Auxiliary and Approximating Relations
نویسنده
چکیده
The aim of this paper is to formalize the second part of Chapter I Section 1 (1.9–1.19) in [12]. Definitions of Scott’s auxiliary and approximating relations are introduced in this work. We showed that in a meet-continuous lattice, the way-below relation is the intersection of all approximating auxiliary relations (proposition (40) — compare 1.13 in [12, pp. 43–47]). By (41) a continuous lattice is a complete lattice in which ≪ is the smallest approximating auxiliary relation. The notions of the strong interpolation property and the interpolation property are also introduced.
منابع مشابه
Auxiliary and Approximating Relations1
The aim of this paper is to formalize the second part of Chapter I Section 1 (1.9–1.19) in [10]. Definitions of Scott’s auxiliary and approximating relations are introduced in this work. We showed that in a meet-continuous lattice, the way-below relation is the intersection of all approximating auxiliary relations (proposition (40) — compare 1.13 in [10, pp. 43–47]). By (41) a continuous lattic...
متن کاملCompletely Precontinuous Posets
In this paper, concepts of strongly way below relations, completely precontinuous posets, coprimes and Heyting posets are introduced. The main results are: (1) The strongly way below relations of completely precontinuous posets have the interpolation property; (2) A poset P is a completely precontinuous poset iff its normal completion is a completely distributive lattice; (3) An ω-chain complet...
متن کاملMeet Precontinuous Posets
In this paper, we introduce the concept of meet precontinuous posets, a generalization of meet continuous lattices to posets. The main results are: (1) A poset P is meet precontinuous iff its normal completion is a meet continuous lattice iff a certain system γ(P ) which is, in the case of complete lattices, the lattice of all Scott-closed sets is a complete Heyting algebra; (2) A poset P is pr...
متن کاملFunctional Dependency Driven Auxiliary Relation Selection for Materialized Views Maintenance
In a data warehouse system, maintaining materialized views can speed up query processing. These views need to be maintained in response to updates in the base relations. This is often done for reasons of data currency, using incremental techniques rather than re-computing the view from scratch. However, when the data source changes, the views in the warehouse can become inconsistent with the ba...
متن کاملOn the Quantifier-Free Dynamic Complexity of Reachability
The dynamic complexity of the reachability query is studied in the dynamic complexity framework of Patnaik and Immerman, restricted to quantifier-free update formulas. It is shown that, with this restriction, the reachability query cannot be dynamically maintained, neither with binary auxiliary relations nor with unary auxiliary functions, and that ternary auxiliary relations are more powerful ...
متن کامل