Temporal Data Modeling and Reasoning for Information Systems

Temporal knowledge representation and reasoning is a major research field in Artificial Intelligence, in Database Systems, and in Web and Semantic Web research. The ability to model and process time and calendar data is essential for many applications like appointment scheduling, planning, Web services, temporal and active database systems, adaptive Web applications, and mobile computing applications. This article aims at three complementary goals. First, to provide with a general background in temporal data modeling and reasoning approaches. Second, to serve as an orientation guide for further specific reading. Third, to point to new application fields and research perspectives on temporal knowledge representation and reasoning in the Web and Semantic Web

Expressiveness of Temporal Query Languages: On the Modelling of Intervals, Interval Relationships and States

Storing and retrieving time-related information are important, or even critical, tasks on many areas of Computer Science (CS) and in particular for Artificial Intelligence (AI). The expressive power of temporal databases/query languages has been studied from different perspectives, but the kind of temporal information they are able to store and retrieve is not always conveniently addressed. Here we assess a number of temporal query languages with respect to the modelling of time intervals, interval relationships and states, which can be thought of as the building blocks to represent and reason about a large and important class of historic information. To survey the facilities and issues which are particular to certain temporal query languages not only gives an idea about how useful they can be in particular contexts, but also gives an interesting insight in how these issues are, in many cases, ultimately inherent to the database paradigm. While in the area of AI declarative languages are usually the preferred choice, other areas of CS heavily rely on the extended relational paradigm. This paper, then, will be concerned with the representation of historic information in two well known temporal query languages: it Templog in the context of temporal deductive databases, and it TSQL2 in the context of temporal relational databases. We hope the results highlighted here will increase cross-fertilisation between different communities. This article can be related to recent publications drawing the attention towards the different approaches followed by the Databases and AI communities when using time-related concepts

Temporalized logics and automata for time granularity

Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym: TPLP Category: Paper for Special Issue (Verification and Computational Logic) Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September 200

Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

On the Semantics of "Now" in Databases

While "now" is expressed in SQL as CURRENT-TIMESTAMP within queries, this value cannot be stored in the database. However, this notion of an ever-increasing current-time value has been reflected in some temporal data models by inclusion of database-resident variables, such as "now," "until-changed," "â," "@" and "-." Time variables are very desirable, but their use also leads to a new type of database, consisting of tuples with variables, termed a variable database. This paper proposes a framework for defining the semantics of the variable databases of temporal relational data models. A framework is presented because several reasonable meanings may be given to databases that use some of the specific temporal variables that have appeared in the literature. Using the framework, the paper defines a useful semantics for such databases. Because situations occur where the existing time variables are inadequate, two new types of modeling entities that address these shortcomings, timestamps which we call now-relative and now-relative indeterminate, are introduced and defined within the framework. Moreover, the paper provides a foundation, using algebraic bind operators, for the querying of variable databases via existing query languages. This transition to variable databases presented here requires minimal change to the query processor. Finally, to underline the practical feasibility of variable databases, we show that database variables can be precisely specified and efficiently implemented in conventional query languages, such as SQL, and in temporal query languages, such as TSQL2.Information Systems Working Papers Serie

Lorenz, G\"{o}del and Penrose: New perspectives on determinism and causality in fundamental physics

Despite being known for his pioneering work on chaotic unpredictability, the key discovery at the core of meteorologist Ed Lorenz's work is the link between space-time calculus and state-space fractal geometry. Indeed, properties of Lorenz's fractal invariant set relate space-time calculus to deep areas of mathematics such as G\"{o}del's Incompleteness Theorem. These properties, combined with some recent developments in theoretical and observational cosmology, motivate what is referred to as the `cosmological invariant set postulate': that the universe $U$ can be considered a deterministic dynamical system evolving on a causal measure-zero fractal invariant set $I_U$ in its state space. Symbolic representations of $I_U$ are constructed explicitly based on permutation representations of quaternions. The resulting `invariant set theory' provides some new perspectives on determinism and causality in fundamental physics. For example, whilst the cosmological invariant set appears to have a rich enough structure to allow a description of quantum probability, its measure-zero character ensures it is sparse enough to prevent invariant set theory being constrained by the Bell inequality (consistent with a partial violation of the so-called measurement independence postulate). The primacy of geometry as embodied in the proposed theory extends the principles underpinning general relativity. As a result, the physical basis for contemporary programmes which apply standard field quantisation to some putative gravitational lagrangian is questioned. Consistent with Penrose's suggestion of a deterministic but non-computable theory of fundamental physics, a `gravitational theory of the quantum' is proposed based on the geometry of $I_U$, with potential observational consequences for the dark universe.Comment: This manuscript has been accepted for publication in Contemporary Physics and is based on the author's 9th Dennis Sciama Lecture, given in Oxford and Triest

Coherent States of Accelerated Relativistic Quantum Particles, Vacuum Radiation and the Spontaneous Breakdown of the Conformal SU(2,2) Symmetry

We give a quantum mechanical description of accelerated relativistic particles in the framework of Coherent States (CS) of the (3+1)-dimensional conformal group SU(2,2), with the role of accelerations played by special conformal transformations and with the role of (proper) time translations played by dilations. The accelerated ground state $\tilde\phi_0$ of first quantization is a CS of the conformal group. We compute the distribution function giving the occupation number of each energy level in $\tilde\phi_0$ and, with it, the partition function Z, mean energy E and entropy S, which resemble that of an "Einstein Solid". An effective temperature T can be assigned to this "accelerated ensemble" through the thermodynamic expression dE/dS, which leads to a (non linear) relation between acceleration and temperature different from Unruh's (linear) formula. Then we construct the corresponding conformal-SU(2,2)-invariant second quantized theory and its spontaneous breakdown when selecting Poincar\'e-invariant degenerated \theta-vacua (namely, coherent states of conformal zero modes). Special conformal transformations (accelerations) destabilize the Poincar\'e vacuum and make it to radiate.Comment: 25 pages, LaTeX, 3 figures. Additional information (resulting in four extra pages) and a slight change of focus has been introduced in order to make the line of arguments more clear. Title changed accordingl

State-of-the-art on evolution and reactivity

This report starts by, in Chapter 1, outlining aspects of querying and updating resources on the Web and on the Semantic Web, including the development of query and update languages to be carried out within the Rewerse project. From this outline, it becomes clear that several existing research areas and topics are of interest for this work in Rewerse. In the remainder of this report we further present state of the art surveys in a selection of such areas and topics. More precisely: in Chapter 2 we give an overview of logics for reasoning about state change and updates; Chapter 3 is devoted to briefly describing existing update languages for the Web, and also for updating logic programs; in Chapter 4 event-condition-action rules, both in the context of active database systems and in the context of semistructured data, are surveyed; in Chapter 5 we give an overview of some relevant rule-based agents frameworks