Download Failure Reasoning in Multiple-Strategy Proof Planning Erica Melis joint work with Andreas Meier

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