Cognitive Compositional Semantics using Continuation Dependencies

Cognitive Compositional Semantics using Continuation Dependencies William Schuler Department of Linguistics The Ohio State University schuler@ling.osu.edu Adam Wheeler Department of Linguistics The Ohio State University wheeler@ling.osu.edu Abstract This paper describes a graphical semantic representation based on bottom-up ‘con- tinuation’ dependencies which has the im- portant property that its vertices define a usable set of discourse referents in work- ing memory even in contexts involving conjunction in the scope of quantifiers. An evaluation on an existing quantifier scope disambiguation task shows that non-local continuation dependencies can be as reli- ably learned from annotated data as repre- sentations used in a state-of-the-art quanti- fier scope resolver, suggesting that contin- uation dependencies may provide a natural representation for scope information. 1 Introduction It is now fairly well established that at least shal- low semantic interpretation informs parsing deci- sions in human sentence processing (Tanenhaus et al., 1995; Brown-Schmidt et al., 2002), and re- cent evidence points to incremental processing of quantifier implicatures as well (Degen and Tanen- haus, 2011). This may indicate that inferences about the meaning of quantifiers are processed di- rectly in working memory. Human working mem- ory is widely assumed to store events (includ- ing linguistic events) as re-usable activation-based states, connected by a durable but rapidly mutable weight-based memory of cued associations (Marr, 1971; Anderson et al., 1977; Murdock, 1982; Mc- Clelland et al., 1995; Howard and Kahana, 2002). Complex dependency structures can therefore be stored in this associative memory as graphs, with states as vertices and cued associations as directed edges (e.g. Kintsch, 1988). This kind of represen- tation is necessary to formulate and evaluate algo- rithmic claims (Marr, 1982) about cued associa- tions and working memory use in human sentence processing (e.g. van Schijndel and Schuler, 2013). But accounting for syntax and semantics in this way must be done carefully in order to preserve linguistically important distinctions. For example, positing spurious local dependencies in filler-gap constructions can lead to missed integrations of dependency structure in incremental processing, resulting in weaker model fitting (van Schijndel et al., 2013). Similar care may be necessary in cases of dependencies arising from anaphoric corefer- ence or quantifier scope. Unfortunately, most existing theories of compo- sitional semantics (Montague, 1973; Barwise and Cooper, 1981; Bos, 1996; Baldridge and Kruijff, 2002; Koller, 2004; Copestake et al., 2005) are defined at the computational level (Marr, 1982), employing beta reduction over complete or under- specified lambda calculus expressions as a precise description of the language processing task to be modeled, not at the algorithmic level, as a model of human language processing itself. The struc- tured expressions these theories generate are not intended to represent re-usable referential states of the sort that could be modeled in current theo- ries of associative memory. As such, it should not be surprising that structural adaptations of lambda calculus expressions as referential states exhibit a number of apparent deficiencies: First, representations based on lambda calculus expressions lack topologically distinguishable ref- erents for sets defined in the context of outscop- ing …

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