Journal of Logic, Language and Information

, Volume 18, Issue 2, pp 159-198

First online:

Polyadic Dynamic Logics for HPSG Parsing

  • Anders SøgaardAffiliated withTheoretische Computerlinguistik, Institut für Linguistik, Universität Potsdam Email author 
  • , Martin LangeAffiliated withTheoretische Informatik, Institut für Informatik, Ludwig-Maximilians-Universität München

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Head-driven phrase structure grammar (HPSG) is one of the most prominent theories employed in deep parsing of natural language. Many linguistic theories are arguably best formalized in extensions of modal or dynamic logic (Keller, Feature logics, infinitary descriptions and grammar, 1993; Kracht, Linguistics Philos 18:401–458, 1995; Moss and Tiede, In: Blackburn, van Benthem, and Wolther (eds.) Handbook of modal logic, 2006), and HPSG seems to be no exception. Adequate extensions of dynamic logic have not been studied in detail, however; the most important aspect is the reference to sets of substructures. In this paper, an adequate extension is identified, and some important results are established: Satisfiability is highly undecidable, and model checking is shown to be in EXPTIME and PSPACE-hard. A fragment with polynomial time model checking procedures is identified; it is shown to cover considerable fragments of HPSG.


Dynamic logic HPSG Model checking Parsing