Finitary Semantics of Linear Logic and Higher-Order Model-Checking

  • Charles GrelloisEmail author
  • Paul-André MellièsEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9234)


In this paper, we explain how the connection between higher-order model-checking and linear logic recently exhibited by the authors leads to a new and conceptually enlightening proof of the selection problem originally established by Carayol and Serre using collapsible pushdown automata. The main idea is to start from an infinitary and colored relational semantics of the \(\lambda \,Y\)-calculus formulated in a companion paper, and to replace it by a finitary counterpart based on finite prime-algebraic lattices. Given a higher-order recursion scheme \(\mathcal {G}\), the finiteness of its interpretation in the resulting model enables us to associate to any MSO formula \(\varphi \) a higher-order recursion scheme \(\mathcal {G}_{\varphi }\) resolving the selection problem.


Higher-order model-checking Linear logic Selection problem Finitary semantics Parity games 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Laboratoire PPSUniversité Paris DiderotSorbonne Paris CitéFrance

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