Efficient inference and computation of optimal alternatives for preference languages based on lexicographic models

We analyse preference inference, through consistency, for general preference languages based on lexicographic models. We identify a property, which we call strong compositionality , that applies for many natural kinds of preference statement, and that allows a greedy algorithm for determining consistency of a set of preference statements. We also consider different natural definitions of optimality, and their relations to each other, for general preference languages based on lexicographic models. Based on our framework, we show that testing consistency, and thus inference, is polynomial for a specific preference language L′ pqT , which allows strict and non-strict statements, comparisons between outcomes and between partial tuples, both ceteris paribus and strong statements, and their combination. Computing different kinds of optimal sets is also shown to be polynomial; this is backed up by our experimental results

Temporal Representation and Reasoning in OWL 2

The representation of temporal information has been in the center of intensive research activities over the years in the areas of knowledge representation, databases and more recently, the Semantic Web. The proposed approach extends the existing framework of representing temporal information in ontologies by allowing for representation of concepts evolving in time (referred to as “dynamic” information) and of their properties in terms of qualitative descriptions in addition to quantitative ones (i.e., dates, time instants and intervals). For this purpose, we advocate the use of natural language expressions, such as “before” or “after”, for temporal entities whose exact durations or starting and ending points in time are unknown. Reasoning over all types of temporal information (such as the above) is also an important research problem. The current work addresses all these issues as follows: The representation of dynamic concepts is achieved using the “4D-fluents” or, alternatively, the “N-ary relations” mechanism. Both mechanisms are thoroughly explored and are expanded for representing qualitative and quantitative temporal information in OWL. In turn, temporal information is expressed using either intervals or time instants. Qualitative temporal information representation in particular, is realized using sets of SWRL rules and OWL axioms leading to a sound, complete and tractable reasoning procedure based on path consistency applied on the existing relation sets. Building upon existing Semantic Web standards (OWL), tools and member submissions (SWRL), as well as integrating temporal reasoning support into the proposed representation, are important design features of our approach

On the Consistent Histories Approach to Quantum Mechanics

We review the consistent histories formulations of quantum mechanics developed by Griffiths, Omn\`es and Gell-Mann and Hartle, and describe the classification of consistent sets. We illustrate some general features of consistent sets by a few simple lemmas and examples. We consider various interpretations of the formalism, and examine the new problems which arise in reconstructing the past and predicting the future. It is shown that Omn\`es' characterisation of true statements --- statements which can be deduced unconditionally in his interpretation --- is incorrect. We examine critically Gell-Mann and Hartle's interpretation of the formalism, and in particular their discussions of communication, prediction and retrodiction, and conclude that their explanation of the apparent persistence of quasiclassicality relies on assumptions about an as yet unknown theory of experience. Our overall conclusion is that the consistent histories approach illustrates the need to supplement quantum mechanics by some selection principle in order to produce a fundamental theory capable of unconditional predictions.Comment: Published version, to appear in J. Stat. Phys. in early 1996. The main arguments and conclusions remain unaltered, but there are significant revisions from the earlier archive version. These include a new subsection on interpretations of the formalism, other additions clarifying various arguments in response to comments, and some minor corrections. (87 pages, TeX with harvmac.

Logical Dreams

We discuss the past and future of set theory, axiom systems and independence results. We deal in particular with cardinal arithmetic