The Qualitative Spatial Dynamics of Motion in Language

Abstract

In this paper, we discuss the strategies that languages employ to express motion, focusing on the distinction between path predicates, such as enter, arrive, and leave and manner-of-motion predicates, such as walk, bike, and roll. We present an overview of some qualitative spatiotemporal models of movement, and discuss their adequacy for capturing motion constructions in natural languages. Building on many aspects of these qualitative models, we introduce a framework within dynamic logic for the characterization of spatial change. This model, called Dynamic Interval Temporal Logic (DITL), is developed to analyze both classes of motion predicates, as well as complex compositional constructions involving spatial and manner Prepositional Phrases. Further, DITL serves as a semantics for a linguistically expressive markup language for annotating spatiotemporal information in text, called Spatiotemporal Markup Language (STML). We outline the syntax of this language, and discuss how DITL provides for a natural interpretation of the annotation specification for use in a variety of applications.

Keywords:

• spatial language
• qualitative reasoning
• common sense models of space
• dynamic logic
• temporal logic

Notes

¹ http://www.rideforclimate.com

²(Palmer, Gildea, & Kingsbury, 2003)

³For a discussion of these issues, see (Freksa & Zimmermann, 1992; Noyon, Claramunt, & Devogele, 2007) and (Freksa, 1992; Mitra, 2004; Renz & Mitra, 2004).

⁴Subsequent work on this includes (Jackendoff, 1983; Talmy, 2000; Choi & Bowerman, 1991).

⁵This classification is modified and extended somewhat in (Pustejovsky & Moszkowicz, 2008), where semantic considerations from (Asher & Sablayrolles, 1995) are incorporated into Muller's set.

⁶The matrix used in our discussion is notationally different than what they present in their paper, for purposes of presentation.

⁷We would like to thank one of our reviewers for pointing out the inconsistencies with interpreting the directed LR intersection over temporal indexes.

⁸Work by (Nr, Doherty, Gustafsson, Karssson, & Kvarnstrom, 1998) and references therein attempt to represent pre- and post-conditions in change, within action logics and other models adopting Sandewall's features and fluents.

⁹We assume the syntax of Propositional Dynamic Logic (PDL) (Harel et al., 2000).

¹⁰Cf. also (Kröger & Merz, 2008; Allen, 1984; Moszkowski, 1986; Manna & Pnueli, 1995). We will avoid the use of temporal operators in the following discussion when not necessary.

¹¹This will have the effect of a skip operation to the next program in the sequence.

¹²12As in modal logic, the “diamond” operator is the dual of “box”, where 〈α〉φ means, “There is a computation of α that terminates in a state satisfying φ.”

¹³See (Groenendijk & Stokhof, 1989) and (Eijck & Stokhof, 2005) for discussion of dynamic assignment strategies in computational semantics.

¹⁴We focus on the single spatial attribute of location in this paper. Conceptually, this treatment is close to Galton's (Galton, 2000) analysis of movement as change of position and to (BhattLoke & Loke, 2008) and their definition of primitive change of spatial relationship between two objects.

¹⁵We say Kleene iterated because α⁺ indicates one application of α followed by α^*.

¹⁶Notice that this definition allows some fairly diverse movement types (such as oscillations and rotations), since it only requires a Markov change in location; that is, location values can be revisited arbitrarily.

¹⁷J. Pustejovsky is editor of the Work Item within ISO for this effort.

¹⁸ISO-Space also draws heavily on (Bateman, Hois, Ross, & Tenbrink, 2010) for spatially relevant categories.

¹⁹Capturing explicit temporal expressions such as the next day and 4 hours allows us to ground the annotation on a timeline just as capturing explicit locations is needed to ground the annotation on a map.

²⁰In addition to temporal links, ISO-TimeML includes subordinating links that are used to capture information about irrealis events. This allows temporal links to be created even when the participating events may or may not have happened.

²¹Note that we do not include the entire annotation of locations or motion events in our examples here since this part of the annotation is handled by ISO-Space and TimeML, respectively.

²²Spatial prepositions that are used to describe locations such as behind in behind the store are captured in ISO-Space with the S_FUNCTION tag, but these are beyond the purview of STML.