees of truth, that is, preserving the lower bounds of the truth degrees of the premises. These logics are axiomatizable by using a restricted form of Modus Ponens together with the rule of A...

متن کامل

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 کامل

Truth-values as Labels: A General Recipe for Labelled Deduction

We introduce a general recipe for presenting non-classical logics in a modular and uniform way as labelled deduction systems. Our recipe is based on a labelling mechanism where labels are general entities that are present, in one way or another, in all logics, namely truth-values. More specifically, the main idea underlying our approach is the use of algebras of truth-values, whose operators re...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008