Qualitative Constraint Networks Research Articles

Exact Learning of Qualitative Constraint Networks from Membership Queries

A Qualitative Constraint Network (QCN) is a constraint graph representing problems under qualitative temporal or spatial relations. More formally, a QCN includes a set of entities and a list of qualitative constraints defining the possible scenarios between these entities. Qualitative constraints are expressed as disjunctions of binary relations capturing the (incomplete) knowledge between the involved entities. QCNs effectively represent various real-world applications, including scheduling and planning, configuration, and Geographic Information Systems (GIS). It is, however, challenging to elicit, from the user, the QCN representing a given problem. To overcome this difficulty in practice, we propose a new algorithm for learning, through membership queries, a QCN from a non-expert. Membership queries are asked to elicit temporal or spatial relationships between pairs of temporal or spatial entities. To improve the time performance of our learning algorithm, constraint propagation and ordering heuristics are enforced. The goal is to reduce the number of membership queries needed to reach the target QCN. We conducted several experiments on randomly generated temporal and spatial QCN instances to assess the practical effect of constraint propagation and ordering heuristics. The results of the experiments are encouraging and promising.

Dynamic branching in qualitative constraint-based reasoning via counting local models

We introduce and evaluate dynamic branching strategies for solving Qualitative Constraint Networks (QCNs), which are networks for representing and reasoning about spatial and temporal information in a natural manner, e.g., a constraint can be “Task A is scheduled after or during Task C”. Specifically, we propose heuristics that dynamically associate a weight with a relation in the branching decisions that occur during backtracking search, based on the count of local models that the relation is involved with in a given QCN. Experimental results with a random and a structured dataset of QCNs of Interval Algebra show that it is possible to achieve up to 5 times better performance for structured instances, whilst maintaining non-negligible gains of around 20% for random ones. Finally, we show that these results may be notably improved via a selection protocol algorithm that synthesizes the involved heuristics into an overall better performing meta-heuristic in the phase transition.

On neighbourhood singleton-style consistencies for qualitative spatial and temporal reasoning

Given a qualitative constraint network (QCN), a singleton-style consistency focuses on each base relation (atom) of a constraint separately, rather than the entire constraint altogether. This local consistency is essential for tackling fundamental reasoning problems associated with QCNs, such as minimal labeling, but can suffer from redundant constraint checks, especially when checks occur far from where the pruning usually takes place. In this paper, we propose singleton-style consistencies that are applied just on the neighbourhood of a singleton-checked constraint instead of the whole network. We make a theoretical comparison with existing consistencies and consequently prove some properties of the new ones. Further, we propose algorithms to enforce our consistencies, as well as parsimonious variants thereof, that are more efficient in practice than the state of the art. An experimental evaluation with random and structured QCNs of Allen's Interval Algebra in the phase transition region demonstrates the potential of our approach.

Collective singleton-based consistency for qualitative constraint networks: Theory and practice

Partial singleton weak path-consistency, or partial ▪-consistency for short, is essential for tackling challenging fundamental reasoning problems associated with qualitative constraints networks. Briefly put, partial ▪-consistency ensures that each base relation of each of the constraints of a qualitative constraint network can define a singleton relation in its corresponding partially weakly path-consistent, or partially ⋄-consistent for short, subnetwork. In this paper, we propose a stronger local consistency that couples ▪-consistency with the idea of collectively deleting certain unfeasible base relations by exploiting singleton checks. We then propose an algorithm for enforcing this new consistency and a lazy variant of that algorithm for approximating the new consistency that, given a qualitative constraint network, both outperform the respective algorithm for enforcing partial ▪-consistency in that network. With respect to the lazy algorithmic variant in particular, we show that it runs up to 5 times faster than our original exhaustive algorithm whilst exhibiting very similar pruning capability. We formally prove certain properties of our new local consistency and our algorithms, and motivate their usefulness through demonstrative examples and a thorough experimental evaluation with random qualitative constraint networks of the Interval Algebra and the Region Connection Calculus from the phase transition region of two different generation models. Finally, we provide evidence of the crucial role of the new consistency in tackling the minimal labeling problem of a qualitative constraint network, which is the problem of finding the strongest implied constraints of that network.

Leveraging Variable Elimination for Efficiently Reasoning about Qualitative Constraints

We introduce, study, and evaluate a novel algorithm in the context of qualitative constraint-based spatial and temporal reasoning that is based on the idea of variable elimination, a simple and general exact inference approach in probabilistic graphical models. Given a qualitative constraint network [Formula: see text], our algorithm utilizes a particular directional local consistency, which we denote by [Formula: see text]-consistency, in order to efficiently decide the satisfiability of [Formula: see text]. Our discussion is restricted to distributive subclasses of relations, i.e., sets of relations closed under converse, intersection, and weak composition and for which weak composition distributes over non-empty intersections for all of their relations. We demonstrate that enforcing [Formula: see text]-consistency in a given qualitative constraint network defined over a distributive subclass of relations allows us to decide its satisfiability, and obtain similar useful results for the problems of minimal labelling and redundancy. Further, we present a generic method that allows extracting a scenario from a satisfiable network, i.e., an atomic satisfiable subnetwork of that network, in a very simple and effective manner. The experimentation that we have conducted with random and real-world qualitative constraint networks defined over a distributive subclass of relations of the Region Connection Calculus and the Interval Algebra, shows that our approach exhibits unparalleled performance against state-of-the-art approaches for checking the satisfiability of such constraint networks.

Ontology-Based Photogrammetry Survey for Medieval Archaeology: Toward a 3D Geographic Information System (GIS)

This paper presents certain reflections concerning an interdisciplinary project between medieval archaeologists from the University of Florence (Italy) and computer science researchers from CNRS, National Center for Scientific Research, (France), aiming towards a connection between 3D spatial representation and archaeological knowledge. We try to develop an integrated system for archaeological 3D survey and all other types of archaeological data and knowledge by incorporating observable (material) and non-graphic (interpretive) data. Survey plays a central role, since it is both a metric representation of the archaeological site and, to a wider extent, an interpretation of it (being also a common basis for communication between the two teams). More specifically, 3D survey is crucial, allowing archaeologists to connect actual spatial assets to the stratigraphic formation processes (i.e., to the archaeological time) and to translate spatial observations into historical interpretation of the site. It is well known that laser scanner, photogrammetry and computer vision are very useful tools for archaeologists, although the integration of the representation of space, as well as archaeological time has not yet found a methodological standard of reference. We propose a common formalism for describing photogrammetric survey and archaeological knowledge stemming from ontologies: indeed, ontologies are fully used to model and store 3D data and archaeological knowledge. We equip this formalism with a qualitative representation of time, starting from archaeological stratigraphy. Stratigraphic analyses (both of excavated deposits and of upstanding structures) are closely related to Edward Cecil Harris’s theory of the “Unit of Stratigraphication” (referred to as “US”, while a stratigraphic unit of an upstanding structure Unita Stratigrafica Murale, in Italian, will be referred to as “USM”). Every US is connected to the others by geometric, topological and, eventually, temporal links, and these are recorded by the 3D photogrammetric survey. However, the limitations of the Harris matrix approach led us to use another formalism for representing stratigraphic relationships, namely Qualitative Constraints Networks (QCN), which was successfully used in the domain of knowledge representation and reasoning in artificial intelligence for representing temporal relations.

SURVEYING MEDIEVAL ARCHAEOLOGY: A NEW FORM FOR HARRIS PARADIGM LINKING PHOTOGRAMMETRY AND TEMPORAL RELATIONS

Abstract. The paper presents some reflexions concerning an interdisciplinary project between Medieval Archaeologists from the University of Florence (Italy) and ICT researchers from CNRS LSIS of Marseille (France), aiming towards a connection between 3D spatial representation and archaeological knowledge. It is well known that Laser Scanner, Photogrammetry and Computer Vision are very attractive tools for archaeologists, although the integration of representation of space and representation of archaeological time has not yet found a methodological standard of reference. We try to develop an integrated system for archaeological 3D survey and all other types of archaeological data and knowledge through integrating observable (material) and non-graphic (interpretive) data. Survey plays a central role, since it is both a metric representation of the archaeological site and, to a wider extent, an interpretation of it (being also a common basis for communication between the 2 teams). More specifically 3D survey is crucial, allowing archaeologists to connect actual spatial assets to the stratigraphic formation processes (i.e. to the archaeological time) and to translate spatial observations into historical interpretation of the site. We propose a common formalism for describing photogrammetrical survey and archaeological knowledge stemming from ontologies: Indeed, ontologies are fully used to model and store 3D data and archaeological knowledge. Xe equip this formalism with a qualitative representation of time. Stratigraphic analyses (both of excavated deposits and of upstanding structures) are closely related to E. C. Harris theory of “Stratigraphic Unit” (“US” from now on). Every US is connected to the others by geometric, topological and, eventually, temporal links, and are recorded by the 3D photogrammetric survey. However, the limitations of the Harris Matrix approach lead to use another representation formalism for stratigraphic relationships, namely Qualitative Constraints Networks (QCN) successfully used in the domain of knowledge representation and reasoning in artificial intelligence for representing temporal relations.

Checking the Consistency of Combined Qualitative Constraint Networks

We study the problem of consistency checking for constraint networks over combined qualitative formalisms. We propose a framework which encompasses loose integrations and a form of spatio-temporal reasoning. In particular, we identify sufficient conditions ensuring the polynomiality of consistency checking, and we use them to find tractable subclasses.

Special issue on temporal representation and reasoning (TIME’13)

In September 2013, we organized the 20th International Symposium on Temporal Representation and Reasoning (TIME’13) that took place in Pensacola, FL (USA). After 20years, the Symposium returned to the venue where it originally started. TIME has grown since its original incarnation as a workshop to become an international symposium encompassing several different areas of computer science which deal, in some way or another, with the concept of time, its representation, reasoning and applications. This event has provided an opportunity for scientific exchange for researchers coming from different areas such as artificial intelligence, databases, temporal logic, and formal methods. The work presented at the 2013 Symposium concerned several different temporal aspects of information and computation and comprises a unique combination of innovative theoretical results and successful applications. This special issue of Acta Informatica originates from a call for papers sent out right after the symposium, in which we invited the authors of the highest ranked papers—according to the reviews carried out by the Program Committee members—to submit an extended version. After two rounds of reviews performed by additional experts the following papers were selected for publication in the special issue.We thank all reviewers for their commitment and dedication. The paper “A Faster Execution Algorithm for Dynamically Controllable Simple Temporal Networks with Uncertainty”, by Luke Hunsberger, presents novel algorithms for managing the execution of dynamically controllable simple temporal networks with uncertainty. For the first time, full proofs of the correctness of these algorithms in a self-contained manner are presented. The paper “Optimization in Temporal Qualitative Constraint Networks” by Jean-Francois Condotta, Souhila Kaci and Yakoub Salhi presents a variety of results about temporal quali-

Optimization in temporal qualitative constraint networks

Various formalisms for representing and reasoning about temporal information with qualitative constraints have been studied in the past three decades. The most known are definitely the Point Algebra $$(\mathsf {PA})$$(PA) and the Interval Algebra $$({\mathsf {IA}})$$(IA) proposed by Allen. In this paper, for both calculi, we study a problem that we call the minimal consistency problem $$(\mathsf {MinCons})$$(MinCons). Given a temporal qualitative constraint network $$(\mathsf {TQCN})$$(TQCN) and a positive integer $$k$$k, this problem consists in deciding whether or not this $$\mathsf {TQCN}$$TQCN admits a solution using at most $$k$$k distinct points on the line.We show that $$\mathsf {MinCons}$$MinCons for $$\mathsf {PA}$$PA can be encoded into the finitary versions of Godel logic. Furthermore, we prove that the $$\mathsf {MinCons}$$MinCons problem is $$\mathsf {NP}$$NP-complete for both $$\mathsf {PA}$$PA and $${\mathsf {IA}}$$IA, in the general case. However, we show that for $$\mathsf {TQCN}$$TQCNs defined on the convex relations, $$\mathsf {MinCons}$$MinCons is polynomial. For such $$\mathsf {TQCN}$$TQCNs, we give a polynomial method that allows one to obtain compact scenarios.

Ordering

Sketch maps are externalizations of cognitive maps which are typically distorted, schematized, incomplete, and generalized. Processing spatial information from sketch maps automatically requires reliable formalizations which are not subject to schematization, distortion or other cognitive effects in sketch maps. Based on previous empirical work, the authors identified different sketch aspects such as ordering, topology and orientation to align and integrate spatial information from sketch maps with metric maps qualitatively. This research addresses the question how these qualitative sketch aspects can be formalized for a computational approach for sketch map alignment. In this study, the authors focus on the ordering aspect: ordering of landmarks and street segments along routes and around junctions. The authors first investigate different qualitative representations and propose suitable representations to formalize these aspects. The proposed representations capture qualitative relations between spatial objects in the form of qualitative constraint networks. The authors then evaluate the proposed representations by testing the accuracy of qualitative constraints between sketched objects and their corresponding objects in a metric map. The results of the evaluation show that the proposed representations are suitable for the alignment of spatial objects from sketch maps with metric maps.

Spatial reasoning with rectangular cardinal relations

Qualitative spatial representation and reasoning plays a important role in various spatial applications. In this paper we introduce a new formalism, we name RCD calculus, for qualitative spatial reasoning with cardinal direction relations between regions of the plane approximated by rectangles. We believe this calculus leads to an attractive balance between efficiency, simplicity and expressive power, which makes it adequate for spatial applications. We define a constraint algebra and we identify a convex tractable subalgebra allowing efficient reasoning with definite and imprecise knowledge about spatial configurations specified by qualitative constraint networks. For such tractable fragment, we propose several polynomial algorithms based on constraint satisfaction to solve the consistency and minimality problems. Some of them rely on a translation of qualitative networks of the RCD calculus to qualitative networks of the Interval or Rectangle Algebra, and back. We show that the consistency problem for convex networks can also be solved inside the RCD calculus, by applying a suitable adaptation of the path-consistency algorithm. However, path consistency can not be applied to obtain the minimal network, contrary to what happens in the convex fragment of the Rectangle Algebra. Finally, we partially analyze the complexity of the consistency problem when adding non-convex relations, showing that it becomes NP-complete in the cases considered. This analysis may contribute to find a maximal tractable subclass of the RCD calculus and of the Rectangle Algebra, which remains an open problem.

Negotiation in Constraint-Based Design

A design problem usually involves multiple perspectives, each with own set of constraints that may interact. The objective of this paper is to develop a methodology to assist in negotiation of constraints from multiple perspectives. The proposed approach is based on qualitative reasoning that provides each perspective with negotiation information for making design decisions. A qualitative constraint network is used to characterize the qualitative and quantitative relationship between design variables. It provides means for tracking dependencies among perspectives for a set of constraints and determines the impact of design changes. When a conflict occurs, effective negotiation strategies are generated. A negotiation procedure for an ill-structured negotiation process is presented. The effectiveness of the negotiation process is improved with the procedure proposed. A valve design problem illustrates the concepts discussed in the paper.