Interpolation Property and Principle of Variable Separation in Substructural Logics
نویسنده
چکیده
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., Wroński [3] and so on. Our main aim is to show relations among these properties in substructural logics and to clarify how structural rules affect algebraic characterizations of them. This study comes out of my joint work with N. Galatos [1] and H. Kihara (in preparation).
منابع مشابه
Maksimova ON VARIABLE SEPARATION IN MODAL LOGICS
It was proved in [4] that interpolation properties of propositional normal modal logics (n.m.l.) are closely connected with amalgamation properties of associated varieties of modal algebras. In this paper we find an algebraic equivalent of the Hallden property in modal logics, namely, we prove that the Hallden-completeness in any n.m.l. is equivalent to the so-called Super-Embedding Property of...
متن کاملSubstructural Logics over Fl I: Algebraization, Parametrized Local Deduction Theorem and Interpolation
Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation pro...
متن کاملRelevance Principle for Substructural Logics with Mingle and Strong Negation
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.
متن کاملNikolaos Galatos
Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation pro...
متن کاملInterpolation Properties, Beth Definability Properties and Amalgamation Properties for Substructural Logics
This paper develops a comprehensive study of various types of interpolation properties and Beth definability properties for substructural logics, and their algebraic characterizations through amalgamation properties and epimorphisms surjectivity. In general, substructural logics are algebraizable but lack many of the basic logical properties that modal and superintuitionistic logics enjoy (cf. ...
متن کامل