Abstract
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.
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© 2011 Springer-Verlag Berlin Heidelberg
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Kaiser, Ł. (2011). Logics, Structures and Presentations. In: Logic and Games on Automatic Structures. Lecture Notes in Computer Science(), vol 6810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22807-0_1
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DOI: https://doi.org/10.1007/978-3-642-22807-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22806-3
Online ISBN: 978-3-642-22807-0
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