Abstract
A Rasiowa-Sikorski proof system is presented for an elementary set theory which can act as a target language for translating propositional modal logics. The proposed system permits a modular analysis of (modal) axioms in terms of deductive rules for the relational apparatus. Such an analysis is possible even in the case when the starting modal logic does not possess a first-order correspondent. Moreover, the formalism enables a fine-tunable and uniform analysis of modal deductions in a simple and purely set-theoretic language.
Work partially supported by MURST/MIUR project Aggregate- and number-reasoning for computing: from decision algorithms to constraint programming with multisets, sets, and maps. This research benefited from collaborations fostered by the European action COST n. 274 (TARSKI, see www.tarski.org).
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Omodeo, E., Orłowska, E., Policriti, A. (2004). Rasiowa-Sikorski Style Relational Elementary Set Theory. In: Berghammer, R., Möller, B., Struth, G. (eds) Relational and Kleene-Algebraic Methods in Computer Science. RelMiCS 2003. Lecture Notes in Computer Science, vol 3051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24771-5_19
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DOI: https://doi.org/10.1007/978-3-540-24771-5_19
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