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JSYML
2002

Representability in Second-Order Propositional Poly-Modal Logic

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Representability in Second-Order Propositional Poly-Modal Logic
A propositional system of modal logic is second-order if it contains quantifiers p and p, which, in the standard interpretation, are construed as ranging over sets of possible worlds (propositions). Most second-order systems of modal logic are highly intractable; for instance, when augmented with propositional quantifiers, K, B, T, K4 and S4 all become effectively equivalent to full second-order logic. An exception is S5, which, being interpretable in monadic second-order logic, is decidable. In this paper we generalize this framework by allowing multiple modalities. While this does not affect the undecidability of K, B, T, K4 and S4, poly-modal secondorder S5 is dramatically more expressive than its mono-modal counterpart. As an example, we establish the definability of the transitive closure of finitely many modal operators. We also take up the decidability issue, and, using a novel encoding of sets of unordered pairs by partitions of the leaves of certain graphs, we show that the se...
Gian Aldo Antonelli, Richmond H. Thomason
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 2002
Where JSYML
Authors Gian Aldo Antonelli, Richmond H. Thomason
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