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Proof Planning
 PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON AI PLANNING SYSTEMS, (AIPS
, 1996
"... We describe proof planning, a technique for the global control of search in automatic theorem proving. A proof plan captures the common patterns of reasoning in a family of similar proofs and is used to guide the search for new proofs in this family. Proof plans are very similar to the plans cons ..."
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Cited by 24 (2 self)
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We describe proof planning, a technique for the global control of search in automatic theorem proving. A proof plan captures the common patterns of reasoning in a family of similar proofs and is used to guide the search for new proofs in this family. Proof plans are very similar to the plans constructed by plan formation techniques. Some differences are the nonpersistence of objects in the mathematical domain, the absence of goal interaction in mathematics, the high degree of generality of proof plans, the use of a metalogic to describe preconditions in proof planning and the use of annotations in formulae to guide search.
A Constraintbased Partial Evaluator for Functional Logic Programs and its Application
, 1998
"... The aim of this work is the development and application of a partial evaluation procedure for rewritingbased functional logic programs. Functional logic programming languages unite the two main declarative programming paradigms. The rewritingbased computational model extends traditional functional ..."
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Cited by 12 (0 self)
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The aim of this work is the development and application of a partial evaluation procedure for rewritingbased functional logic programs. Functional logic programming languages unite the two main declarative programming paradigms. The rewritingbased computational model extends traditional functional programming languages by incorporating logical features, including logical variables and builtin search, into its framework. This work is the first to address the automatic specialisation of these functional logic programs. In particular, a theoretical framework for the partial evaluation of rewritingbased functional logic programs is defined and its correctness is established. Then, an algorithm is formalised which incorporates the theoretical framework for the procedure in a fully automatic technique. Constraint solving is used to represent additional information about the terms encountered during the transformation in order to improve the efficiency and size of the residual programs. ...
Proof planning for firstorder temporal logic
 In proceedings of CADE, 20th International Conference on Automated Deduction
, 2005
"... Abstract. Proof planning is an automated reasoning technique which improves proof search by raising it to a metalevel. In this paper we apply proof planning to FirstOrder Linear Temporal Logic (FOLTL), which can be seen as a quantified version of Linear Temporal Logic, overcoming its finitary limi ..."
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Cited by 4 (3 self)
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Abstract. Proof planning is an automated reasoning technique which improves proof search by raising it to a metalevel. In this paper we apply proof planning to FirstOrder Linear Temporal Logic (FOLTL), which can be seen as a quantified version of Linear Temporal Logic, overcoming its finitary limitation. Automated reasoning in FOLTL is hard, since it is nonrecursively enumerable; but its expressiveness can be exploited to precisely model the behaviour of complex, infinitestate systems. In order to demonstrate the potentiality of our technique, we introduce a casestudy inspired by the Feature Interactions problem and we model it in FOLTL; we then describe a set of methods which tackle and solve the validation problem for a number of properties of the model; and lastly we present a set of experimental results showing that the methods we propose capture the common patterns in the proofs presented, guide the search at the object level and let the overall system build large and highly structured proofs. This paper to some extent improves over previous work that showed how proof planning can be used to detect such interactions. 1
ModelGuided Proof Planning
, 2002
"... Proof planning is a form of theorem proving in which the proving procedure is viewed as a planning process. The plan operators in proof planning are called methods. In this paper we propose a strategy for heuristically restricting the set of methods to be applied in proof search. It is based on the ..."
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Cited by 3 (3 self)
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Proof planning is a form of theorem proving in which the proving procedure is viewed as a planning process. The plan operators in proof planning are called methods. In this paper we propose a strategy for heuristically restricting the set of methods to be applied in proof search. It is based on the idea that the plausibility of a method can be estimated by comparing the model class of proof lines newly generated by the method with that of the assumptions and of the theorem. For instance, in forward reasoning when a method produces a new assumption whose model class is not a superset of the model class of the given premises, the method will lead to a situation which is semantically not justified and will not lead to a valid proof in later stages. A semantic restriction strategy is to reduce the search space by excluding methods whose application results in a semantic mismatch. A semantic selection strategy heuristically chooses the method that is likely to make most progress towards filling the gap between the assumptions and the theorem. Each candidate method is evaluated with respect to the subset and superset relation with the given premises. All models considered are taken from a finite reference subset of the full model class. In this contribution we present the modelguided approach as well as first experiments with it.
Chapter 1 MODELGUIDED PROOF PLANNING
"... Proof planning is a form of theorem proving in which the proving procedure is viewed as a planning process. The plan operators in proof planning are called methods. In this paper we propose a strategy for heuristically restricting the set of methods to be applied in proof search. It is based on the ..."
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Proof planning is a form of theorem proving in which the proving procedure is viewed as a planning process. The plan operators in proof planning are called methods. In this paper we propose a strategy for heuristically restricting the set of methods to be applied in proof search. It is based on the idea that the plausibility of a method can be estimated by comparing the model class of proof lines newly generated by the method with that of the assumptions and of the theorem. For instance, in forward reasoning when a method produces a new assumption whose model class is not a superset of the model class of the given premises, the method will lead to a situation which is semantically not justified and will not lead to a valid proof in later stages. A semantic restriction strategy is to reduce the search space by excluding methods whose application results in a semantic mismatch. A semantic selection strategy heuristically chooses the method that is likely to make most progress towards filling the gap between the assumptions and the theorem. Each candidate method is evaluated with respect to the subset and superset relation with the given premises. All models considered are taken from a finite reference subset of the full model class. In this contribution we present the modelguided approach as well as first experiments with it.
Using Models to Guide HumanOriented Proof Search
"... There has been some work to use models to guide traditional machineoriented proof search (e.g. resolution, tableau calculus), and corresponding theorem provers have been built. In humanoriented proof search, by contrast, few attempts have been made in this direction. ..."
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There has been some work to use models to guide traditional machineoriented proof search (e.g. resolution, tableau calculus), and corresponding theorem provers have been built. In humanoriented proof search, by contrast, few attempts have been made in this direction.