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...