Finding Similar or Diverse Solutions in Answer Set Programming

For many computational problems, the main concern is to find a best solution (e.g., a most preferred product configuration, a shortest plan, a most parsimonious phylogeny) with respect to some well-described criteria. On the other hand, in many real-world applications, computing a subset of good solutions that are similar/diverse may be desirable for better decision-making. For one reason, the given computational problem may have too many good solutions, and the user may want to examine only a few of them to pick one; in such cases, finding a few similar/diverse good solutions may be useful. Also, in many real-world applications the users usually take into account further criteria that are not included in the formulation of the optimization problem; in such cases, finding a few good solutions that are close to or distant from a particular set of solutions may be useful. With this motivation, we have studied various computational problems related to finding similar/diverse (resp. close/distant) solutions with respect to a given distance function, in the context of Answer Set Programming (ASP). We have introduced novel offline/online computational methods in ASP to solve such computational problems. We have modified an ASP solver according to one of our online methods, providing a useful tool (CLASP-NK) for various ASP applications. We have showed the applicability and effectiveness of our methods/tools in three domains: phylogeny reconstruction, AI planning, and biomedical query answering. Motivated by the promising results, we have developed computational tools to be used by the experts in these areas.

[1]  Vladimir Lifschitz,et al.  Thirteen Definitions of a Stable Model , 2010, Fields of Logic and Computation.

[2]  Martin Gebser,et al.  Conflict-Driven Answer Set Solving , 2007, IJCAI.

[3]  Bart Selman,et al.  Planning as Satisfiability , 1992, ECAI.

[4]  Eugene Goldberg,et al.  BerkMin: A Fast and Robust Sat-Solver , 2002, Discret. Appl. Math..

[5]  Esra Erdem,et al.  Comparing ASP, CP, ILP on two challenging applications: wire routing and haplotype inference , 2008 .

[6]  Martin Gebser,et al.  clasp : A Conflict-Driven Answer Set Solver , 2007, LPNMR.

[7]  Victor W. Marek,et al.  On the expressibility of stable logic programming , 2001, Theory and Practice of Logic Programming.

[8]  Esra Erdem,et al.  Theory and applications of answer set programming , 2002 .

[9]  Joao Marques-Silva,et al.  GRASP: A Search Algorithm for Propositional Satisfiability , 1999, IEEE Trans. Computers.

[10]  Timo Soininen,et al.  Extending and implementing the stable model semantics , 2000, Artif. Intell..

[11]  Esra Erdem,et al.  Inferring Phylogenetic Trees Using Answer Set Programming , 2007, Journal of Automated Reasoning.

[12]  W. Gilks,et al.  A novel algorithm and web-based tool for comparing two alternative phylogenetic trees , 2006, Bioinform..

[13]  Ming-Yang Kao,et al.  Improved Phylogeny Comparisons: Non-shared Edges, Nearest Neighbor Interchanges, and Subtree Transfers , 2000, ISAAC.

[14]  Vladimir Lifschitz,et al.  Action Languages, Answer Sets, and Planning , 1999, The Logic Programming Paradigm.

[15]  Jonathan L. Gross,et al.  Handbook of graph theory , 2007, Discrete mathematics and its applications.

[16]  Subbarao Kambhampati,et al.  Domain Independent Approaches for Finding Diverse Plans , 2007, IJCAI.

[17]  Esra Erdem,et al.  PHYLO-ASP: Phylogenetic Systematics with Answer Set Programming , 2009, LPNMR.

[18]  Daniel R. Brooks,et al.  The Phylogenetic Perspective. (Book Reviews: Phylogeny, Ecology, and Behavior. A Research Program in Comparative Biology.) , 1991 .

[19]  Richard W. Hamming,et al.  Error detecting and error correcting codes , 1950 .

[20]  Vladimir Lifschitz,et al.  Nested expressions in logic programs , 1999, Annals of Mathematics and Artificial Intelligence.

[21]  V. S. Subrahmanian,et al.  Heterogeneous Active Agents, II: Algorithms and Complexity , 1999, Artif. Intell..

[22]  Vineet Bafna,et al.  Sorting by Transpositions , 1998, SIAM J. Discret. Math..

[23]  Esra Erdem,et al.  Bridging the Gap between High-Level Reasoning and Low-Level Control , 2009, LPNMR.

[24]  D. Robinson,et al.  Comparison of phylogenetic trees , 1981 .

[25]  Martin D. F. Wong,et al.  Rectilinear Steiner Tree Construction Using Answer Set Programming , 2004, ICLP.

[26]  Dong-Guk Shin,et al.  Nodal distance algorithm: calculating a phylogenetic tree comparison metric , 2003, Third IEEE Symposium on Bioinformatics and Bioengineering, 2003. Proceedings..

[27]  B. Dasgupta,et al.  On distances between phylogenetic trees , 1997, SODA '97.

[28]  Esra Erdem,et al.  Temporal phylogenetic networks and logic programming , 2005, Theory and Practice of Logic Programming.

[29]  E. N. Adams.  Consensus Techniques and the Comparison of Taxonomic Trees , 1972 .

[30]  James F. O'Connell,et al.  A prehistory of Australia, New Guinea, and Sahul , 1982 .

[31]  R. Sokal,et al.  A METHOD FOR DEDUCING BRANCHING SEQUENCES IN PHYLOGENY , 1965 .

[32]  Esra Erdem,et al.  Character-Based Cladistics and Answer Set Programming , 2005, PADL.

[33]  Ivan Serina,et al.  Planning Through Stochastic Local Search and Temporal Action Graphs in LPG , 2003, J. Artif. Intell. Res..

[34]  Subbarao Kambhampati,et al.  Planning as constraint satisfaction: Solving the planning graph by compiling it into CSP , 2001, Artif. Intell..

[35]  Pierre Marquis,et al.  DISTANCE-SAT: Complexity and Algorithms , 1999, AAAI/IAAI.

[36]  R. Thorne,et al.  Phenetic and Phylogenetic Classification , 1964, Nature.

[37]  Zhi-Zhong Chen,et al.  The complexity of selecting maximal solutions , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.

[38]  Vladimir Lifschitz,et al.  Weight constraints as nested expressions , 2003, Theory and Practice of Logic Programming.

[39]  Olivier Bodenreider,et al.  A preliminary report on answering complex queries related to drug discovery using answer set programming , 2008 .

[40]  Victor W. Marek,et al.  The Logic Programming Paradigm: A 25-Year Perspective , 2011 .

[41]  Barry O'Sullivan,et al.  Finding Diverse and Similar Solutions in Constraint Programming , 2005, AAAI.

[42]  Ilkka Niemelä,et al.  Developing a Declarative Rule Language for Applications in Product Configuration , 1999, PADL.

[43]  Chiaki Sakama,et al.  Logic Programming for Multiagent Planning with Negotiation , 2009, ICLP.

[44]  Koustuv Dasgupta,et al.  Adaptation inWeb Service Composition and Execution , 2006, 2006 IEEE International Conference on Web Services (ICWS'06).

[45]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[46]  Tandy Warnow,et al.  Indo‐European and Computational Cladistics , 2002 .

[47]  Tran Cao Son,et al.  Adapting Golog for Composition of Semantic Web Services , 2002, KR.

[48]  Barry O'Sullivan,et al.  Distance Constraints in Constraint Satisfaction , 2007, IJCAI.

[49]  Charles Semple,et al.  A supertree method for rooted trees , 2000, Discret. Appl. Math..

[50]  Michael Gelfond,et al.  Classical negation in logic programs and disjunctive databases , 1991, New Generation Computing.