Frame Theory with First-Order Comparators: Modeling the Lexical Meaning of Punctual Verbs of Change with Frames

The first part of the paper proposes a formal foundation of a theory of frames. Frames are embedded into a general ontology. On this background, we introduce a formal model-theoretic semantics for frames and thereby an interface to formal semantics. The model-theoretic semantics allows us to define central notions of frame theory such as the “satisfaction type” for a node in a given frame, and a semantic definition of subsumption. The second part presents a case study of decomposition: frames for subtypes of intransitive punctual verbs of change, such as punctual ‘grow’ and ‘go from A to B’. We introduce times, events, and time-dependent attributes in the ontology. A crucial element of the analysis is “comparators”, a novel type of attribute in frame theory. Comparators are partial two-place attributes that compare two individuals of the same sort and return comparison values such as ‘=’ vs. ‘≠’ or ‘<’ vs. ‘=’ vs. ‘>’. Comparators allow us to model within frames and AVMs conditions in terms of basic abstract relations. The approach proposed offers simplifications of alternative proposals for the frame-theoretical decomposition of these types of verb: (i) standard PL1 is used as a frame description language; (ii) with comparators, the use of non-functional relations as additional components in frames can be avoided; (iii) meanings of punctual verbs of change can be represented within one frame.