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Bidirectional Natural Deduction
 AI*IA Notizie
, 1993
"... The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well defined formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. Thi ..."
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The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well defined formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. This paper, primarily aimed at developing a deeper theoretical understanding of bidirectional reasoning, provides basic concepts to be incorporated into an innovative theorem prover to support interactive proofs construction in general domains. 1
MRG: Building planners for real world complex applications
 APPLIED ARTIFICIAL INTELLIGENCE
, 1994
"... ..."
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...
Structured Proof Procedures
 OF STRUCTURED PROOF PROCEDURES, THIRD BARILAN SYMPOSIUM ON THE FOUNDATIONS OF ARTIFICIAL INTELLIGENCE. ALSO DISTTECHNICAL REPORT 930015
, 1993
"... In this paper we address the problem of enriching an interactive theorem prover with complex proof procedures. We show that the approach of building complex proof procedures out of deciders for (decidable) quantifierfree theories has many advantages: (i) deciders for quantifierfree theories pro ..."
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In this paper we address the problem of enriching an interactive theorem prover with complex proof procedures. We show that the approach of building complex proof procedures out of deciders for (decidable) quantifierfree theories has many advantages: (i) deciders for quantifierfree theories provide powerful, high level functionalities which greatly simplify the activity of designing and implementing complex and higher level proof procedures; (ii) this approach is of wide applicability since most of the proof procedures are composed by steps of propositional reasoning intermixed with steps carrying out higher level strategical functionalities; (iii) decidability and efficiency are retained on important (decidable) subclasses, while they are often sacrificed by uniform proof strategies for the sake of generality; finally (iv), from a software engineering perspective, the modularity of the procedures guarantees that any modification in the implementation can be accomplished ...
The OMRS Project: State of the Art
, 1998
"... The state of the art for reasoning systems is unsatisfactory in several respects. In most cases, provers are poorly specified, hardly interconnectible, and they require a deep insight of their custom features in order to fully exploit their capabilities. The OMRS project is aimed at providing a gene ..."
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The state of the art for reasoning systems is unsatisfactory in several respects. In most cases, provers are poorly specified, hardly interconnectible, and they require a deep insight of their custom features in order to fully exploit their capabilities. The OMRS project is aimed at providing a general framework for specifying, structuring, and interoperating provers. This paper surveys the current achievements of the research performed within the OMRS project, under both the theoretical and the experimental side, and provides a perspective of its future evolution.
Abstract Contextual Reasoning
"... It is widely agreed on that most cognitive processes are contextual in the sense that they depend on the environment, or context, inside which they are carried on. Even concentrating on the issue of contextuality in reasoning, many different notions of context can be found in the Artificial Intellig ..."
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It is widely agreed on that most cognitive processes are contextual in the sense that they depend on the environment, or context, inside which they are carried on. Even concentrating on the issue of contextuality in reasoning, many different notions of context can be found in the Artificial Intelligence literature, see for instance [Giunchiglia 1991a,
Bidirectional Reasoning
"... The goal of this paper is to present a formal system FB for bidirectional reasoning which integrates forward and backward deduction. FB is proved equivalent to Gentzen's classical system of propositional natural deduction. FB is the logic of a theorem prover which supports interactive proof ..."
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The goal of this paper is to present a formal system FB for bidirectional reasoning which integrates forward and backward deduction. FB is proved equivalent to Gentzen's classical system of propositional natural deduction. FB is the logic of a theorem prover which supports interactive proof construction in general domains. 1
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...