INCOMPACTNESS OF THE A1 FRAGMENT OF BASIC SECOND ORDER PROPOSITIONAL RELEVANT LOGIC

In this note we provide a simple proof of the incompactness over Routley-Meyer B-frames of the A1 fragment of the second order propositional relevant language

A Remark on Maksimova's Variable Separation Property in Super-Bi-Intuitionistic Logics

We provide a sucient frame-theoretic condition for a super bi-intuitionistic logic to have Maksimova's variable separation property. We conclude that bi-intuitionistic logic enjoys the property. Furthermore, we offer an algebraic characterization of the super-bi-intuitionistic logics with Maksimova's property

Introduction to the special issue ‘Valerie Plumwood’s contributions to Logic’

This is an introduction to the special issue of the AJL on Val Plumwood's manuscript "False Laws of Logic" and her other work in logic

A parametrised axiomatization for a large number of restricted second-order logics

By limiting the range of the predicate variables in a second-order language one may obtain restricted versions of second-order logic such as weak second-order logic or definable subset logic. In this note we provide an infinitary strongly complete axiomatization for several systems of this kind having the range of the predicate variables as a parameter. The completeness argument uses simple techniques from the theory of Boolean algebras

Frame definability in finitely-valued modal logics

In this paper we study frame definability in finitely valued modal logics and establish two main results via suitable translations: (1) in finitely valued modal logics one cannot define more classes of frames than are already definable in classical modal logic (cf. [27, Thm. 8]), and (2) a large family of finitely valued modal logics define exactly the same classes of frames as classical modal logic (including modal logics based on finite Heyting and MV-algebras, or even BL-algebras). In this way one may observe, for example, that the celebrated Goldblatt–Thomason theorem applies immediately to these logics. In particular, we obtain the central result from [26] with a much simpler proof and answer one of the open questions left in that paper. Moreover, the proposed translations allow us to determine the computational complexity of a big class of finitely valued modal logics

Variable Sharing in Substructural Logics: an Algebraic Characterization

We characterize the non-trivial substructural logics having the variable sharing property as well as its strong version. To this end, we find the algebraic counterparts over varieties of these logical properties.The work was supported by the Austrian Science Fund (FWF): project I 1923-N25 (New perspectives on residuated posets)