Abstract
The paper provides an alternative interpretation of ‘pair points’, discussed in [3]. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This yields a general soundness and completeness result for a variety of (positive) substructural logics with respect to multimodal Kripke frames with binary accessibility relations. In addition, an epistemic interpretation of pair models is provided.
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Notes
- 1.
- 2.
- 3.
A familiar example of similar ‘inter-model’ truth conditions are the conditions for public announcement formulas \([A]B\) in public announcement logic. See [11].
- 4.
Needless to point out, the interpretation is rather close to the Ramsey Test.
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Acknowledgments
This work was carried out at the Department of Logic and Methodology of Sciences, Comenius University, as a part of the research project ‘Semantic models, their explanatory power and applications’, supported by the grant VEGA 1/0046/11. I wish to express my gratitude to the audience at Trends in Logic XI for helpful discussion and to two anonymous referees for enabling me to improve the paper by providing a number of constructive suggestions. Thanks are also due to Jc Beall, Mike Dunn, Ed Mares and Graham Priest: their encouragement is much appreciated.
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Sedlár, I. (2014). Inter-Model Connectives and Substructural Logics. In: Ciuni, R., Wansing, H., Willkommen, C. (eds) Recent Trends in Philosophical Logic. Trends in Logic, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-319-06080-4_14
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