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Failure Reasoning in Multiple-Strategy Proof Planning Erica Melis joint work with Andreas Meier German Research Center for Artificial Intelligence (DFKI) Source: Meier&Melis ARW Edinburgh Multi-Strategy Proof Planning [Meier-PhD] - Proof planning - methods - method-level control - Mutli-strategy proof planning - new hierarchical level of strategies - refinement and modification algorithms - Including various reasoners as strategies - (declarative) strategic control Source: Meier&Melis ARW Edinburgh Failure Reasoning in Multi-Strategy PP - Impasse => modification needed => choice of strategy - Symptom patterns => choice of alternative strategy – failure analysis by reasoning at strategy level – flexible choice among alternative strategies IF desirable(M) AND match-residuum(M,r) THEN speculate(r) IF desirable(Inst) AND notDeterminedInstance(v) THEN re-open constraintGoals(v) Source: Meier&Melis ARW Edinburgh Results • Reasoning and Implementation for – case-split introductions – lemma speculations – object construction – backtrackings • Experiments + considerably more problems solvable - potentially larger search space Examples + Comparison to related work => poster Source: Meier&Melis ARW Edinburgh Motivation • Failure Reasoning in Mathematics: – important ingredient of problem solving [Schoenfeld] – failure can hold key to discover a solution • Failure Reasoning in Automated Theorem Proving: requires - reasoning about failed attempts - alternative reactions to failures - flexible control of alternatives Source: Meier&Melis ARW Edinburgh