Towards a semantic view of an extended entity-relationship model

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Abstract
Nearly all query languages discussed recently for the Entity-Relationship (ER) model do not possess a formal semantics. Languages are often defined by means of examples only. The reason for this phenomenon is the essential gap between features of query languages and theoretical foundations like algebras and calculi. Known languages offer arithmetic capabilities and allow for aggregates, but algebras and calculi defined for ER models do not. This paper introduces an extended ER model concentrating nearly all concepts of known so-called semantic data models in a few syntactical constructs. Moreover, we provide our extended ER model with a formal mathematical semantics. On this basis a well-founded calculus is developed taking into account data operations on arbitrary user-defined data types and aggregate functions. We pay special attention to arithmetic operations, as well as multivalued terms allowing nested queries, in a uniform and consistent manner. We prove our calculus only allows the formulation of safe terms and queries yielding a finite result, and to be (at least) as expressive as the relational calculi.

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