1. CSE-291: Ontologies in Data & Process Integration Department of Computer Science & Engineering University of California, San Diego CSE-291: Ontologies in Data and Process Integration Spring 2004 Bertram Ludäscher LUDAESCH@SDSC.EDU

2. CSE-291: Ontologies in Data & Process Integration A riddle … This thing all things devours: Birds, beasts, trees, flowers; Gnaws iron, bits steel; Grinds hard stones to meal; Slays king, ruins town, And beats high mountains down. J. R. R. Tolkien, The Hobbit

3. CSE-291: Ontologies in Data & Process Integration Time! Ticking away the moments that make up the dull day You fritter and waste the hours in an off hand way Kicking around on a piece of ground in your home town Waiting for someone or something to show you the way Tired of lying in the sunshine staying home to watch the rain You are young and life is long and there is time to kill today And then one day you find that ten years have got behind you No one told you when to run, you missed the starting gun And you run and run to catch up with the sun, but it's sinking And racing around to come up behind you again The sun is the same in a relative way, but you're older Shorter of breath and one day closer to death Every year is getting shorter, never seem to find the time Plans that either come to naught or a half page of scribbled lines Hanging on in a quiet desperation is the English way The time is gone the song is over, thought I'd something more to say

4. CSE-291: Ontologies in Data & Process Integration Outline Temporal Databases and StatelogTemporal Databases and Statelog Introduction to Modal LogicIntroduction to Modal Logic –[Modal Logic, James Garson, Stanford Encyclopedia of Philosophy] Introduction to Temporal LogicIntroduction to Temporal Logic –[Temporal Logic, Antony Galton, Stanford Encyclopedia of Philosophy]

5. CSE-291: Ontologies in Data & Process Integration Active Databases: Events, Conditions, Actions

6. CSE-291: Ontologies in Data & Process Integration Event-Condition-Action (ECA) Rules

7. CSE-291: Ontologies in Data & Process Integration Example

8. Events

9. Primitive Events

10. CSE-291: Ontologies in Data & Process Integration Composite/Complex Events

11. CSE-291: Ontologies in Data & Process Integration Event Consumption Modes

12. CSE-291: Ontologies in Data & Process Integration Conditions

13. Actions

14. Example using Logic Rules

15. CSE-291: Ontologies in Data & Process Integration Basic Statelog Execution Model

16. CSE-291: Ontologies in Data & Process Integration Statelog Syntax

17. CSE-291: Ontologies in Data & Process Integration Reified Syntax

18. CSE-291: Ontologies in Data & Process Integration First-Order Predicate Logic: Semantics

19. CSE-291: Ontologies in Data & Process Integration Statelog Semantics

20. CSE-291: Ontologies in Data & Process Integration Statelog Semantics

21. CSE-291: Ontologies in Data & Process Integration Temporal Semantics

22. CSE-291: Ontologies in Data & Process Integration Statelog Rules in Temporal Logic

23. CSE-291: Ontologies in Data & Process Integration Refined Execution Model With this: Programming change and reasoning about.. Termination Expressiveness complexity

24. CSE-291: Ontologies in Data & Process Integration Application Examples

25. CSE-291: Ontologies in Data & Process Integration Modal Logic Modal:Modal: –expressions (like ‘necessarily’ or ‘possibly’) to qualify the truth of a judgement Modal logic:Modal logic: –study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that’ –a family of logics for belief, for tense and other temporal expressions, for the deontic (moral) expressions such as ‘it is obligatory that’ and ‘it is permitted that’, … –Use: for formal analysis of philosophical argument, where expressions from the modal family are both common and confusing

26. CSE-291: Ontologies in Data & Process Integration What is Modal Logic?

27. CSE-291: Ontologies in Data & Process Integration Possible World Semantics Def. Kripke Frame (G, R)Def. Kripke Frame (G, R) –Set of possible worlds G –Binary Accessibility Relation R Propositional Kripke Structure K = (G, R, v)Propositional Kripke Structure K = (G, R, v) –v is a valuation function v: P x G  {True, False} –… mapping each proposition p (= 0-ary predicate) in P to either True or False, depending on the world g in G

28. CSE-291: Ontologies in Data & Process Integration Formula Evaluation in Kripke Structures iff v(g,p) = true iff g |= F and g |= H iff g |= F or g |= H iff (not g |= F) or g |= H iff not g |= F iff for all h s.t. R(g,h): h |= F iff for some h s.t. R(g,h): h |= F Given Kripke Structure K = (G, R, v), define

29. CSE-291: Ontologies in Data & Process Integration Correspondence Theory for Propositional Modal Logic Linking the structure of R to valid formulas: Properties of R characterizing axioms

30. CSE-291: Ontologies in Data & Process Integration Modal Logic Primer Modal Logic Stanford Encyclopedia of Philosophy James Garson http://plato.stanford.edu/entries/logic-modal/

31. CSE-291: Ontologies in Data & Process Integration Temporal Logic Primer Temporal Logic Stanford Encyclopedia of Philosophy Antony Galton http://plato.stanford.edu/entries/logic-temporal/