Failure Reasoning in Multiple-Strategy Proof Planning

1
Failure Reasoning in Multiple-Strategy Proof
Planning

• Erica Melis
• joint work with Andreas Meier
• German Research Center for Artificial
  Intelligence (DFKI)

2
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

3
Failure Reasoning in Multi-Strategy PP

• Impasse gt modification needed gt choice of
  strategy
• Symptom patterns gt 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)

4
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 gt poster

5
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