Data Models for Conceptual Structures

A well-founded data model for Conceptual Structures can help in understanding issues of definitional semantics, efficient implementations and even syntax of proposed languages. This paper presents several useful data models of increasing complexity and applicability that can support Conceptual Structures definitional semantics. The models are presented in Haskell, a non-strict, stronglytyped functional language that allows easy definition of recursive data types, and also in hand generated XML using the proposed Schema standard that allows some of the same features. This paper then goes on to discuss how these models can be used by a schema-based XML version of an interchange format for Conceptual Graphs in comparison with CGIF. For the model presented in Haskell, a Haskell parser for CGIF syntax uses this model as a target, and this allows generation of XML output as a back-end to the parser. An XSLT style sheet that generates CGIF completes the cycle. All of the models are compared and contrasted. 1 Usefulness of Data Models Conceptual Structures, CS, as defined in Sowa's book [1], expresses knowledge as a connected multilabeled bipartite oriented graph. There exists a mapping from each of these graphs, Conceptual Graphs, CG, to formulae in first-order logic. The Conceptual Graph Interchange Format, CGIF, was intended for easy interchange of CGs and until this present year was maintained as an ANSI standard [2] and updated by the community [3]. The definition of CS as presented in [2], among other things, not only gives the interchange format CGIF, but also a semantic model of CG. This paper aims to improve the semantic portion of [2] by tying the semantics of CG to formal data models. One view of CGIF is that it is a persistent version of the internal data structures that a processor for conceptual structures must maintain. This is not of course its only use, and was not the main focus of its beginnings. Originally CGIF was a means to define a format for transmitting conceptual structures electronically. However, any processor that uses CGIF as its input-output format has to address the issue of what is the end result of parsing a CGIF file; that is, what internal data structures will be created and filled. One might question if there are good and bad target data structures, or if are they all equally good (or bad). The authors contend that CGIF has a small number of ‘natural’ data structures that lead to efficient parsing, and that an examination of the data models for these structures is useful for implementers of conceptual structure processors. Without such an examination, arbitrary choices can lead to inefficient internal data structures for the processors and potential errors.