Melis, E. and Meier, A. (2000). Proof planning with multiple strategies. In Proceedings of the First International Conference on Computational Logic, volume 1861 of LNAI . Springer Verlag.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....relevant control rules could be of the form Expand only de nitions of the current theory or Prefer de nition expansion of the head symbol of the formula to prove . A set of methods together with a set of control rules de nes a planning strategy of mega s multi strategy proof planner Multi [9]. Note that control rules of a strategy are used not only for determining the parameters of methods, but also to prefer or reject methods according to the current proof situation. For each learnt method outline we automatically build a method for which its precondition is ful lled if there is a ....

E. Melis and A. Meier, `Proof planning with multiple strategies', in First International Conference on Computational Logic, eds., J. Loyd et al., LNAI 1861, pp. 644-659, (2000). Springer Verlag.

....and proofs and can perform type checking, de nition expansion and semantic search. MBase is still under development but a preliminary version already serves mathematical documents to the ActiveMath system. Constraint Solvers. MathWeb currently o ers two constraint solving systems. CoSIE [Zim00, MMZ00] is a constraint solver for non linear arithmetic constraints over the real numbers. Chorus [KN00] is a special constraint solver developed in computational linguistics which handles dominance constraints to resolve ambiguities in natural language sentences. The current structure of the MathWeb ....

....mechanism is a perfect application domain for a blackboard architecture (cf. section 3.3) Multi agent Planning. In recent years, the mega group has made signi cant progress in proof planning, for instance, in the Limit domain [Mel97] and in group theory. The latest development is MULTI [MM00], a multi strategy planner. Up to now, proof planning in mega is totally serialized, i.e. at every time the proof planner only plans one speci c subgoal. Also in MULTI di erent planning strategies can only be applied in sequential order. A consequent step for a further improvement of proof ....

Erica Melis and Andreas Meier. Proof Planning with Multiple Strategies. In J. Loyd, V. Dahl, U. Furbach, M. Kerber, K. Lau, C. Palamidessi, L.M. Pereira, and Y. Sagivand P. Stuckey, editors, First International Conference on Computational Logic (CL-

....a given residue class set together with one or two operations in terms of its algebraic structure. During this classification process proof obligations for proving or refuting single properties are generated. These proof obligations are passed to Omega mega s multi strategy proof planner Multi [5] that constructs a proof with the help of Gap and Maple [7] Since the presented exploration module has originated from work done in the context of tutor systems, the motivation is not to obtain new results in finite algebra. It shall rather enable a user to learn fundamental algebraic notions by ....

E. Melis and A. Meier. Proof planning with multiple strategies. In Proc. of the First International Conference on Computational Logic, London, United Kingdom, 2000. Springer Verlag, Berlin, Germany.

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Melis, E. and Meier, A. (2000). Proof planning with multiple strategies. In Proceedings of the First International Conference on Computational Logic, volume 1861 of LNAI . Springer Verlag.

No context found.

E. Melis and A. Meier. Proof planning with multiple strategies. In Proceedings of the First International Conference on Computational Logic, volume 1861 of LNAI. Springer Verlag, Germany, 2000.

No context found.

E. Melis and A. Meier. Proof planning with multiple strategies. In Proceedings of the First International Conference on Computational Logic, volume 1861 of LNAI. Springer Verlag, Germany, 2000.

No context found.

E. Melis and A. Meier. Proof Planning with Multiple Strategies. In Proc. of CL-2000, LNAI 1861. Springer, 2000.

No context found.

E. Melis and A. Meier. Proof planning with multiple strategies. In Proceedings of the First International Conference on Computational Logic, volume 1861 of LNAI. Springer Verlag, Germany, 2000.

....are represented at various levels of granularity and abstraction. The proof plans are developed and then classi ed with respect to a taxonomy of mathematical theories, which is currently being replaced by the mathematical data base MBase [26, 31] The users of mega, the proof planner Multi [37], or the suggestion mechanism Ants [11] modify the PDS during proof development until a complete proof plan has been found. They can also invoke heterogeneous external reasoning systems such as computer algebra systems (CASs) higher and rst order automated theorem proving systems (ATPs) ....

E. Melis and A. Meier. Proof planning with multiple strategies. In J. Loyd, V. Dahl, U. Furbach, M. Kerber, K. Lau, C. Palamidessi, L.M. Pereira, and Y. Sagivand P. Stuckey, editors, Proc. of the First International Conference on Computational Logic, volume 1861 of LNAI, pages 644-659. Springer-Verlag, 2000.

....alternative list, prefer reorders the alternative list such that the specified candidates are at the beginning, and order before reorders pairs in the alternative list such that one candidate is ordered before another candidate. 2. 2 Multi Strategy Proof Planning Multi strategy proof planning [16] is an extension of knowledge based proof planning. Omega mega s multi strategy proof planner Multi enables the specification and combination of a number of planning strategies and switching flexibly between them during the proof planning process. A strategy can be roughly described as a ....

Erica Melis and Andreas Meier. Proof planning with multiple strategies. In John W. Lloyd, Ver'onica Dahl, Ulrich Furbach, Manfred Kerber, Kung-Kiu Lau, Catuscia Palamidessi, Lu'is Moniz Pereira, Yehoshua Sagiv, and Peter J. Stuckey, editors, Proceedings of the First International Conference on Computational Logic (CL2000.

....mega employs also control rules and strategies to formalize domain knowledge. Control rules encode heuristic knowledge about when and how mathematical inferences (operators) should be applied. Furthermore, strategies re ect the knowledge about di erent proof techniques for a class of problems [9]. ....

E. Melis and A. Meier, `Proof planning with multiple strategies', in Proc. of the First International Conference on Computational Logic, LNAI 1861, pp. 644-659. Springer, (2000).

....a as one side and another term b as the other side. The application of =Subst reduces then goal t[a] to the new goal t[b] which is the same term as t[a] except for the occurrence of a. As basic proof planner for the experiments described in this paper we used the proof planner of the MEGA system [8, 7]. MEGA s proof planner employs both backward and forward planning. 3 The Domain of Residue Classes In this section, we describe the domain of residue classes over the integers. A detailed description of the domain can be found in [6] A residue class set RSn over the integers is the set of all ....

E. Melis and A. Meier. Proof planning with multiple strategies. In Proc. of the First International Conference on Computational Logic (CL

....alternative list, prefer reorders the alternative list such that the specified candidates are at the beginning, and order before reorders pairs in the alternative list such that one candidate is ordered before another candidate. 2. 2 Multi Strategy Proof Planning Multi strategy proof planning [16] is an extension of knowledge based proof planning. Omega mega s multi strategy proof planner Multi enables the specification and combination of a number of planning strategies and switching flexibly between them during the proof planning process. A strategy can be roughly described as a ....

Erica Melis and Andreas Meier. Proof planning with multiple strategies. In John W. Lloyd, Ver'onica Dahl, Ulrich Furbach, Manfred Kerber, Kung-Kiu Lau, Catuscia Palamidessi, Lu'is Moniz Pereira, Yehoshua Sagiv, and Peter J. Stuckey, editors, Proceedings of the First International Conference on Computational Logic (CL

....steps as well as knowledge particular to a mathematical domain. Moreover, control rules specify how to traverse the search space by in uencing the ordering of method application and the choice of the next goal depending on certain domains or proof situations. mega s new proof planner, Multi [14], allows also for the speci cation of di erent planning strategies to control the overall planning behavior. Methods in mega are essentially tactics known from tactical theorem proving augmented with pre and postconditions, so called premises and conclusions. Premises and conclusions indicate ....

....In particular, we employ control rules to prefer a particular instance from a list of possible variable instantiations. As example we present the select instance control rule in the next section. In mega di erent proof techniques for a problem class can be realized by di erent planner strategies [14]. The planner strategies can employ di erent sets of methods and control rules and can thus allow to tackle the same problem in di erent ways. The reasoning about which strategy to employ on a problem (provided there are several applicable strategies) and about the switching of strategies is an ....

E. Melis and A. Meier. Proof planning with multiple strategies. In Proc. of the First International Conference on Computational Logic. Springer, 2000.

....as first removes some elements from the alternative list which we need nevertheless in particular situation. Then a more specific insert control rule which is applied later on can introduce again the elements we need. 2. 2 Multi Strategy Proof Planning Multi strategy proof planning ( MM00] is an extension of knowledge based proof planning. Omega mega s multi strategy proof planner Multi enables the specification and combination of a number of planning strategies and to switch flexibly between them during the proof planning process. A strategy can be roughly described as a ....

.... is the case C interrupt selects interrupt (encoded in the THEN part of C which is a select action) To cause a backtracking in Multi that removes all plan refinements done by the application of S, C interrupt sends a suggestion to Multi to apply the backtracking strategy BackTrackStrategy (see [MM00] how such a suggestion is done) BackTrackStrategy is a strategy of the algorithm BackT rack that removes all proof plan refinements introduced during the application of another strategy. One of the strategic control rules of Multi states that suggestions from interrupted strategies should be ....

Erica Melis and Andreas Meier. Proof planning with multiple strategies. In Proc. of the First International Conference on Computational Logic. Springer, Germany, 2000.

....module that constructs proof obligations with respect to given sets and operations. These proof obligations are theorems of the form: the set is closed under the operation, or the operation is not associative, etc. Proof obligations are passed to mega s multi strategy proof planner Multi ([25]) which allows to employ di erent proving techniques for a problem class encoded in di erent strategies. Since we work with problems in a nite domain an obvious choice for a proving technique is to analyze exhaustively all possible cases of a problem. This naive approach, however, is bound to ....

....from the list of alternative methods. Other actions are reject and prefer . The former removes all alternatives speci ed in the control rule from a given alternative list, whereas the latter reorders the alternative list. 3. 2 Multi Strategy Proof Planning Multi strategy proof planning ([25]) is an extension of knowledge based proof planning. mega s multi strategy proof planner Multi enables the speci cation and combination of a number of planning strategies and to switch exibly between them during the proof planning process. A strategy can be roughly described as a parametrization ....

E. Melis and A. Meier. Proof planning with multiple strategies. In Proc. of the First International Conference on Computational Logic. Springer, Germany, 2000.

....module that constructs proof obligations with respect to a given set and operation. These proof obligations are theorems of the form: the set is closed under the operation, or the operation is not associative, etc. Proof obligations are passed to mega s multi strategy proof planner Multi [12] that constructs a proof with the help of the two computer algebra systems Maple [14] and Gap [4] Although the proofs are not very pretentious in their own right they need to be constructed in a way that di erent proving techniques can be taught to a user of the interactive course. This is ....

....can encode general proving steps as well as knowledge particular to a mathematical domain. Moreover, control rules specify how to traverse the search space by preferring, rejecting, or enforcing the application of methods in certain domains or proof situations. mega s new proof planner, Multi [12], allows also for the speci cation of di erent planning strategies to control the overall planning behavior. Proof plans in mega result in proof objects in a variant of the natural deduction calculus [5] We will present them in this paper in a linearized style as introduced in [1] A proof line ....

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E. Melis and A. Meier. Proof planning with multiple strategies. In Proc. of the First International Conference on Computational Logic, 2000. Springer.

....about the status of the problem solving process is stated on a blackboard that can be accessed and changed by the knowledge sources. Multi s architecture is similar to the BB1 blackboard system [10] The architecture of Multi is summarized in the following and described in more detail in [16]. The architecture has two blackboards, one for the solution problem and one for the control problem. The solution blackboard contains the partial proof plan and a store which contains the status of the execution of strategies. The strategies are the knowledge sources which work on this solution ....

E. Melis and A. Meier. Proof planning with multiple strategies. Seki report SR99 -06, Universitat des Saarlandes, FB Informatik, 1999.

....of my work I shall work in are education systems and formal software verification. Numerous theoretical and practical problems have still to be solved to make proof planning and analogy a powerful and reliable technology. My research becomes much broader now through the supervision of PhD students [22, 24] and the collaboration with other researchers. For instance, currently I investigate proof planning and mathematical meta reasoning for new mathematical domains in collaboration with PhD students Martin Pollet and Volker Sorge (Saarbrucken) This research is being extended to a formal ....

E. Melis. Proof planning with multiple strategies. In B. Gramlich and F. Pfenning, editors, CADE-15 workshop on Strategies in Automated Deduction, pages 57--68, 1998.

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E. Melis. Proof planning with multiple strategies. In CADE-15 workshop: Strategies in Automated Deduction, 1998.

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