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On Sahlqvist Formulas in Relevant Logic
1Department of Knowledge-Based Mathematical Systems, Johannes Kepler Universität, Linz, Austria.
Abstract:
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.
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