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The Relative Succinctness and Expressiveness of Modal Logics Can Be Arbitrarily Complex
We study the relative succinctness and expressiveness of modal logics, and
prove that these relationships can be as complex as any countable partial
order. For this, we use two uniform formalisms to define modal operators, and
obtain results on succinctness and expressiveness in these two settings. Our
proofs are based on formula size games introduced by Adler and Immerman and
bisimulations.Comment: 29 page