Abstract
Correspondence theory regarding the bimodal language for subset spaces can be based on a certain pseudo-monadic second-order language arising from the relevant semantics. Since the latter language is reducible to a two-sorted language of first-order predicate logic, one can apply well-established model-theoretic techniques to studying expressivity issues. In this way, a subset space analogue to a popular definability result of ordinary modal logic is proved first in this paper. On the other hand, subset spaces can easily be related to usual Kripke models, for which we have a (one-sorted) relational first-order correspondence language. Both of the concurrent correspondents are then used in the main part of the paper, where, among other things, some Goldblatt-Thomason style results as related to subset frames are proved.
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Heinemann, B. (2013). Subset Space vs Relational Semantics of Bimodal Logic: Bringing Out the Difference. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2013. Lecture Notes in Computer Science, vol 7734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35722-0_16
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