Brief Overview of Research October 10, 2001 Debasis Mitra Florida Institute of Technology

1. Brief Overview of Research October 10, 2001 Debasis Mitra Florida Institute of Technology

2. Mutiple directions • => Theoretical thrusts • Application plans / works • Experimental plans /works

3. Reasoning Problem Input: B {Northeast | Southwest} A, C {South} B, D {North, East, Northeast} A, C {South, Southeast, East, Northwest} A Question: (1) Are they consistent?, (2) Find one/all consistent solution Representation: A D B C

4. Star Ontology

6. Some Observations  basic relations r and l, (1) r.r = r (2) r,r = r.r = either T, when r is a two dimensional region, or {r, 0, r-inverse}, when r is one-dimensional region, with ris the inverse of r (3) r.l = l.r (commutative) (4) r.l = inverse(r. l), where inverse of a set comprises of inverse of the elements in the original set

7. Star Ontology-6 (Tasks) • Develop Composition table • Study symmetries in the composition table (e.g., a.a =a) • Complexity of consistency checking (NP-hard for sure!) • Find maximal tractable algebra (by observing symmetries) • Develop domain-theoretic algorithms (geometrical algorithms as opposed to algebraic algorithms with the axiomatic Composition-table) • Write papers!!!

8. Generalized Star Ontology-Alpha • Space divided with 360/alpha, for some integer alpha, starting with ‘East’ • Previous one was star-ontology(6), Cardinal ontology was star ontology(4) • For odd alpha there is no algebra! • All previous questions revisited

9. Generalized Spatio-temporal reasoning • An ontology-independent framework: • Basic relations w.r.t. a reference object (B) • Connectivity/topology of the basic relations (a qualitative space) • Property of the basic relations (e.g., dimensionality) • What criteria determines complexity (NP-hardness vs tractability) • Domain-theoretic study, algorithms (geometrical) • Specialize to known+unknown ontologies (benefit to applications)

10. A Qualitative space

11. Uncertainty-based Spatio-temporal reasoning With Peter Haddawy, U of Wisconsin. Millwaukee: Preference structure elicitation for user modeling (e-commerce), using Knowledge-based ANN, extend KBANN with STR

12. Application Plans / Works • Robotics (Swedish support from UAV project??): • Direction-interval algebra of Renz • Star algebra(alpha) • Occlusion algebra (Qualitative algebra for objects hiding behind each other) • Bio-informatics: (1) identify qualitative reasoning problems and (2) find out the underlying ontologies • “Geometrical modeling” and qualitative reasoning!! Computer and arts: Picasso/cartoon

13. Experimental Plans / Works: Background • Big-Oh notation is a big hoax!! (Sorry) • It only provides a very vague (agreed – genuine) idea on a problem’s inherent complexity wrt some canonical parameter (‘size’) • Number of problem instances is infinite, problems have more complex structures than just one parameter (wake up computer “scientists”) • We need to do statistical study, identify structures, develop more stochastic algorithms (which are ‘hot’ algorithms? which areas are succeeding most?)

14. Experimental Plans / Works • Phase transitions: e.g., Hamiltonian Ckt problem is hardest at ~4.5 arcs/node, 3-SAT is hardest at 4.3 literals per clause • Studied Allen’s algorithm, identified some problem structures using stat-tools (significance studies) • Study star algebra empirically • Develop stochastic algorithms for the generalized algebra

15. Class-project level to Ph.D. level problems • N-Queens “hybrid” algorithm: implementation, generalize to other CSP areas • Island-based search algorithm: a “practical” add-on heuristic, implement • Multi-dimensional datamodel for numerical data: theoretical study + implement • Deploy AI planning for Component-oriented programming • Visualize spatio-temporal information: [HisViz, Spying-info, etc.]  [Backend database issue, Reasoning algorithms and Data structures issue, GUI issue, etc.]