Abstract
In this article we develop a theory of bridging inferences in a dynamic frame theory that is an extension of Incremental Dynamics. In contrast to previous approaches bridging is seen as based on predictions/expectations that are triggered by discourse referents in a particular context where predictions are (more specific) instances of Questions under Discussion. In our frame theory each discourse referent is associated with a frame f that contains the information known about it in the current context. Predictions/QuDs are modelled as sets F of extensions of this frame relative to a (possibly complex) attribute about whose value no information is given so far. A continuation of the current context answers a question if it introduces a frame \(f'\) that contains information about the value of the attribute corresponding to the question. The set F is constrained by a probability distribution on the domain of frames. Only those extensions are considered whose conditional probability in the current context is high. The relation between f and \(f'\) can be restricted in several ways. Bridging inferences correspond to those restrictions in which (i) the frames belong to the semantic representations of two clauses and (ii) the relation is established by a separate update operation (The research was supported by the German Science Foundation (DFG) funding the Collaborative Research Center 991. We would like to thank the two reviewers as well as the editors for helpful comments and suggestions).
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Notes
- 1.
- 2.
Alternatively, it can be taken as a frame scheme or a frame type. In this case it refers to the set of weddings which have a location and in which the meal is made up by a starter, a main course and a dessert. In the text, a frame depicted is always meant as an instantiated frame in the sense that each node has a particular object as value.
- 3.
Strictly speaking, it assigns to a frame f a 1-place function as attributes are required to be functional.
- 4.
If possible worlds and frames are taken as relational models, the relation between them can be made precise in the following way. Each frame is a particular submodel \(\mathcal {M}\) of a possible world \(\mathcal {M}_w\). \(\mathcal {M}\) is constructed from \(\mathcal {M}_w\) as follows. In a first step one forms the reduct \(\mathcal {M}'\) of \(\mathcal {M}_w\) to the language \(\mathfrak {L}\) on which the frame is based. In a second step, one considers the set S of submodels \(\mathcal {N}\) of \(\mathcal {M}'\) that satisfy the axioms imposed on the frame. A frame is then any minimal model in S. See [NP17] for details.
- 5.
Though the elements are relations, we write for example \(\pi \,{\cap \uparrow }\sigma \) instead of \([\![\pi \,{\cap \uparrow }\sigma ]\!]\) to ease readability.
- 6.
This definition of closure under prefixes assumes a function that maps each \(\textsc {attr}\) to its target sort \(\sigma \). In [NP17] this functional relation between an attribute and a sort is defined in an extension of the current theory that is based on an order-sorted logic for attributes and sorts. In particular, one has in the signature of this logic a \(\textit{Sort} \times \textit{Sort}\)-indexed family of sets of (attribute) function symbols \((\mathcal {A}_{\sigma ,\sigma '})_{\sigma , \sigma ' \in \textit{Sort}}\). For \(\textsc {attr} \in \mathcal {A}_{\sigma ,\sigma '}\), one writes \(\textsc {attr} : \sigma \rightarrow \sigma '\). \(\sigma \) is called the \(\textit{source sort}\) and \(\sigma '\) the \(\textit{target sort}\) of \(\textsc {attr}\). See [NP17] for details.
- 7.
See [Pn97] for a formal analysis in which achievement verbs like ‘arrive’ are analyzed as boundary events of other, non-boundary events.
- 8.
We leave out the information related to the verb ‘take’.
- 9.
Recall that \(\varDelta \,{\cap \downarrow }\phi \) restricts the relation expressed by \(\downarrow \phi \) to those elements \(\langle o, o' \rangle \) from \(D_o \times D_o\) for which one has \(o = o'\), i.e. \(\downarrow \phi \) is restricted to the diagonal of \(D_o \times D_o\).
- 10.
Requiring that \(F_o\) be a subset of the non-factual \(\pi \)-extensions of \(f_o\) raises the question of how this set can be further restricted. In general we taken the determination of the initial \(F_o\) to be context-specific, based on probabilities. We will come back to this question at the end of this section.
- 11.
Recall from Sects. 2 and 3 that an information state is a set of possibilities and that a possibility is a pair \(\langle c,w\rangle \) consisting of a stack c and a world w. In contrast to Sect. 3 our stack elements are now pairs \(\langle o, \langle f_o,F_o\rangle \rangle \) with object o, its frame \(f_o\) and a set of \(\pi \)-extensions \(F_o\). In (25)–(27) o is used for objects, f for frames, F for sets of frames, c for stacks, i, j for stack indices and s for possibilities. Note that while \(\pi \) is used for chains of attributes, \(\pi ^1\) and \(\pi ^2\) denote the projection function.
- 12.
\(c \approx _i c'\) says that the stacks c and \(c'\) differ at most w.r.t. the value assigned to position i.
- 13.
In the definitions of \(\cdot \) and \(\cup \), \(\phi \) and \(\psi \) map possibilities (i.e. pairs \(\langle c, w\rangle \) consisting of a stack and a world) to sets of possibilities.
- 14.
Recall that the value of \(\theta \) for a frame f is closed under supersorts. Hence, \(\theta (f_{o'})\) is, in effect the set \(\{ \varDelta \,{\cap \downarrow } \mathbf{dog }, \textsc {behaviour}\,{\cap \uparrow }\mathbf{friendly }, \textsc {behaviour}\,{\cap \uparrow }{\mathbf{behaviour }}\}\). This set is a superset of the set \(\theta (f^{\textsc {behaviour}}_{o})\) given next.
- 15.
References
Asher, N., Lascarides, A.: Bridging. J. Semant. 15, 83–113 (1998)
Burkhardt, P.: Inferential bridging relations reveal distinct neural mechanisms: evidence from event-related brain potentials. Brain Lang. 98(2), 159–168 (2006)
Clark, H.H., Haviland, S.E.: Comprehension and the given-new contract. In: Freedle, R.O. (ed.) Discourse Production and Comprehension, pp. 1–40. Ablex Publishing, Hillsdale (1977)
Charniak, E.: Passing markers: a theory of contextual influence in language comprehension. Cogn. Sci. 7, 171–190 (1983)
Chierchia, G.: Dynamics of Meaning: Anaphora, Presupposition and the Theory of Grammar. University of Chicago Press, Chicago (1995)
Clark, H.: Bridging. In: Johnson-Laird, P., Wason, P. (eds.) Thinking: Readings in Cognitive Science, pp. 411–420. Cambridge University Press, Cambridge (1977)
Geurts, B.: Accessibility and anaphora. In: von Heusinger, K., Maienborn, C., Portner, P. (eds.) Semantics. Handbooks of Linguistics and Communication Science, vol. 2, pp. 1988–2011. DeGruyter (2011). Chapter 75
Hobbs, J.R., Stickel, M.E., Appelt, D.E., Martin, P.A.: Interpretation as abduction. Artif. Intell. 63(1–2), 69–142 (1993)
Kehler, A., Rohde, H.: Evaluating an expectation-driven question-under-discussion model of discourse interpretation. Discourse Process. 54(3), 219–238 (2017)
Nouwen, R.: Plural pronominal anaphora in context. Ph.D. thesis, Netherlands Graduate School of Linguistics Dissertations, LOT, Utrecht (2003)
Naumann, R., Petersen, W., Thomas, G.: Underspecified changes: a dynamic, probabilistic frame theory for verbs. In: Sauerland, U., Solt, S. (eds.) Proceedings of Sinn und Bedeutung 22, vol. 2 (2018)
Piñón, C.: Achievements in an event semantics. In: Lawson, A. (ed.) Proceedings SALT VII, pp. 276–293. Cornell University, Ithaca (1997)
Reyle, U., Riester, A.: Joint information structure and discourse structure analysis in an underspecified DRT framework. In: Hunter, J., Simons, M., Stone, M. (eds.) Proceedings of the 20th Workshop on the Semantics and Pragmatics of Dialogue (JerSem), New Brunswick, pp. 15–24. Rutgers University (2016)
van Eijck, J.: Context and the composition of meaning. In: Bunt, H., Muskens, R. (eds.) Computing Meaning, vol. 83, pp. 173–193. Springer, Dordrecht (2007). https://doi.org/10.1007/978-1-4020-5958-2_8
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Naumann, R., Petersen, W. (2019). Bridging Inferences in a Dynamic Frame Theory. In: Silva, A., Staton, S., Sutton, P., Umbach, C. (eds) Language, Logic, and Computation. TbiLLC 2018. Lecture Notes in Computer Science(), vol 11456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-59565-7_12
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