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Event Calculus MultiAgent Planning Using an Abductive Event Calculus Christoph G Jung Klaus Fischer Alastair Burt Graduiertenkol legKognitionswissenschaftUniversitat des Saarlandes Acknowledgements Wewould like to thank Prof Dr Jorg Siekmann for sup ervising the development of the planning system that is describ ed in this rep ort We appreciate the work of Prof Dr Rob ert Kowalski and his group at the Imp erial College London They created the original formulation of the Event Calculus and were the rst to apply it to planning The immediate inspiration for our approach however has b een the work of Lo de Missiaen Maurice Bruyno oghe and Marc Denecker from the KU Leuven Besides their planning system CHICA they have also develop ed the foundations of SLDNFA the basic proof procedure used in our implementation EVE Further acknowledgements are due to the Programming Systems Lab of the DFKI GmbH and its head Prof Dr Gert Smolka for the design and the implemen tation of the wonderful Oz calculus the c onstraintbased implementation platform of EVE The group esp ecially Christian Schulte were always ready to give as sistance Without Christians backing and the discussions ab out constraintbased programming and encapsulatedsearch EVE would have never come to life and what would have Adam said to that Gero Vierke has b een a valuable help by pro ofreading this rep ort Christoph G Jung would also like to thank the Graduiertenkol leg Kognition swissenschaft at the Universitat des Saarlandes for their unique supp ort Contents Preface Intro duction Logic Planning EVEs Architecture Theory of Time and Action the Event Calculus Requirements The Situation Calculus The Event Calculus byKowalski Shanahan The Event Calculus by Missiaen The Simple Event Calculus of EVE The Extended Event Calculus of EVE Remarks Summary Theorem Proving with Ab duction SLDNFA Resolution SLD Negation As Failure SLDNF Constructive Negation SLDCNF SLDNF Ecient Negation in SLDNF Ab duction SLDA Negation and Ab duction SLDNFA SLDCNFA SLDNFA Remarks Summary The Event Calculus under SLDNFA Planning by Theorem Proving Plan Analysis and Evaluation Plan Synthesis and Mo dication Ab ductive Predicates and their Maintenance Treatment of Negations SLDRule Choice Points and Heuristics Execution of the Simple Event Calculus of EVE Execution of the Extended Event Calculus of EVE Summary SLDNFA by Constraint Logic Programming The Oz calculus Resolution in Oz Negation As Failure in Oz Constructive Negation in Oz Ab duction in Oz Remarks Summary The ConstraintBased Event Calculus MetaProgramming Heuristics Ob jectOriented Ab duction wledge Base Interface The default Ab ducibles and the Kno Summary Ob jectOriented Representation Representation of Prop erties The Planning Service Class EVE The Event Class UrEvent The Default Ab ducibles The Knowledge Base Ob ject Summary EVE in the MultiAgentBlocksworld Domain EVE in a MultiAgent System The InteRRaP Architecture EVE within the Lo cal Planning Layer EVE in the Loading Do ck Domain Summary Related Work Planning with a logical framework Situation CalculusBased Systems Planning using Temp oral Logics Event CalculusBased Systems Pro cedural Nonlinear Planning Plan Graph Analysis MultiAgent Planning Summary Future Research Planning in a MultiAgent Architecture Extensions to the Event Calculus Maintenance Events with Duration ContextDep endent Conditions Probability in Planning Sensing Actions Hierarchical Planning Generic Resources Heuristics Ab duction constraint logic programming Summary Conclusion A EVE Installation A Dep endencies and Compilation A A Counting Example A Summary B Axiomatisation of the MultiAgentBlockworld C Axiomatisation of the Loading Do ck Scenario List of Figures References Index Preface Since its early b eginnings Articial Intelligence research in the eld of planning has had to cop e with the frame problem The rst logicbased systems using the Situation Calculus showed that this theory of time and action has not b een able to solve the frame problem eciently b ecause at least in its original formulation it is restricted to a linear form of planning Later approaches however have shown that a theory originally designed for calculating database up dates and narrative understanding the Event Calculus is capable of improving on these disapp ointing results promising expressive nonlinear temp oral reasoning and thus nonlinear planning In this rep ort werstfocusontheclausebased evolution from the Situa tion Calculus to the Event Calculus and derive two axiomatisations of the Event Calculus that are suitable for nonlinear planning using a common action representation based around preconditions and postconditions Section The development is guided by the exploration of soundness and completeness issues with resp ect to strong nonlinear plans as solutions The theorem proof pro cedure Section that underlies the theories of time and action has to supply resolution and negation as failure in order to analyse and evaluate plans Plan synthesis and modication can be achieved through a formhypothetical reasoning intro duced by the abduction principle We therefore use a new pro of pro cedure SLDNFA derived from a description in that correctly merges the ab ove three inference techniques with an extension based on constructive negation Its completeness concentrates on a least commit ment class of hypotheses and solution substitutions with clause programs restricted to allowonly nite domain variables within negated goals The main problems that this algorithm is mainly faced with include the high interference b etween nonmonotonic negation and ab duction In addition we demonstrate howtoimprove the treatment of negation in SLDNFA for most calculi so that the nite domain requirement can be dropp ed This holds in particular for pro ofs with the axiomatisations of Event Calculus we use We investigate this matter closely with resp ect to the capabilities of SLDNFA in Section Based on the implementation platform Oz ahigherorder constraintbased programming language oering many features suchasconcurrency abstraction en capsulatedsearch and object orientationweshowhow to realize the SLDNFA pro cedure by syntactical transformation functions Section that turn clausebased programs into constraints The selection rule is hereby handed out to the reduc tion strategy of Oz and is can b e inuenced by many constructs of the language Treatment of disjunctive choicepoints dep ends on the driver pro cedure that guides the encapsulated search pro cess Again transformation techniques that guide the dynamic creation of choice p oints from within the computation spaces giveusthe power to implement dierent heuristics We exemplary show such a mechanism within the abduction step A discussion of some sp ecial issues of our implementation EVE follows in Sections and EVE represents a generic planning mo dule written in Oz that can b e used in varietyofArticialIntelligence architectures Ob jectoriented techniques help to mo del the necessary concepts in planning and furthermore provide com fortable extensions like objectorientedabduction and an improved constraintbased t embedding of translation of the Event Calculus Furthermore the concurren the temp oral reasoning pro cess is investigated After a rst evaluation of the EVE system in the multiagentblocksworld do main Section we explore its prototypical application within the agent archi tecture InteRRaP Section Multiagent systems
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