Relevance Principle for Substructural Logics with Mingle and Strong Negation
نویسنده
چکیده
We introduce intuitionistic and classical substructural logics with structural rules mingle and connective strong negation, and investigate the cut-elimination property and the relevance principle for these logics. The relevance principle does not hold for substructural logics with mingle and usual negation, but holds for those with mingle and strong negation.
منابع مشابه
A Logic for Conceptual Hierarchies
We propose a proof-theoretical way of obtaining detailed and precise information on conceptual hierarchies. The notion of concept finding proof, which represents a hierarchy of concepts, is introduced based on a substructural logic with mingle and strong negation. Mingle, which is a structural inference rule, is used to represent a process for finding a more general (or specific) concept than s...
متن کاملInterpolation Property and Principle of Variable Separation in Substructural Logics
We will discuss Craig’s interpolation property (CIP), deductive interpolation property (DIP), pseudo-relevance property (PRP), principle of variable separation (PVS) and Halldén completeness (HC) of substructural logics, and give algebraic characterizations of these properties. These characterizations have been studied for modal and superintuitionistic logics, e.g. in Maksimova (1977), [2] etc....
متن کاملModal translations in substructural logics
Substructural logics are logics obtained from a sequent formulation of intuitionistic or classical logic by rejecting some structural rules. The substructural logics considered here are linear logic, relevant logic and BCK logic, It is proved that first-order variants of these logics with an intuitionistic negation cm be embedded by modal translations into M-type extensions of these logics with...
متن کاملDisplaying and Deciding Substructural Logics 1: Logics with Contraposition
Many logics in the relevant family can be given a proof theory in the style of Belnap's display logic (Belnap 1982). However, as originally given, the proof theory is essentially more expressive than the logics they seek to model. In this paper, we consider a modi ed proof theory which more closely models relevant logics. In addition, we use this proof theory to provide decidability proofs for ...
متن کاملModels for Substructural Arithmetics
This paper explores models for arithmetics in substructural logics. In the existing literature on substructural arithmetic, frame semantics for substructural logics are absent. We will start to fill in the picture in this paper by examining frame semantics for the substructural logics C (linear logic plus distribution), R (relevant logic) and CK (C plus weakening). The eventual goal is to find ...
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:
- J. Log. Comput.
دوره 12 شماره
صفحات -
تاریخ انتشار 2002