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Extensions of Constraint Solving for Proof Planning
 In European Conference on Artificial Intelligence
, 1999
"... The integration of constraint solvers into proof planning has pushed the problem solving horizon. Proof planning benefits from the general functionalities of a constraint solver such as consistency check, constraint inference, as well as the search for instantiations. However, offtheshelf constrai ..."
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Cited by 7 (6 self)
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The integration of constraint solvers into proof planning has pushed the problem solving horizon. Proof planning benefits from the general functionalities of a constraint solver such as consistency check, constraint inference, as well as the search for instantiations. However, offtheshelf constraint solvers need to be extended in order to be be integrated appropriately: In particular, for correctness, the context of constraints and Eigenvariableconditions have to be taken into account. Moreover, symbolic and numeric constraint inference are combined. This paper discusses the extensions to constraint solving for proof planning, namely the combination of symbolic and numeric inference, firstclass constraints, and context trees. We also describe the implementation of these extensions in the constraint solver CoSIE.
Nontrivial Symbolic Computations in Proof Planning
 In Proc. of FroCoS 2000, LNCS 1794
, 2000
"... We discuss a pragmatic approach to integrate computer algebra into proof planning. It is based on the idea to separate computation and verification and can thereby exploit the fact that many elaborate symbolic computations are trivially checked. In proof planning the separation is realized by using ..."
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Cited by 6 (3 self)
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We discuss a pragmatic approach to integrate computer algebra into proof planning. It is based on the idea to separate computation and verification and can thereby exploit the fact that many elaborate symbolic computations are trivially checked. In proof planning the separation is realized by using a powerful computer algebra system during the planning process to do nontrivial symbolic computations. Results of these computations are checked during the refinement of a proof plan to a calculus level proof using a small, selfimplemented, system that gives us protocol information on its calculation. This protocol can be easily expanded into a checkable lowlevel calculus proof ensuring the correctness of the computation. We demonstrate our approach with the concrete implementation in the Omega system.
Integrating Constraint Solving into Proof Planning
, 2000
"... In proof planning mathematical objects with theoryspecific properties have to be constructed. More often than not, mere uni cation oers little support for this task. However, the integration of constraint solvers into proof planning can sometimes help solving this problem. We present ..."
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Cited by 5 (3 self)
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In proof planning mathematical objects with theoryspecific properties have to be constructed. More often than not, mere uni cation oers little support for this task. However, the integration of constraint solvers into proof planning can sometimes help solving this problem. We present
Main Research Contributions
"... of calculuslevel proof steps, i.e. a large step, and thus relieves the user from applying too many single inference rules in a row. The overall motivation of the work in proof planning and theorem proving by analogy has been the disappointment with the results in traditional ATP that caused the \Om ..."
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of calculuslevel proof steps, i.e. a large step, and thus relieves the user from applying too many single inference rules in a row. The overall motivation of the work in proof planning and theorem proving by analogy has been the disappointment with the results in traditional ATP that caused the \Omega mega group as well as others to develop another vision for automated theorem proving. Proof planning was originally conceived as a mere extension of tactical theorem proving [2]. The idea is as follows: Plan operators, called methods, are created from tactics by adding specifications: preconditions, postconditions, and application conditions. Proof planning searches for a plan, i.e., for a sequence of methods, where the precondition of a method matches the postcondition of its predecessor in that sequence. 2 KnowledgeBased Proof Planning Problems The first proof planner, CL A M [3], was designed to prove theorems