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An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
An Ontological Formalization Of The Planning Task
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An Ontological Formalization Of The Planning Task

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An Ontological Formalization Of The Planning Task

An Ontological Formalization Of The Planning Task

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  • 1. An Ontological Formalization of the Planning Task Dnyanesh Rajpathak and Enrico Motta Knowledge Media Institute, The Open University, Walton Hall, Milton Keynes, UK. {d.g.rajpathak, e.motta}@open.ac.uk
  • 2. Goals of the Research <ul><li>Analytical Objective: </li></ul><ul><ul><li>To provide a precise and comprehensive formalization of the space of planning problems, independently of any application domain or reasoning method; </li></ul></ul><ul><li>Engineering Objective: </li></ul><ul><ul><li>To provide a practical and operational model to support knowledge acquisition for planning problems. </li></ul></ul>
  • 3. Limitations of Existing Proposals <ul><li>A number of formalizations of the planning problem have been proposed…. </li></ul><ul><li>However: </li></ul><ul><ul><li>Analysis tends to be coarse-grained </li></ul></ul><ul><ul><ul><li>e.g., see [Valente, 1999] ; </li></ul></ul></ul><ul><ul><li>Analysis tends to be paradigm-specific </li></ul></ul><ul><ul><ul><li>e.g., see [Valente, 1999; Tate, 1994] ; </li></ul></ul></ul><ul><ul><ul><li>Only exception is work from [Gil and Blythe, 2000]; </li></ul></ul></ul><ul><ul><li>Important concepts are either missing or underspecified e.g., see [Gil and Blythe, 2000, Tate, 1994] ; </li></ul></ul><ul><ul><li>Optimality issues are not taken into account </li></ul></ul><ul><ul><ul><li>e.g., see [Valente, 1999; Tate, 1999] . </li></ul></ul></ul>
  • 4. Key Features of our Approach <ul><li>Formal analysis of the space of planning problems using ontologies; </li></ul><ul><li>Based on Task-Method-Domain-Application framework (Motta, 1999) </li></ul><ul><ul><li>Part of on-going research on knowledge modelling </li></ul></ul><ul><ul><ul><li>Follows work on Parametric design, classification, and scheduling </li></ul></ul></ul>
  • 5. Epistemological Framework <ul><li>Task-Method-Domain-Application </li></ul><ul><ul><li>Key ingredients: Ontologies and PSMs </li></ul></ul>PSMs E.g. Propose &amp; Revise Domains E.g. Rover, Satellite, etc. Applications Solving Rover Planning by applying P&amp;R Generic Problem Types Planning Task Planning Task Ontology
  • 6. Key Features Cont. <ul><li>Use of Ontology Projection approach </li></ul><ul><ul><li>(Borst &amp; Akkermans, 1997) </li></ul></ul><ul><li>Fine-grained and comprehensive analysis of planning concepts, relations, and axioms; </li></ul><ul><li>Abstracts from key paradigms: </li></ul><ul><ul><li>Classical Planning (Fikes and Nilson, 1971) </li></ul></ul><ul><ul><li>Decision Theoretic Planning (Blythe, 1999) </li></ul></ul><ul><ul><li>Hierarchical Task Network (Erol et al., 1994) </li></ul></ul><ul><li>Tackles also optimality issues. </li></ul>
  • 7. Ontology Projection <ul><li>3 types of Ontology Projections are considered based on Borst and Akkerman’s (1997) work on Engineering Ontologies: </li></ul><ul><ul><li>Include and Extend: an imported ontology is extended with new concepts and relations; </li></ul></ul><ul><ul><li>Include and Specialise: imported concepts are specialised according to relevant domain knowledge; </li></ul></ul><ul><ul><li>Include and Project: different viewpoints are joined together. </li></ul></ul><ul><li>Why?.... </li></ul><ul><ul><li>Provides ‘broad and stable’ coverage to conceptual distinctions over various viewpoints; </li></ul></ul><ul><ul><li>The result is an individual new ontology. </li></ul></ul>
  • 8. Ontology Inclusion Hierarchy Planning Task Ontology Scheduling Task Ontology Simple Time Ontology Parametric Design Task Ontology Base Ontology Ontology Projection PLANET Plan Ontology (Tate) Valente’s Knowledge-Level Analysis Individual Ontology Legend
  • 9. Case 1 - Ontology Projection of Plan Ontology Original viewpoint: Agent Activity (Plan-Task) Action Time Issue Variable constraint Auxiliary constraint Preference Documentation and Annotation. <ul><li>Include and Extend </li></ul><ul><li>Initial state </li></ul><ul><li>Goal state </li></ul><ul><li>Cost function </li></ul><ul><li>Parameters </li></ul><ul><li>Axioms </li></ul><ul><li>Include and Project </li></ul><ul><li>Heterogeneous constraints are merged into a first-class concept, “constraint” ; </li></ul><ul><li>Preferences are associated with a cost function; </li></ul><ul><li>Documentation and annotation is excluded as it’s not part of ontology; </li></ul><ul><li>Notion of Issue is excluded; </li></ul><ul><li>Auxiliary constraints are modelled as Ordering Relations . </li></ul><ul><li>Include and Specialise </li></ul><ul><li>Agent is given a specific availability period; </li></ul><ul><li>Explicit relationship between plan-task and agent and vice versa; </li></ul><ul><li>Fine-grained representation of Activity Time Range ; </li></ul><ul><li>Activity duration is taken into account. </li></ul>
  • 10. &nbsp;
  • 11. Informal IO Spec of the Planning Task Solution-Plan Solution-Plan = {…&lt;Pt i . Agi&gt;…} Initial-World-State Goal-State Plan Tasks Actions Agents Parameters Time-Horizon Constraints Preferences Cost-Function Solution-Criterion Planning Task
  • 12. Initial and Goal State <ul><li>Initial state: planning world at the beginning of the planning process; </li></ul><ul><li>Goal state: a desired state of the world to be achieved through the planning process. </li></ul>A B Earth Initial State Goal State KMI Martian surface A B
  • 13. Plan Task <ul><li>Plan task: intermediate goals to be accomplished to achieve the final goal; </li></ul><ul><li>Parameters: meta-level pointers to the domain entities; </li></ul><ul><li>Pre and Post condition: what must be true before and after executing a plan task; </li></ul><ul><li>Actions: events to be achieved to accomplish a plan task; </li></ul><ul><li>Agents: required to achieve a plan-task; </li></ul><ul><li>Time-Range: a time-window </li></ul><ul><li>within which a plan-task takes place. </li></ul>Plan Task Parameters Precondition Postcondition Actions Agents Time-Range
  • 14. Agent <ul><li>Agent: a person, group, or an entity that holds a purpose to execute a plan-task; </li></ul><ul><li>Purpose: states cognitive attitude of an agent, e.g. physical entity or another agent (cf. SUMO (Niles and Pease, 2001) ); </li></ul><ul><li>Time-window: a time slot within which an agent accomplishes a plan-task. </li></ul>Agent Executes plan task Holds purpose Time window
  • 15. Constraints <ul><li>Constraints define a set of properties that must not be violated by a plan </li></ul><ul><ul><li>Typical constraints are ordering , variable binding , auxiliary , and interval preservation [Tate, 1996] ; </li></ul></ul><ul><li>In contrast with I-N-OVA [Tate, 1996] , our framework does not limit plan validation only to specific types of constraints; </li></ul><ul><li>Social and Cognitive constraints: </li></ul><ul><ul><li>Properties that are external to the core planning world. </li></ul></ul>
  • 16. Preferences and Optimization Criterion <ul><li>Preferences are a set of criteria to partially rank the competing plans necessary to model plan optimization criterion; </li></ul><ul><li>Plan optimization is handled by Preferences and Cost Function ; </li></ul><ul><li>Task ontology includes 2 axioms: </li></ul><ul><ul><li>Cost-Subsumes-Preferences </li></ul></ul><ul><ul><li>Cost-Preference-Consistency . </li></ul></ul>
  • 17. Axioms <ul><li>Plan-Task-Ordering-Maintains-Pre&amp;Post-Condition: </li></ul><ul><ul><li>If two plan-tasks, say Pt 1 and Pt 2 , are constrained by the ordering relation ( Follows (Pt 2 Pt 1 ) ), then the precondition of Pt 2 must hold after executing Pt 1 ; </li></ul></ul><ul><li>Plan-Maintains-Complete-Exclusion: </li></ul><ul><ul><li>No two plan-tasks can occur at the same time if they are consuming the same agent; </li></ul></ul><ul><li>Condition-Consistency-Among-Plan-Task-And-Action: </li></ul><ul><ul><li>For a plan-task, say Pt i , which has a sequence of actions {A i1 , …, A in }, then the precondition of Pt i must hold by the first action A i1 and postcondition of Pt i must hold after executing A in . </li></ul></ul>
  • 18. Coarse Grained View of Task Ontology PLANNING-TASK PLAN-TASK ACTION AGENT CONSTRAINT PREFERENCE COST FUNCTION TIME RANGE PARAMETER PLAN COST Plan-Task Agent PLAN-DESCRIPTION Plan-Is-Complete Plan-Is-Valid Agent-Executes-Plan-Task Plan-Task-Is-Achieved PLAN INITIAL STATE GOAL STATE Plan-Task-Has-Agent Plan-Task-Is-Unachieved Domain Range
  • 19. Conclusion &amp; Future Research <ul><li>Version 1 of the planning task ontology is completed; </li></ul><ul><li>Formal, fine-grained, comprehensive and generic characterization of the space of planning problems; </li></ul><ul><li>Evaluation of the TO is under way </li></ul><ul><ul><li>http://planning.cis.strath.ac.uk/competition/ </li></ul></ul><ul><li>TO will be used as the basis to develop library of planning problem-solvers. </li></ul>
  • 20. &nbsp;

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