Extension Of Dynamic Logic Research Articles

Polyadic Dynamic Logics for HPSG Parsing

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.

A dynamic logic of events and states for the interaction between plural quantification and verb aspect in natural language

The influence NPs can have on the aspectual behaviour of verbal expressions, witness the pair 'eat an apple in ten minutes/*for ten minutes' and 'eat apples *in ten minutes/for ten minutes, requires an analysis of how static semantic information (NP) interacts with dynamic semantic information (verb). An interpretation of verbs and NPs is presented in which the interaction is analyzed by using an extension of dynamic logic (DL). First, models for DL are extended by adding a domain E of events (together with an event structure E). The intuition behind this addition is that each transition (pair of states) which is an element of the relation denoted by a program in DL is brought about by an event from E. This makes it possible to view a change either as an object (event) or as a transformation of a state. Second, in addition to sequential programs, parallel programs (relations between sets of states) are introduced. At the level of E this corresponds to the distinction between events and sets of events. The dynamic component of a verbal expression denotes an event-type P that corresponds to a program (relation between states) at the level of the transition structure S. This program has particular properties in terms of which aspectual distinctions are defined. The parallel program corresponding to sets of events is partly determined by the cardinality information introduced by the determiner as part of an argument NP. At the level of E this information functions as a boolean condition expressing the result that is brought about by the set of events. Static information therefore interacts with dynamic information by providing a condition that must hold upon termination of events.