Seminar Details
Date 
5122003 
Time 
9:30 
Room/Location 
218 
Title 
Denotational semantics for Viewbased Database Mappings 
Speaker 
Zoran Majkic 
Affiliation 
Univ. di Roma 
Link 

Abstract 
This document presents a categorical denotational semantics for
database mapping, based on views, in the most general framework,
databaseintegration/exchange and Peertopeer. The base database
category DB (instead of traditional Set category) , with objects
databaseinstances and with morphisms (mappings which are not
functions) between them, is used (at instance level) as a proper
semantic domain for a database mappings based on a set of complex
query computations. The higher (logical) level schema mappings
between databases, usually written in some high expressive logical
language (for example, LAV, GAV, GLAV, tuple generating dependency)
may be functorially translated into this base "computation" category.
The new approach based on the behavioral point of view for databases
is assumed, and are established behavioural equivalences for databases
and their mappings. The introduction of observations, which are
computations without sideeffects, also defines the fundamental (from
Universal algebra) monad endofunctor T, which is also the closure
operator for objects and for morphisms such that the database lattice
is an algebraic (complete and compact) lattice,
where Ob{DB} is a set of all objects (database instances) of DB
category and "\preceq" is a preorder relation between them. The join
and meet operators of this database lattice are Merging and Matching
database operators respectively. The resulting 2category DB is
symmetric (also a mapping is represented as an object, that is, a
database instance), so, a mappings between mappings are a 1cell
morphisms for all higher metatheories: each mapping is a homomorphism
from a Kleisli monadic Tcoalgebra into the cofree monadic
Tcoalgebra. The database category DB has nice properties: it is
equal to its dual, complete and cocomplete, locally small and locally
finitely presentable, and monoidal biclosed Vcategory enriched over
itself. The monad derived from the endofunctor T is an enriched monad.
Generally, database mappings are not simply programs from values
(relations) into computations (views) but an equivalence of
computations: because of that each mapping, from any two databases A
and B, is equivalently reversible and gives a duality property to the
category DB. The denotational semantics of database mappings is given
by morphisms of the Kleisli category DB_T which may be "internalized"
in DB category as "computations". Special attention is devoted to
some practical examples: query definition, query rewriting in the
Databaseintegration environment, P2P mappings and their equivalent
GAV translation.



