Informally speaking, diversification of search results refers to a trade-off between relevance and diversity in the set of results. In this article, we present a unifying framework for search result diversification using the axiomatic approach. The characterization provided by the axiomatic framework can help design and compare diversification systems, and we illustrate this using several examp...

Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms Group Theory; but some much deeper, Complete Ordered Fields with which Real Analysis starts. Groups abound in sciences, while by Dedekind's theorem there exists only one complete ordered field, up to isomorphism. Cayley's Abstract Alge...

We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined, embodying the equational properties of iteration theories. We prove a general completeness theorem for iteration operators, relying on a new, purely syntactic characterisation of the free iteration theory. We then show how iteration operators arise in axiomatic domain theory. One re...

We are living in a world where complexity of systems created and studied by people grows beyond all imaginable limits. Computers, their software and their networks are among the most complicated systems of our time. Science is the only efficient tool for dealing with this overwhelming complexity. One of the methodologies developed in science is the axiomatic approach. It proved to be very power...

Multi staged programming provides a new paradigm for constructing e cient solutions to complex problems Techniques such as program generation multi level partial evaluation and run time code generation respond to the need for general purpose solutions which do not pay run time interpretive overheads This paper provides a foundation for the formal analysis of one such system We introduce a multi...

Multi-staged programming provides a new paradigm for constructing eecient solutions to complex problems. Techniques such as program generation, multi-level partial evaluation, and run-time code generation respond to the need for general purpose solutions which do not pay run-time interpretive overheads. This paper provides a foundation for the formal analysis of one such system. We introduce a ...

Informally speaking, diversification of search results refers to a trade-off between relevance and diversity in the set of results. In this article, we present a unifying framework for search result diversification using the axiomatic approach. The characterization provided by the axiomatic framework can help design and compare diversification systems, and we illustrate this using several examp...