72 research outputs found
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
Robinson consistency in many-sorted hybrid first-order logics
In this paper we prove a Robinson consistency theorem for a class of many-sorted hybrid logics as a consequence of an Omitting Types Theorem. An important corollary of this result is an interpolation theorem
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