Soundness and completeness proofs by coinductive methods

We show how codatatypes can be employed to produce compact, high-level proofs of key results in logic: the soundness and completeness of proof systems for variations of first-order logic. For the classical completeness result, we first establish an abstract property of possibly infinite derivation trees. The abstract proof can be instantiated for a wide range of Gentzen and tableau systems for various flavors of first-order logic. Soundness becomes interesting as soon as one allows infinite proofs of first-order formulas. This forms the subject of several cyclic proof systems for first-order logic augmented with inductive predicate definitions studied in the literature. All the discussed results are formalized using Isabelle/HOL’s recently introduced support for codatatypes and corecursion. The development illustrates some unique features of Isabelle/HOL’s new coinductive specification language such as nesting through non-free types and mixed recursion–corecursion

A survey on managing users' preferences in ambient intelligence

Understanding the importance of preference management in ambient intelligent environments is key to providing systems that are better prepared to meet users' expectations. This survey provides an account of the various ways that preferences have been handled in Artificial Intelligence. Our analysis indicates that most of those techniques lack the ability to handle ambiguity and the evolution of preferences over time. Further exploration shows that argumentation can provide a feasible solution to complement existing work. We illustrate our claim by using an intelligent environment case study