Quantification in frame semantics with binders and nominals of hybrid logic

Abstract

This paper aims to integrate logical operators into frame-based semantics. Frames are semantic graphs that allow lexical meaning to be captured in a fine-grained way but that do not come with a natural way to integrate logical operators such as quantifiers. The approach we propose stems from the observation that modal logic is a powerful tool for describing relational structures, including frames. We use its hybrid logic extension in order to incorporate quantification and thereby allow for inference and reasoning. We integrate our approach into a type theoretic compositional semantics, formulated within Abstract Categorial Grammars. We also show how the key ingredients of hybrid logic, nominals and binders, can be used to model semantic coercion, such as the one induced by the begin predicate. In order to illustrate the effectiveness of the proposed syntax-semantics interface, all the examples can be run and tested with the Abstract Categorial Grammar development toolkit. frames and lexical semanticsFrames emerged as a representation format of conceptual and lexical knowledge (Fillmore 1977;Barsalou 1992;Löbner 2014a). They * This work was supported by the INRIA sabbatical program and by the CRC 991 "The Structure of Representations in Language, Cognition, and Science" funded by the German Research Foundation (DFG). Journal of Language Modelling Vol 5, No 2 (2017), pp. 357-383Laura Kallmeyer et al. are commonly presented as semantic graphs with labelled nodes and edges, such as the one in Figure 1, where nodes correspond to entities (individuals, events, …) and edges correspond to (functional or nonfunctional) relations between these entities. In Figure 1 all relations except part-of are meant to be functional. Structuring the knowledge as frames offers a fine-grained and systematic decomposition of meaning. This conception of frames is however not to be confused with the somewhat simpler FrameNet frames, although the former can help to capture the structural relations of the latter (see Osswald and Van Valin 2014).Frames can be formalized as extended typed feature structures (Petersen 2007; Kallmeyer and Osswald 2013) and specified as models of a suitable logical language, the labelled attribute-value description (LAVD) language. Such a language allows for the composition of lexical frames on the sentential level by means of an explicit syntax-semantics interface (Kallmeyer and Osswald 2013). 1.1 Logical representation of feature structuresThe syntax-semantics interface of (Kallmeyer and Osswald 2013) relies on a formal representation of semantic frames as base-labelled feature structure with types and relations. This definition extends the standard definition of feature structures in two respects. First, in addition to features, proper relations between nodes can be expressed. Moreover, it is not required that every node be accessible from a single root node via a feature path; instead, it is required that every node be accessible from one of the base-labelled nodes. Semantic frames defined in this way can...

Perception, Types and Frames

“…(13) The temperature rose during the week AmbTempFrame can be related to a directed graph similar to those discussed by Kallmeyer and Osswald (2013), Kallmeyer et al (2017) in connection with frames. We let the labels in the record type be labels on the edges and the types be labels on the nodes.…”

“…This would indicate that ambient temperature has three attributes: a real number (here labelled as the attribute 'x'), a location and a constraint (here labelled as the attribute 'e') that the real number is the temperature at the location. Both the record type (11) and the directed graph ( 14) could be coded in terms of hybrid logic in the manner suggested in Kallmeyer et al (2017) as in ( 15). ( 15)…”

“…This certainly gives us a more intuitive looking Düsseldorf frame. Also the representation of this in hybrid logic, given in ( 18), corresponds more closely to the use of hybrid logic by Kallmeyer et al (2017).…”

“…A possible disadvantage with this, though, is that the relationship between the record type and the directed graph is less direct than in the first suggestion that we presented. This discussion raises the interesting question of whether a general relationship could be shown between TTR and hybrid logic and more specifically between frames modelled in terms of records and record types and frames as modelled by Kallmeyer and Osswald (2013), Kallmeyer et al (2017). Then it is interesting to consider whether the particular linguistic analyses offered in the two approaches to frames can be intuitively represented in both TTR and DF.…”

Introduction

“…Cooper gives an introduction to the essentials of TTR with special reference to the conception of "record types" and their instantiation by particular records both of which play a central role within this theory. Moreover, Cooper discusses how his model is related to Fillmore frames and to cognitive frames in the sense of Barsalou (1992a, b) and their formal adoption by Löbner (2014Löbner ( , 2015, Kallmeyer & Osswald (2013) and Kallmeyer et al (2017) among others.…”