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

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

On Sahlqvist formulas in relevant logic

This paper defines a Sahlqvist fragment for relevant logic and establishes that each class of frames in the Routley-Meyer semantics which is definable by a Sahlqvist formula is also elementary, that is, it coincides with the class of structures satisfying a given first order property calculable by a Sahlqvist-van Benthem algorithm. Furthermore, we show that some classes of Routley-Meyer frames definable by a relevant formula are not elementary