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Managing Structural Information by HigherOrder Colored Unification
 JOURNAL OF AUTOMATED REASONING
, 1999
"... Coloring terms (rippling) is a technique developed for inductive theorem proving which uses syntactic dierences of terms to guide the proof search. Annotations (colors) to symbol occurrences in terms are used to maintain this information. This technique has several advantages, e.g. it is highly go ..."
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Coloring terms (rippling) is a technique developed for inductive theorem proving which uses syntactic dierences of terms to guide the proof search. Annotations (colors) to symbol occurrences in terms are used to maintain this information. This technique has several advantages, e.g. it is highly goal oriented and involves little search. In this paper we give a general formalization of coloring terms in a higherorder setting. We introduce a simplytyped calculus with color annotations and present appropriate algorithms for the general, pre and pattern unification problems. Our work is a formal basis to the implementation of rippling in a higherorder setting which is required e.g. in case of middleout reasoning. Another application is in the construction of natural language semantics, where the color annotations rule out linguistically invalid readings that are possible using standard higherorder unification.
Learning From Previous Proof Experience: A Survey
, 1999
"... We present an overview of various learning techniques used in automated theorem provers. We characterize the main problems arising in this context and classify the solutions to these problems from published approaches. We analyze the suitability of several combinations of solutions for different app ..."
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Cited by 3 (0 self)
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We present an overview of various learning techniques used in automated theorem provers. We characterize the main problems arising in this context and classify the solutions to these problems from published approaches. We analyze the suitability of several combinations of solutions for different approaches to theorem proving and place these combinations in a spectrum ranging from provers using very specialized learning approaches to optimally adapt to a small class of proof problems, to provers that learn more general kinds of knowledge, resulting in systems that are less efficient in special cases but show improved performance for a wide range of problems. Finally, we suggest combinations of solutions for various proof philosophies.
Equalizing Terms by Difference Reduction Techniques
 In Proceedings Gramlich, B., Kirchner, H. (Eds.) Workshop on Strategies in Automated Deduction
, 1997
"... In the field of inductive theorem proving syntactical differences between the induction hypothesis and induction conclusion are used in order to guide the proof [BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling / coloring terms and there is considerable evidence of ..."
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Cited by 3 (0 self)
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In the field of inductive theorem proving syntactical differences between the induction hypothesis and induction conclusion are used in order to guide the proof [BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling / coloring terms and there is considerable evidence of its success on practical examples. For equality reasoning we use these annotated terms to represent syntactical differences of formulas. Based on these annotations and on hierarchies of function symbols we define different abstractions of formulas which are used for a hierarchical planning of proofs. Also rippling techniques are used to refine single planning steps, e.g. the application of a bridge lemma, on a next planning level. 1 Introduction In the field of inductive theorem proving syntactical differences between the induction hypothesis and induction conclusion are used in order to guide the proof [BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling ...
Island Planning and Refinement
, 1996
"... Proof planning is an alternative to classical theorem proving. Proof planning is classical planning with no goal interaction. It faces search problems because of long solutions and possibly infinite branching. It is also required to provide plans comprehensible for the user. This article introduces ..."
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Proof planning is an alternative to classical theorem proving. Proof planning is classical planning with no goal interaction. It faces search problems because of long solutions and possibly infinite branching. It is also required to provide plans comprehensible for the user. This article introduces new planning strategies inspired by proof planning examples in order to tackle the searchspaceproblem and the structuredplanproblem. Island planning and refinement as well as subproblem refinement are integrated into a general planning framework and some exemplary control knowledge suitable for proof planning is given. We think that planning for other realistic problems even in a static and deterministic environment with complete information faces similar problems and can make use of our approach. 1 Introduction Refinement planning as unguided search is notoriously hard because of the combinatorial search involved. For realistic planning problems the intractable search space prevents ma...
Proceedings of the CADE14 Workshop on Strategies in Automated Deduction
, 1997
"... After introducing the basic notions of reflective logic and internal strategies, we discuss in detail how reflection can be systematically exploited to design a strategy language internal to a reflective logic in the concrete case of rewriting logic and Maude; and we illustrate the advantages of thi ..."
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After introducing the basic notions of reflective logic and internal strategies, we discuss in detail how reflection can be systematically exploited to design a strategy language internal to a reflective logic in the concrete case of rewriting logic and Maude; and we illustrate the advantages of this new approach to strategies by showing how the rules of inference for KnuthBendix completion can be given strategies corresponding to completion procedures in a completely modular way, not requiring any change whatsoever to the inference rules themselves.