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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Logics, Structures and Presentations
verfasst von : Łukasz Kaiser
Erschienen in: Logic and Games on Automatic Structures
Verlag: Springer Berlin Heidelberg
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In this chapter we review the standard notions of first-order and monadic second-order logic. We introduce linear orders and trees and state a few elementary properties of these structures. We recall the correspondence between monadic second-order logic and automata on infinite words together with basic facts from automata theory . We introduce automatic structures using presentations by automata and characterize them both by first-order and by monadic second-order to first-order interpretations. Finally, we discuss the composition method for monadic second-order logic over linear orders and trees.