A Formal Approach to the Semantics of a Frame Data Model

Standard knowledge representa t ion languages are se r i ous l y lack ing an e x p l i c i t formal semantic s p e c i f i c a t i o n . This may cause considerable t r oub le when appl ied to la rge amounts of r a p i d l y changing da ta . Based on an abs t rac t data type view of knowledge representa t ion languages a formal d e f i n i t i o n of a frame data model is presented in terms of a denota t iona l semantics approach using a subset of META-IV. A f te r in t roduc ing some bas ic concepts of the model several semantic i n t e g r i t y cons t ra in t s are ou t l i ned which u l t i m a t e l y lead to the formulat i o n of a set of operat ions in the frame data model. 1 . I n t roduc t i on Standard knowledge representa t ion languages such as KRL (BOBROW/WINOGRAD 1977) or FRL (ROBERTS/ GOLDSTEIN 1977) are almost exc lus i ve l y charact e r i z e d by syn tac t i c s p e c i f i c a t i o n s , but no a t t e n t i o n i s paid to the formal s p e c i f i c a t i o n o f t h e i r semantics. Recent ly, severa l formalisms have been devised which prov ide e x p l i c i t semantic s p e c i f i c a t i o n s , KL-ONE (as o u t l i n e d in BRACHMAN 1979) being one of the most promising proposals. Exhaustive formal cond i t ions on the operat ions on knowledge representa t ion s t ruc tu res c l e a r l y lead to an abs t rac t data type view of knowledge represen ta t ion languages (WEINER/PALMER 1981). The lack of semantic s p e c i f i c a t i o n s in knowledge representa t ion languages may cause severe problems (e .g . unpred ic tab le s ide e f f e c t s and incons is ten t changes in the data base), which obv ious ly become more and more ser ious when la rge numbers of knowledge s t ruc tu res are managed. We consider knowledge base systems to be r e a l i z a t i o n s of f o rma l l y def ined data models. By fo rma l l y spec i f y ing the semantics of the operat ions of an under ly ing frame data model we attempt to s t r i c t l y cons t ra in the ac tua l behavior of a la rge knowledge base system which forms an essen t ia l pa r t of TOPIC, an automatic t e x t understanding and abs t rac t i ng system (TOPIC 1983), c u r r e n t l y under development at the in format ion science department of the U n i v e r s i t y of Constance, W. Germany. The formal s p e c i f i c a t i o n of our frame data model is based on a denota t iona l semantics approach, app ly ing a subset of the META-IV-Language (e .g . as i l l u s t r a t e d in BJORNER 1980). A f te r i n t roducing basic concepts of our model (sect ion 2 ) , we s h a l l g i ve some examples of semantic i n t e g r i t y c o n s t r a i n t s which apply p roper t ies of the p re v i o u s l y def ined concepts (sect ion 3) and f i n a l l y i n d i c a t e the basic operat ions on ob jec ts of the data model (sect ion 4 ) , thus p rov id ing a sketch of what the semantics of a frame data model might look l i k e ( fo r an extended vers ion of t h i s paper see (REIMER/HAHN 1983)) . 2. Basic Concepts of the Data Model The no t ion of a frame is def ined by a mapping FRAMES = Frame —> SLOTS Frame denotes the set of frame SLOTS denotes the set of s l o t s . s l o t is g iven by the mapping SLOTS = Sname —> SENTRY i d e n t i f i e r s and The no t ion of a Sname denotes the domain of s l o t i d e n t i f i e r s and SENTRY denotes the domain of ac tua l and permi t ted s l o t e n t r i e s . The ac tua l and permi t ted e n t r i e s f o r a s l o t are given by the mapping SENTRY = Type —> En t r ies The set Type cons is ts of ac t and perm. The element ac t is mapped to the set o f ac tua l e n t r i e s wh i l e perm is mapped to the se t of permi t ted e n t r i e s , both sets c o n s t i t u t i n g the se t E n t r i e s . A network of r e l a t i o n a l l y connected frames may be constructed from the r e l a t i o n s g iven in the data model. We now consider s i n g l e elements of the mapping domains def ined above. This work was supported by Bundesministerium fuer Forschung und Technologie / Gese l lschaf t fuer In fo rmat ion und Dokumentation under grant no. PT 200.08. 338 U. Reimer and U. Hahn 3. Semantic Integr i ty Constraints The properties of the relations defined above not only put severe restr ic t ions on the possible re lat ional connection between two frames, but require the existence of a relat ional tuple, if two frames share appropriate properties. Further rest r ic t ions are included in the data model in terms of exp l i c i t semantic in tegr i ty constraints (viewing the properties of the relations as imp l i c i t semantic in tegr i ty constraints). U. Reimer and U. Hahn 339 The existence of a relat ional edge between two frames depends only on the existence of two frames with the properties required by the re la t ion. Therefore operations to insert or delete relat ion tuples need not be defined. Applying the de f i n i t ional properties of the Is-a and Parts relat ion and the properties of the equivalence class for each prototype, the semantically correct insertion and deletion of re lat ion tuples and instance frames w i l l be controlled and executed by the knowledge base system which realizes the frame data model.