# B1 - Formal modelling of frames and functional concepts

According to Barsalou 1992 frames as recursive attribute-value structures with constraints form the general format of concepts in human cognition. Based on empirical research, Barsalou’s focus in developing frame theory was not on providing a formal theory. We intend to both sharpen and generalize his intuitive conceptions by developing an adequate mathematical model for frames. By examining the formal properties of frames and modeling frames of different concept types, our goal is to obtain a better understanding of frames and an adequate explanation of cognitive processes. This is necessary for the adoption of frames in various fields of application, such as frame-based semantics, medical diagnosis, scientific classification or frame-based knowledge systems.

Frames describe the objects they represent by using attributes with assigned values. The values can be either atomic, or structured frames themselves. They can be specific, underspecified or unspecified. Our assumption is that attributes assign unique values to objects and thus describe functional relations. Hence, the attributes can be seen as the primes of concept formation. As discussed in Petersen 2007, frames can be represented by directed graphs with labeled nodes and arcs. Each node is labeled with a type and each arc is labeled with an attribute.

A model-theoretic interpretation of the graphs will be developed by assigning to each node a type in an appropriate type signature and to each arc an appropriate partial function. To achieve the goal of building an adequate mathematical model for frames, we have chosen to approach the frame structure from two perspectives: (a) we will investigate how the node-types can be ordered in a type signature such that the set of admissible frames becomes restricted and (b) we will determine and examine the space of attributes. By advancing a proper model-theoretic semantics of frames, the foundations will be established for deploying frames in the various fields of application in a formally rigorous approach.