Journal of Philosophical Logic 36 (5):489 - 509 (2007)

We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order correspondence language, so both can express the same input–output behavior of processes.
Keywords arrow logic  expressive power  fork algebra  modal logic  relation algebra  standard translation
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DOI 10.1007/s10992-006-9043-x
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Arrow Logic and Multi-Modal Logic.Maarten Marx, Laszls Pslos & Michael Masuch - 1996 - Center for the Study of Language and Information Publications.

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