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An extended Relational Algebra on Abstract Objects for summarizing answers to queries

Demolombe R.

Fundamenta Informaticae

2003

Vol. 57, nr 1

1--15

Answers to queries in terms of abstract objects are defined in the logical framework of first order predicate calculus. A partial algebraic characterisation of the supremum and of the infimum of abstract answers is given in an extended Relational Algebra of the Cylindric Algebra kind. Then, the form of queries is restricted in order to be able to compute answers without the cylindrification operator. For these restricted queries we give a technique to compute an upper bound and a lower bound of abstract answers using only the operators of the standard Relational Algebra.

An Application of Deontic Logic to Information System Constraints

Carmo J., Demolombe R., Jones A.J.I.

Fundamenta Informaticae

2001

Vol. 48, nr 2,3

165-181

In the field of information systems the term ``constraint'' is applied to statements of various kinds. Here we start from the analysis of a simple example to characterise the different kinds of constraints. It is shown that constraints may be necessary truths or deontic constraints. Moreover, deontic constraints are classified into three different types: deontic constraints about the world, deontic constraints about the representation of the world (self-completeness), and deontic constraints about the links between the world and its representation (validity and completeness). We describe a modal logical framework to define the different types of constraints, to characterise their violations, and to show how to repair their violations. Two different general forms of deontic constraints are considered, namely O(fŽ y) and fŽ O y, and it is shown that, except for deontic constraints about the world, the latter is more appropriate. Special issues related to the definition of quantifiers in the context of modal operators are also considered.