An Integrated First-Order Theory of Points and Intervals over Linear Orders (Part I)

There are two natural and well-studied approaches to temporal ontology and reasoning: point-based and interval-based. Usually, interval-based temporal reasoning deals with points as a particular case of duration-less intervals. A recent result by Balbiani, Goranko, and Sciavicco presented an explicit two-sorted point-interval temporal framework in which time instants (points) and time periods (intervals) are considered on a par, allowing the perspective to shift between these within the formal discourse. We consider here two-sorted first-order languages based on the same principle, and therefore including relations, as first studied by Reich, among others, between points, between intervals, and inter-sort. We give complete classifications of its sub-languages in terms of relative expressive power, thus determining how many, and which, are the intrinsically different extensions of two-sorted first-order logic with one or more such relations. This approach roots out the classical problem of whether or not points should be included in a interval-based semantics

Analysing imperfect temporal information in GIS using the Triangular Model

Rough set and fuzzy set are two frequently used approaches for modelling and reasoning about imperfect time intervals. In this paper, we focus on imperfect time intervals that can be modelled by rough sets and use an innovative graphic model [i.e. the triangular model (TM)] to represent this kind of imperfect time intervals. This work shows that TM is potentially advantageous in visualizing and querying imperfect time intervals, and its analytical power can be better exploited when it is implemented in a computer application with graphical user interfaces and interactive functions. Moreover, a probabilistic framework is proposed to handle the uncertainty issues in temporal queries. We use a case study to illustrate how the unique insights gained by TM can assist a geographical information system for exploratory spatio-temporal analysis

The Energetic Reasoning Checker Revisited

Energetic Reasoning (ER) is a powerful filtering algorithm for the Cumulative constraint. Unfortunately, ER is generally too costly to be used in practice. One reason of its bad behavior is that many intervals are considered as relevant by the checker of ER, although most of them should be ignored. In this paper, we provide a sharp characterization that allows to reduce the number of intervals by a factor seven. Our experiments show that associating this checker with a Time-Table filtering algorithm leads to promising results.Comment: CP Doctoral Program 2013, Uppsala : Sweden (2013

An Integrated First-Order Theory of Points and Intervals over Linear Orders (Part II)

There are two natural and well-studied approaches to temporal ontology and reasoning: point-based and interval-based. Usually, interval-based temporal reasoning deals with points as a particular case of duration-less intervals. A recent result by Balbiani, Goranko, and Sciavicco presented an explicit two-sorted point-interval temporal framework in which time instants (points) and time periods (intervals) are considered on a par, allowing the perspective to shift between these within the formal discourse. We consider here two-sorted first-order languages based on the same principle, and therefore including relations, as first studied by Reich, among others, between points, between intervals, and inter-sort. We give complete classifications of its sub-languages in terms of relative expressive power, thus determining how many, and which, are the intrinsically different extensions of two-sorted first-order logic with one or more such relations. This approach roots out the classical problem of whether or not points should be included in a interval-based semantics. In this Part II, we deal with the cases of all dense and the case of all unbounded linearly ordered sets.Comment: This is Part II of the paper `An Integrated First-Order Theory of Points and Intervals over Linear Orders' arXiv:1805.08425v2. Therefore the introduction, preliminaries and conclusions of the two papers are the same. This version implements a few minor corrections and an update to the affiliation of the second autho

Unifying Practical Uncertainty Representations: II. Clouds

There exist many simple tools for jointly capturing variability and incomplete information by means of uncertainty representations. Among them are random sets, possibility distributions, probability intervals, and the more recent Ferson's p-boxes and Neumaier's clouds, both defined by pairs of possibility distributions. In the companion paper, we have extensively studied a generalized form of p-box and situated it with respect to other models . This paper focuses on the links between clouds and other representations. Generalized p-boxes are shown to be clouds with comonotonic distributions. In general, clouds cannot always be represented by random sets, in fact not even by 2-monotone (convex) capacities.Comment: 30 pages, 7 figures, Pre-print of journal paper to be published in International Journal of Approximate Reasoning (with expanded section concerning clouds and probability intervals

Modal Logics of Topological Relations

Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the Egenhofer-Franzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the two-variable fragment of first-order logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to highly undecidable, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity

Rethinking Pointer Reasoning in Symbolic Execution

Symbolic execution is a popular program analysis technique that allows seeking for bugs by reasoning over multiple alternative execution states at once. As the number of states to explore may grow exponentially, a symbolic executor may quickly run out of space. For instance, a memory access to a symbolic address may potentially reference the entire address space, leading to a combinatorial explosion of the possible resulting execution states. To cope with this issue, state-of-the-art executors concretize symbolic addresses that span memory intervals larger than some threshold. Unfortunately, this could result in missing interesting execution states, e.g., where a bug arises. In this paper we introduce MemSight, a new approach to symbolic memory that reduces the need for concretization, hence offering the opportunity for broader state explorations and more precise pointer reasoning. Rather than mapping address instances to data as previous tools do, our technique maps symbolic address expressions to data, maintaining the possible alternative states resulting from the memory referenced by a symbolic address in a compact, implicit form. A preliminary experimental investigation on prominent benchmarks from the DARPA Cyber Grand Challenge shows that MemSight enables the exploration of states unreachable by previous techniques

Expert systems tools for Hubble Space Telescope observation scheduling

The utility of expert systems techniques for the Hubble Space Telescope (HST) planning and scheduling is discussed and a plan for development of expert system tools which will augment the existing ground system is described. Additional capabilities provided by these tools will include graphics-oriented plan evaluation, long-range analysis of the observation pool, analysis of optimal scheduling time intervals, constructing sequences of spacecraft activities which minimize operational overhead, and optimization of linkages between observations. Initial prototyping of a scheduler used the Automated Reasoning Tool running on a LISP workstation