A Mechanism to Restrict the Scope of Clause-Bounded Quantifiers in ‘Continuation’ Semantics

Proceedings of Recent Advances in Natural Language Processing, pages 495–502, Hissar, Bulgaria, 12-14 September 2011. A Mechanism to Restrict the Scope of Clause-Bounded Quantifiers in ‘Continuation’ Semantics Anca Dinu Faculty of Foreign Languages and Literatures, University of Bucharest anca_d_dinu@yahoo.com Abstract This paper presents a formal mechanism to properly constrain the scope of negation and of certain quantificational determiners to their minimal clause in continuation semantics framework introduced in Barker and Shan (2008) and which was subsequently extended from sentential level to discourse level in Dinu (2011). In these works, type shifting is employed to account for side effects such as pronominal anaphora binding or quantifier scope. However, allowing arbitrary type shifting will result in overgenerating interpretations impossible in natural language. To filter out some of these impossible interpretations, once the negation or the quantifiers reach their maximal scope limits (that is their minimal clause), one should force their scope closing by applying a standard type shifter Lower. But the actual mechanism that forces the scope closing was left underspecified in previous work on continuation semantics. We propose here such a mechanism, designed to ensure that no lexical entries having the scope bounded to their minimal clause (such as not, no, every, each, any, etc) will ever take scope outside. 1 Introduction The starting point of this paper is the continuation semantics introduced in Barker and Shan (2008) and extended from sentential level to discourse level in Dinu (2011). In this framework, type shifting is used to account for side effects such as pronominal anaphora binding or quantifier scope. However, allowing arbitrary type shifting will result in overgenerating interpretations impossible in natural language. To filter out these impossible interpretations, we first need to understand the scope behavior of each scope-taking lexical entry: its maximal scope limits and the scope precedence preferences w.r.t. other lexical entries. Second, we should force the scope closing of the quantifiers by applying a standard type shifter Lower (which is equivalent to identity function application), once their scope limits were reached. But the actual mechanism that ensures the scope closing was left underspecified in previous work on continuation semantics. In what follows, we propose such a mechanism, designed to ensure that no lexical entry having the scope bounded to its minimal clause (such as not, no, every, each, any, etc) will ever take scope outside, thus getting right discourse truth conditions. The programming language concept of continuations was successfully used by Barker and Shan in a series of articles (Barker 2002, Barker 2004, Shan 2005, Shan and Barker 2006, Barker and Shan 2008) to analyze intra-sentential linguistic phenomena (focus fronting, donkey anaphora, presupposition, crossover, superiority, etc). Moreover, (de Groote, 2006) proposed an elegant discourse semantics based on continuations. Continuations are a standard tool in computer science, used to control side effects of computation. They are a notoriously hard to understand notion. Actually, understanding what a continuation is per se is not so hard. What is more difficult is to understand how a grammar based on continuations (a …

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