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Proof Planning By Abstraction
, 1994
"... Devising powerful heuristics or shifting the control to humans have probably been the two most common solutions to keep the search space in theorem proving manageable. In this paper we take advantage of both, by using abstraction [GW92b] as a tool to plan proofs by induction and by proving its eecti ..."
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Devising powerful heuristics or shifting the control to humans have probably been the two most common solutions to keep the search space in theorem proving manageable. In this paper we take advantage of both, by using abstraction [GW92b] as a tool to plan proofs by induction and by proving its eectiveness in ABSFOL (an interactive theorem prover built on top of GETFOL [GT91]). 1 Introduction The complexity of problems in logic is a limit to the results that can be achieved by theorem provers; hence the need of developing powerful heuristics, or of shifting the control to humans. We have chosen both solutions, by developing and using an interactive theorem prover which implements abstraction. ABSFOL [GW92a, GSVW96, Vil93] is a theorem prover built on top of GETFOL [GT91] 1 ; ABSFOL provides tools for using abstractions and inherits from GETFOL all the tools for building proofs. Abstraction is a powerful heuristic which captures the idea of simplication of a problem: when reasoni...
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...
Reasoning by Analogy via Abstraction
, 1996
"... ion Adolfo Villafiorita January 1996 Technical Report MRG/DIST # 960030 universit`a di genova facolt`a di ingegneria dipartimento informatica sistemistica telematica Reasoning by Analogy via Abstraction Adolfo Villafiorita Mechanized Reasoning Group I. I., University of Ancona, via B ..."
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ion Adolfo Villafiorita January 1996 Technical Report MRG/DIST # 960030 universit`a di genova facolt`a di ingegneria dipartimento informatica sistemistica telematica Reasoning by Analogy via Abstraction Adolfo Villafiorita Mechanized Reasoning Group I. I., University of Ancona, via Brecce Bianche, 60131 Ancona, Italy, DIST, University of Genova, viale Causa 15, 16146 Genova, Italy. adolfo@mrg.dist.unige.it Abstract Abstraction has been used in theorem proving as a heuristic to reduce the search space (see, for instance, [ Simpson, 1988 ] ) and as a tool for explanation (see, for instance, [ Bundy et al., 1993 ] ). We use abstraction to model certain forms of reasoning by analogy. 1 Introduction Reasoning by analogy can be described as the process of finding the solution of a problem (the target problem) by using the known solution of a similar problem (the source problem). This process consists of "extracting" the relevant information from the source problem,...
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.
Adolfo Villaorita
, 1993
"... Content areas: abstraction, automated reasoning, interactive theorem proving The goal of the work described in this paper is the development of a system, called ABSFOL, which allows the user to state declaratively abstractions and to use them according to the desired control strategy. ABSFOL has be ..."
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Content areas: abstraction, automated reasoning, interactive theorem proving The goal of the work described in this paper is the development of a system, called ABSFOL, which allows the user to state declaratively abstractions and to use them according to the desired control strategy. ABSFOL has been successfully tested on many examples. So far we have failed to nd an interesting abstraction whose implementation requires a major programming eort. Alan Bundy provided much of the inspiration for the solution of the Goedel example. The authors ' names are purely alphabetical. 1 1