Abstract
Several mechanisms for combining logics have appeared in the literature. Synchronization is one of the simplest: the language of the combined logic is the disjoint union of the given languages, but the class of models of the resulting logic is a subset of the cartesian product of the given classes of models (the interaction between the two logics is imposed by constraining the class of pairs of models). Herein, we give both a model-theoretic and a proof-theoretic account of synchronization as a categorial construction (using coproducts and cocartesian liftings). We also prove that soundness is preserved by possibly constrained synchronization and state sufficient conditions for preservation of model existence and strong completeness. We provide an application to the combination of dynamic logic and linear temporal logic.
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Sernadas, A., Sernadas, C., Caleiro, C. (1997). Synchronization of logics with mixed rules: Completeness preservation. In: Johnson, M. (eds) Algebraic Methodology and Software Technology. AMAST 1997. Lecture Notes in Computer Science, vol 1349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000490
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DOI: https://doi.org/10.1007/BFb0000490
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