Deliverable N : R413. Covering period June.2003-May.2004

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1 REV!GIS REV!GIS: Uncertain Geographic Knowledge, Maintenance and Revision <IST > Algorithms for complex knowledge revision, v2 Deliverable N : R413 Covering period June.2003-May.2004 Report Version: 1 Report Preparation Date: April 17 th, 2004 Classification: Int Contract Start Date: June 2000 Duration: 48 months Project Co-ordinator: Université de Provence, Marseille (Dr. R. Jeansoulin) Partners: ITC (NL), U. Keele (UK), U. Leicester (UK), TU Vienna (AT), CNR/ISTI (IT), U. Toulon (FR), CRG U. Laval (CA), Somei (FR) Here: the ST logo I Project funded by the European Community under the Information Society Technologies Programme ( ) Future and Emerging Technologies

2 DELIVERABLE SUMMARY SHEET Project Number: IST Project Acronym: REV!GIS Title: Uncertain Geographic Information Maintenance and Revision Deliverable N : R413 Due date: June, 1 st, 2004 Delivery Date: May, 5 th, 2004 Short Description: This deliverable reports on algorithms and Tractability issues for revision of knowledge. It summarizes the work performed during the previou years of the project, and develops what has been added during the last year of the project, which is: - Prioritized Removed Set Revision, (PRSR) principles, adaptation of smodel algorithms for PRSR,experimentation of PRSR on the flooding problem; - Removed Set Revision tranlated into a SAT problem, experimentation with the MINISAT solver on the flooding problem; - Removed Set Revision and ROBDD; - Revision in STP formalism; - Revision of partial pre-orders: algorithm and application; - Synthesis of Algorithms and Tractability issues. This last section provides basis for a sound selection of a revision strategy according to the characteristics of an application, in term of what structure order can emerge from the semantics of the user problem: the propositional-based revision is always possible, but hardly tractable, polynomial revision is possible if a total pre-order is present, and linear-constraint-based revision is appropriate and very fast, if a total and dense order exists behind the constraints and makes them linear. Partners owning: U. Toulon (Toulon, UK) Partners contributed: U. Provence (FR), U. Artois (FR), U. Laval (CA), U. Keele(UK), CNR (IT), SOMEI (FR), CEMAGREF(FR) Made available to: REV!GIS partners, IST-FET administration, project officer and reviewers. REVIGIS Project IST Delivery R413 2/11

3 Table of Contents: 1 PARTICIPATION AND MEETINGS SCIENTIFIC WORK SUMMARY OF PREVIOUS REPORTS FOR THIS TASK ADDITIONAL WORK DURING YEAR Prioritized Removed Set Revision (PRSR) principles, adaptation of smodel algorithms for PRSR, experimentation of PRSR on the flooding problem; Removed set revision tranlated into a SAT problem, experimentation with the MINISAT solver on the flooding problem; Removed Sets Revision and ROBDD Revision in the STP formalism; Revision of partial pre-orders: algorithm and application to the uncertain constraints on location problem Synthesis of the REVIGIS project-task on Algorithms and Tractability issues REFERENCES FOR THIS SECTION : PROSPECTIVE AND FUTURE WORK LIST OF ANNEXES REVIGIS Project IST Delivery R413 3/11

4 1 Participation and Meetings Task Leader Odile Papini (PhD.) Professor, U. Toulon (Toulon, FR) Main Participants Eric Wurbel (PhD.) Senior Lecturer (Assistant Professor), U. Toulon (Toulon, FR)) Sylvain Lagrue (PhD) Associate Lecturer, SOMEI, and U. Artois (Lens, FR) Jonathan Bennaim (MsSc.) - PhD student, U. Toulon (Toulon, FR) Salem Benferhat (Dr.) Professor, U. Artois (Lens, FR) Mahat Khelfallah (MsSc.) - PhD student, U. Provence (Marseille, FR) Robert Jeansoulin (PhD.) Research fellow, U. Provence (Marseille, FR) Nic Wilson (PhD) post-doc, U. Keele (Keele, UK) Collaborators Christian Puech (PhD) directeur de recherche, CEMAGREF Damien Raclot (PhD) post-doc, CEMAGREF Belaid Benhamou(PhD) Assistant Professor, U. Provence (Marseille, UK) Chiara Renso (PhD) Research Fellow, CNR Pisa Geoffrey Edwards (PhD) Professor, U. Laval (Québec, CA) Mir Abolfazl Mostafavi(PhD) Post-doc, U. Laval (Québec, CA) Meetings (since start date) - Marseille (Full meeting, june 2000) - Keele (WP1 meeting, february 2001) - Quebec (Full meeting april 2001) - Toulouse (Full mee, september 2001) - Montpellier (WP1 meeting, september 2001) - Pisa (WP1 meeting, february 2002) - Marseille (February 2002, march 2002) - Enschede (Full meting, june 2002) - Toulon (Praxitec-Toulon-Cemagref, july 2002) - Marseille (1 st junior meeting, september 2002) - Pisa (CNR-Toulon, october 2002) - Marseille (Praxitec-Provence-Toulon-Keele, january, february 2003) - Marseille (2 nd junior meeting, march 2003), full week - Lens (Praxitec-Lens, march, april 2003) - Marseille (3 rd junior meeting, june 2003), full week - Marseille (4 th junior meeting, september 2003), full week - Marseille (meeting october 2003) - Toulon (WP1. task 1.3 december 2003) - Toulouse(WP1. task 1.3 january 2004) - Marseille (WP1. task 1.3 february -march 2003) - Toulouse (WP1. Task 1.3, january 2004) - Vienna (full meeting, during ISSDQ 2004 conference, april 2004) REVIGIS Project IST Delivery R413 4/11

5 2 Scientific work Introduction and description of the subtask of Task 1.3. Title: Reasoning under uncertainty with geographic knowledge: Algorithmic and Tractability Issues. Within the general objective of the workpackage #1: To survey and to develop the general formalisms for the representation of imperfect GI; To survey and to develop the computational approaches to reasoning with imperfect GI; To detect computational complexity issues and to propose solution whenever possible; To provide a goal oriented approach to integrate langage and architecture issue; To match particular approaches to corresponding classes of applications; To implement a demonstrator to illustrate the above objectives. The expectations and specific objective for Task 1.3 are: Several algorithms of 1.2 are basically NP complex. This task is to assess these algorithms, to define restrictions (linear case, convex subset, or cases isomorphic to "polynomial classes") and their specific algorithms, to implement into task 1.2-version 2 algorithms series of software versions corresponding to time critical algorithms, tuned for specific applications: preliminary R113, specifications R213, v1, v2 (R313, R413) --Sub-tasks: - Testing current divide and revise strategy on the flooding application (Toulon, UP, Cemagref): R Development of divide and revise strategy and assessment of a Prolog implementation (UP, Toulon). The development is expected in year 2: R Representing flooding constraints as DNNF and revision of these (Toulon): R S-models: representing flooding constraints with logic programming, and revision (Toulon, CNR): R Application of Logic of Linear Constraints to flooding application (Keele, Cemagref, UP, Toulon, CNR): R Revision of partial pre-orders: tests on land use application (Toulon, IRIT): R DNNF representation: tests on flooding application (Toulon), will start Mar 02: R S-models tests on flooding application (Toulon), will start Mar 02: R Heuristics for fusion/revision/updating of spatial data for WP3 (UP, TUW, Laval): R Application of generalised belief revision, possibility theory and Dempster-Shafer theory to flooding and similar problems (Keele, Cemagref, UP): part of R Summary of previous reports for this task During Year 1 and 2, we worked mainly on the implementation of the methods investigated in the task 1.2, and their application to the flooding problem. REVIGIS Project IST Delivery R413 5/11

6 Implementing classical formalisms for the flooding problem - Propositional calculus - Representation in Propositional calculus of geographic information - Propositional calculus for the flooding application - Comparison between three revision approaches o The REM algorithm o Formal comparison o Experimental comparison - Fuzzy Constraint Satisfaction Programming Developing algorithmic strategies: - Divide and Revise strategy - Representing constraints as Decomposable Negation Normal Forms - Representing constraints in Logic Programming (S-models) - Representing constraints in the Logic of Linear Constraints Applying it to the flooding problem - Representation in terms of Linear Constraints, and Associated Propagation Algorithms - Applying Uncertainty Formalisms to the Problem Starting investigations on Revision of partial pre-orders (applic. to land-cover classifications) During Year 3, we improved the work according to different directions: - 1 Comparison between different approaches of revision on the Flooding Problem (Toulon with University of Provence, university of Keele and CEMAGREF). A comparison has been conducted on different revision approaches developped so far. These approaches can be classified into two categories: logical approaches of conflict detection and conflict resolution with propagation technics. The pros and the cons of each of these approaches lead to propose a mixed approach taking advantage of each of them. - 2 Divide and revise strategy: piecewise revision for geographic information (University of Provence with university of Laval) In order to take into account the locality of conflicts, the notion of local containment and local reasoning are presented in 2.2, this is detailed in the annexed document Piecewise revision for geographic information, Annex DNNF and BDD approaches of revision (university of Toulon). We explain why the DNNF approach turned out to be problematical. We then investigated another knowledge compilation technique presented in 2.3, and detailed in the attached document Removed set revision and BDDs Annex S-models: revision algorithm and implementation on the Flooding Problem (University of Toulon with university of Lens and CNR). In Annex Year 2 deliverable we showed how logic programming with negation by failure can be successfully applied to the Flooding Problem. In 2.4 we propose an adaptation of S-models algorithm for revision and present an implementation on the Flooding Problem. The results clearly show that among logical approaches of conflict detection, this approach gives the most efficient ones. The approach is detailed in the attached document Answer set programming: an application in the framework of GIS Annex REVIGIS Project IST Delivery R413 6/11

7 - 5 Application of Logic of linear constraints to Flooding Problem (University of Keele with university of Provence and CEMAGREF) In Annex Year 2 deliverable, another new formalism stemming from the Logic of Linear Constraints (LLC), was proposed. In 2.5 it is shown how LLC can be successfully applied to the Flooding Problem. This is detailed in the attached document Geographic information revision based on linear constraints Annex Revision of partial pre-orders: algorithm and application to the uncertain constraints on location problem (PRAXITEC with university of Toulon with university of Artois, Lens). Stemming from the results obtained in WP1.1 about revision of partial pre-orders presented in year 2 deliverable Annex and Annex 211.5, and year 3 deliverable Annex 311.3, we propose in 2.6 an algorithm for performing revision of partially ordered beliefs and we show how our approach can be applied to uncertain constraints on location problem. 2.2 Additional work during Year Prioritized Removed Set Revision (PRSR) principles, adaptation of smodel algorithms for PRSR, experimentation of PRSR on the flooding problem; (university of Toulon, university of Artois, Lens) This is detailed in Annex 34.1 and Annex 34.7 Prioritized Removed Set Revision (PRSR) generalizes the Removed Set Revision, previously proposed R113, R213?, into the case of prioritized belief bases. Let K be a prioritized finite set of clauses, where K is partitioned into n strata, such that clauses in Ki have the same level of priority and are more prioritary than the ones in Kj where i is lower than j. K1 contains the clauses which are the most prioritary beliefs in K, and Kn contains the ones which are the least prioritary in K. When K is prioritized in order to restore consistency the principle of minimal change stems from removing the minimum number of clauses from K1, then the minimum number of clauses in K2, and so on. We introduce the notion of prioritized removed sets which generalizes the notion of removed set in order to perform Removed Sets Revision with prioritized sets of clauses. This generalization requires the introduction of a preference relation between subsets of K reflecting the principle of minimal change for prioritized sets of clauses. We then formalize the Prioritized Removed Sets Revision in terms of answer set programming. We first construct a logic program, in the same spirit of Niemela but, for each clause of K, we introduce a new atom and a new rule, such that the preferred answer sets of this program correspond to the prioritized removed sets of the union of K and A. We then define the notion of preferred answer set in order to perform PRSR. In order to get a one to one correspondence between preferred answer sets and prioritized removed sets, instead of computing the set of preferred answer sets of the union of P and A we compute the set of subsets of literals which are interpretations of Rk and that lead to preferred answer sets. The computation of Prioritized Removed Sets Revision is based on a new adaptation of the smodels system. This is achieved using two algorithms. The first algorithm, Prio, is an adaptation of smodels system algorithm which computes the set of subsets of literals of Rk which lead to preferred answer sets and which minimize the number of clauses to remove REVIGIS Project IST Delivery R413 7/11

8 from each stratum. The second algorithm, Rens, computes the prioritized removed sets of the union of K and A, applying the principle of minimal change for PRSR, that is, stratum by stratum. In the flooding application we have to deal with an aera consisting of 120 compartments and the stratification is usefull to deal with the whole aera. A stratification of S1 is induced from the geographic position of compartments. Compartments located in the north part of the valley are preferred to the compartments located in the south of the valley. An experimental study shows that using a stratification, the Rens algorithm can deal with the whole aera with a reasonable running time Removed set revision tranlated into a SAT problem, experimentation with the MINISAT solver on the flooding problem; (university of Toulon, university of Artois, Lens) This is detailed in Annex 34.7 The revision problem in the context of GIS is represented in propositional calculus and amounts to revise a knwoledge base K represented by a finite set of clauses by a new item of information A represented by another finite set of clauses. The revision method is the Removed Sets Revision which removes the minimal subsets of clauses from the initial knowledge base K, called removed sets, in order to restore consistency, while keeping the new information. We translated the Removed Sets Revision into a satisfiabily problem. We first apply a transformation on K, denoted by H(K), introducing for each clause of K, a new variable, called hypothesis variable, which acts as a clause selector. This transformation was initially proposed by De Kleer for ATMS. The Removed Sets Revision amounts to finding models of the union of H(K) and A which minimize the number of falsified hypothesis variable. In order to conduct an experimentation we used the solver MINISAT which won the 2003 competition for SAT solvers. We have experimented RSR with the MINISAT solver on the flooding problem; Removed Sets Revision and ROBDD (university of Toulon) This is detailed in Annex 34.2 Binary Decision Diagrams (BDD) are a compact and empirically efficient data structure for representing formulae in propositional logic. More precisely, BDDs allow a compact representation of the models of a formula. In the framework of the flooding application, we explored two possible uses of BDDs to achieve revision. The first approach, considering a K*A revision operation, we tried to encode all the knowledge of K and A into a single BDD, and then select suitable models of the revised knowledge. This approach appears to be intractable because of the huge data size. We recently developped a new approach which uses BDD. This approach relies on a semantic characterization of our revision operation, which leads to the building of three separate BDDs : one for the knowledge in K, one for the knowledge in A a a third BDD containing the preferece ordering on the knowledge which defines the revision strategy.this new approach have better partial results of complexity than the first one. REVIGIS Project IST Delivery R413 8/11

9 The theoretical model has been fully described, and now we start an experimental phase. This is a mandatory step when dealing with BDDs, as if the worst case complexity is still high, the mean case is too difficult to express theoretically, thus requiring an experimentation Revision in the STP formalism; (university of Provence) This is detailed in Annex 34.3 and in Annex 34.4 The Simple Temporal Problems formalism (STP), is based on linear constraints. We present a practical revision method based on STP resolution. Our revision method consists in the following steps: - The detection of conflicts: To detect the inconsistencies in an STP, we use an important result which stipulates that an STP is consistent if and only if its corresponding distance graph does not contain negative circuits. Thus, the detection of conflicts in an STP amounts to the detection of negative circuits in its graph of distance. To do this, we apply a modified version of the Floyd-Warshall algorithm (initially dedicated to computing the shortest paths in a graph). - Representation of detected conflicts as a graph, which we call the graph of conflicts. The vertices of this graph are the constraints involved in the conflicts and its edges represent the conflicts. - Identification of the smallest subsets of constraints whose the correction restores the consistency of the STP: amounts to the identification of minimal coverings (according to the cardinality) in the conflict graph. - Correction of the conflicting constraints identified in the previous step. The revision method presented in this section is implemented and tested on the Flooding problem Revision of partial pre-orders: algorithm and application to the uncertain constraints on location problem (SOMEI with university of Toulon and university of Artois, Lens) This detailed in Annex In R313 we proposed an algorithm for dealing with partially ordered constraints. We developped a system, mpropre to manage partially ordered constraints for building a construction. We have shown how to help an expert for finding the best place to build a house (condominium) in an urban area, according to several criteria both defined by city legislation and the property developer. These rules can sometimes be ordered by an expert according to their level of importance. Examples of rules are: 1. Field having a minimal area of m2; 2. Average field maximal slope of 6Â ; 3. Field situated at less than 2 kilometres of a commercial area; 4. Field situated at less than 150 meters from a fire hydrant. Usually, there is no parcel following all these rules. The expert can express its preference between some constraints but he can not always express a preference between all constraints: this leads to incomparablities. Despite this incomparablities, we are able to find the "best" REVIGIS Project IST Delivery R413 9/11

10 locations according to the constraints they satisfy or, dually, according to the constraints they falsify. For that, we need to build a preference relation between all the locations. We conducted an experimentation of our method on a data set on the city of Sherbrooke (Canada). For that, we have integrated mpropre to the commercial Geographic Information System Geomedia from Intergraph. We have considered 2782 parcels and 12 partially ordered constraints. The treatment was immediate and two parcels were chosen. An aerial snapshop confirm the properties of these parcels, what are the best we can find, according of the partial order on the constraints Synthesis of the REVIGIS project-task on Algorithms and Tractability issues (Univ. Provence, Univ. Keele, Univ. Toulon, Univ. Artois-Lens, SOMEI) This detailed in Annex In year 3, in the R313 report we begun a comparison on the different methods and algorithms for revision in the framework of GIS. We enriched this work by a comparative study of different knowledge representation formalisms as well as the corresponding translation of the revision problem. 2.3 References for this section : Please refer to the Annex R413-a1 or R413-a2 for this list of state-of-the-art references. 3 Prospective and future work Most of the work is, and will remain at an academic level. The first prospective step is to apply it in cooperation with application research institutes, such as Cemagref, CEH, etc. and possibly mapping agencies. Software publishers in GIS, and geographical applications are also concerned, at some regional SME in this domain, are invited to attend the review open meeting. The results obtained from the WP 1.3 could be of interest for applied research in the field of environmental science and for the companies that develop activities on GIS in the domain of environmental science, territory managment, and urban planning. 4 List of annexes Annex 34.1 "Révision d'une base de croyances dans le cadre de la programmation logique avec négation par échec : application à l'information géographique "J. Bennaim, DEA report, university of Toulon, june Annex 34.2 ``Revision par la méthode des r-ensembles et ROBDD''. Troisièmes Journées Nationales sur les Modèles de Raisonnement (JNMR'03). Proceedings of Journées sur le Raisonnement Non-Monotone(JNMR'03). Daniel Kayser, Pierre Marquis et Amadeo Napoli ed. pages Paris, novembre REVIGIS Project IST Delivery R413 10/11

11 Annex ``Révision de contraintes temporelles : application au problème de l'inondation.'', B. Benhamou, M. Khelfallah, R. Jeansoulin, Proceedings of of Journées sur le Raisonnement Non-Monotone(JNMR'03). Daniel Kayser, Pierre Marquis et Amadeo Napoli ed. pages Paris, novembre Annex ``Révision d'informations géographiques à base de contraintes temporelles'', B. Benhamou, M. Khelfallah, R. Jeansoulin, Proceedings of RFIA'2004 conference, Toulouse, january 2004 Annex 34.5 "Gestion d'informations partiellement ordonnées : raisonnement, revision et information géographique.", S. Lagrue, PhD Thesis, university of Toulon, december 2003 Annex `` Raisonner qualitativement avec des croyances partiellement ordonnées''. S, Benferhat, S. Lagrue, O. Papini, Proceedings of the conference Reconnaissance des Formes et Intelligence Artificielle (RFIA'04). p Toulouse. january 2004 Annex ``Answer set programming and revision: an application in the framework of GIS'' J. Bennaim, S. Benferhat, O. Papini, E. Wurbel. march 2004 Annex `` Revision in the framework of GIS : REV!GIS project a synthesis ''J. Bennaim, S, Benferhat, R. Jeansoulin, M. Khelfallah, S. Lagrue, O. Papini, N. Wilson, E. Wurbel. april 2004 Other publications : Full texts or Web links, etc. REVIGIS Project IST Delivery R413 11/11