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MRG: Building planners for real world complex applications
 APPLIED ARTIFICIAL INTELLIGENCE
, 1994
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Proving Theorems By Using Abstraction Interactively
 University of Genova, Italy
, 1994
"... ion Interactively Roberto Sebastiani 1 , Adolfo Villafiorita 1 , Fausto Giunchiglia 2;3 1 Mechanized Reasoning Group, D.I.S.T., University of Genoa, Italy 2 Mechanized Reasoning Group, I.R.S.T., 38050 Povo Trento, Italy. 3 University of Trento, Via Inama 5, 38100 Trento, Italy. rseba@dis ..."
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ion Interactively Roberto Sebastiani 1 , Adolfo Villafiorita 1 , Fausto Giunchiglia 2;3 1 Mechanized Reasoning Group, D.I.S.T., University of Genoa, Italy 2 Mechanized Reasoning Group, I.R.S.T., 38050 Povo Trento, Italy. 3 University of Trento, Via Inama 5, 38100 Trento, Italy. rseba@dist.unige.it adolfo@dist.unige.it fausto@irst.it Abstract In this paper we show how an interactive use of abstraction in theorem proving can improve the comprehension and reduce the complexity of many significant problems. For such a task we present a fully mechanized example of the very wellknown map colouring problem. 1 Introduction By "abstraction" we informally mean the process by which, starting from a given representation of a problem (called "ground space"), we construct a new and simpler representation (called "abstract space"), we find a solution for it and hence we use such a simplified solution as an outline for the solution of the original problem. The abstract space is obtained...
Building and Executing Proof Strategies in a Formal Metatheory
 Advances in Artifical Intelligence: Proceedings of the Third Congress of the Italian Association for Artificial Intelligence, IA*AI'93, Volume 728 of Lecture Notes in Computer Science
, 1993
"... This paper describes how "safe" proof strategies are represented and executed in the interactive theorem prover GETFOL. A formal metatheory (MT) describes and allows to reason about object level inference. A class of MT terms, called logic tactics, is used to represent proof strategies. ..."
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This paper describes how "safe" proof strategies are represented and executed in the interactive theorem prover GETFOL. A formal metatheory (MT) describes and allows to reason about object level inference. A class of MT terms, called logic tactics, is used to represent proof strategies. The semantic attachment facility and the evaluation mechanism of the GETFOL system have been used to provide the procedural interpretation of logic tactics. The execution of logic tactics is then proved to be "safe" under the termination condition. The implementation within the GETFOL system is described and the synthesis of a logic tactic implementing a normalizer in negative normal form is presented as a case study. 1 Introduction As pointed out in [GMMW77], interactive theorem proving [GMW79, CAB + 86, Pau89] has been growing up in the continuum existing between proof checking [deB70, Wey80] on one side and automated theorem proving [Rob65, And81, Bib81] on the other. Interactive theorem...
Using Abstraction Interactively
"... In the past, any totally automatic use af abstraction in theorem proving has been experimentally shown less useful than expected. In order to overcome such problem, in a former paper an interactive approach has been proposed. In this paper we show how an interactive use of abstraction in theorem pr ..."
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In the past, any totally automatic use af abstraction in theorem proving has been experimentally shown less useful than expected. In order to overcome such problem, in a former paper an interactive approach has been proposed. In this paper we show how an interactive use of abstraction in theorem proving can improve the comprehension and reduce the complexity of many significant problems. For such a task we present a fully mechanized example of the very wellknown map colouring problem.
Towards a Translation of Computer Algebra Algorithms into Tactics
, 1996
"... CAS 2 Abstract CAS 1 Function Mappings tactics plan result call Translator Interface Tactic Generator result call Figure 1: System architecture of sapper Unlike other proof planners a CAS does not have to search for a plan but only to assemble one as the algorithms have implicit knowledge of the ..."
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CAS 2 Abstract CAS 1 Function Mappings tactics plan result call Translator Interface Tactic Generator result call Figure 1: System architecture of sapper Unlike other proof planners a CAS does not have to search for a plan but only to assemble one as the algorithms have implicit knowledge of the actual computation. Thus sapper can use a relatively simple tactic mechanism for constructing proof plans. It consists of a set of hierarchically structured tactics: ffl simple tactics corresponding to the application of one hypotheses in a proof. ffl complex tactics describing computational steps of computer algebraic algorithms; they are compositions of simple tactics with tacticals. 3 Towards a 1to1 Representation of Tactics and Algorithms Abstraction ND PROOF CA Tactics Expansion Representation simple CA Algorithm Metatheory correspond translation Framework Figure 2: Translations from tactics to algorithms The author has realized a first working implementation of the sappersyste...