Model-Theoretic Incremental Interpretation Based on Discourse Representation Theory

Model-Theoretic Incremental Interpretation Based on Discourse Representation Theory Yoshihide Kato and Shigeki Matsubara Information & Communications, Nagoya University Furo-cho, Chikusa-ku, Nagoya, 464-8601 Japan yoshihide@icts.nagoya-u.ac.jp Abstract This paper proposes a model-theoretic ap- proach to incremental interpretation where all sentence prefixes have semantic values. The proposed semantics is based on Discourse Representation Theory (DRT), where seman- tic representations (called DRSs) are inter- preted as assignment updates. In our seman- tics, a partial DRS of a sentence prefix is inter- preted as two sets which stipulate the assign- ment updates. One denotes possible updates and the other denotes necessary updates. With the proposed semantics, we can assign truth values to sentence prefixes. 1 Introduction Incremental semantic parsers construct semantic representations for each sentence prefix, and are use- ful for incremental dialogue systems (Allen et al., 2001; Aist et al., 2007). While most research on in- cremental semantic parsers has focused on how to construct such representations incrementally (Pul- man, 1985; Milward, 1995; Poesio and Rieser, 2010; Purver et al., 2011; Peldszus and Schlangen, 2012; Sayeed and Demberg, 2012; Kato and Matsubara, 2015), there has been little work on how to formally interpret them. An important issue with incremental interpreta- tion, from a formal semantic viewpoint, is that sen- tence prefixes do not have propositional interpreta- tions (Chater et al., 1995). In other words, standard formal semantics cannot be applied to incremental interpretation directly. This paper proposes a model-theoretic approach to incremental interpretation where each sentence prefix has semantic values. The proposed semantics is an extension of Discourse Representation Theory (DRT) (Kamp and Reyle, 1993). In DRT, seman- tic representations are called discourse representa- tion structures (DRSs) and are interpreted in terms of (non-deterministic) assignment updates (An as- signment is a function that maps discourse referents to entities.) In this paper, we define two types of interpretations of partial DRSs. One denotes possi- ble assignment updates and the other denotes nec- essary updates. The proposed semantics monotoni- cally specifies the semantic values of a sentence on a word-by-word basis, and finally assigns the same value to the sentence in terms of DRT’s semantics. In addition, it can assign truth values to sentence pre- fixes that are not sentential clauses. To the best of our knowledge, this is the first attempt to interpret underspecified semantic representations of sentence prefixes. This paper is organized as follows. Section 2 in- troduces DRT. Section 3 gives an overview of in- cremental semantic parsers that construct a partial DRS for each sentence prefix. Then, Section 4 pro- poses our incremental interpretation method based on DRT. Finally, Section 5 compares our work with previous studies, and Section 6 presents our conclu- sions. 2 Discourse Representation Theory This section provides a brief introduction to Dis- course Representation Theory (DRT). PACLIC 32 254 32nd Pacific Asia Conference on Language, Information and Computation Hong Kong, 1-3 December 2018 Copyright 2018 by the authors 2.1 Discourse Representation Structure In DRT, semantic content is represented as a dis- course representation structure (DRS). A DRS con- …

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