Wiebke Petersen - Frames for sortal, relational, and functional concepts

Concepts can be distinguished with respect to both arity as well as the uniqueness of their reference. Sortal concepts (e.g. stone) denote classical categories and have no unique referents. The referents of relational concepts (e.g. sister) are primarily identified by their relation to a possessor (sister of Liz); furthermore, they can be characterized by additional sortal features (‘SEX: female’). The functional concepts (e.g. mother) form a special case of the relational concepts by establishing a one-to-one correspondence between their potential possessors and referents.    According to Barsalou (1992), frames as recursive attribute-value structures determine the general format of cognitive concepts. Coming from empirical research, Barsalou’s focus in developing the frame theory was not on giving a formal theory. In the talk, we want to both sharpen and generalize his intuitive conceptions by developing an adequate mathematical model for frames of concepts. Our goal is to obtain a better understanding of frames (not just in the specialized cases they have been used in so far, but on a general basis). This is a necessary condition for the adoption of frames in various fields of application.   For our frame model we assume that attributes assign unique values to objects and thus describe functional relations. The values can themselves be structured frames. Attributes in frames are therefore functional concepts and embody the concept type on which the categorization is based. We model frames as connected directed graphs with labeled nodes (value types) and vertices (attributes), and generalize thereby the classical theory of typed feature structures (Carpenter, 1992).    The different concept types mentioned above are reflected by the structure of the corresponding concept frames. E.g., the frames of functional concepts differ from the frames of sortal concepts since their potential referents are the values of an attribute which is identical with the functional concept. Our generalized version of typed feature structures allows us to represent this fundamental difference inherently in the frame graphs. In the first part of the talk we will introduce our formal frame model and discuss how the structure of a frame reflects the concept type of the represented concept.   The second part of the talk concentrates on how the set of admissible frames can be restricted by a type signature which defines an ontology on frames. Guided by the considerations in Guarino (1992), we drop the artifical distinction between attributes and types: the attribute set is merely a subset of the type set. Hence attributes occur in two different roles: as names of binary functional relations between types and as types themselves.    A frame-based semantics has to explain the fact that adjectives in expressions like red apple, big apple and sweet apple modify the values of different attributes in the apple frame (i.e., ‘color’, ‘size’ and ‘taste’) . We will show that our new definition of type signatures offers an elegant solution to this problem. Furthermore, we will demonstrate an implementation of a typed unification-based frame system which is based on our definition of type signatures.

References

Barsalou (1992): Frames, Concepts, and Conceptual Fields. In Lehrer, A. & Kittay, E.F. (eds.): Frames, Fields, and Contrasts, Lawrence Erlbaum Associates Publishers, 21-74.

Carpenter (1992): The Logic of Typed Feature Structures. CUP.

Guarino (1992): Concepts, attributes and arbitrary relations: some linguistic and ontological criteria for structuring knowledge bases. In Data Knowl. Eng., ElsevierScience Publishers B. V., 8, 249-261.