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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...
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
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.
Modularity in Computer Assisted Reasoning Systems 1 Problem being addressed
"... An important problem in the domain of automated reasoning is the development of mechanisms for the integration of disparate provers. The components of a prover may be based on different logics, they may have different domain models, they may use different representations of information and reasoning ..."
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An important problem in the domain of automated reasoning is the development of mechanisms for the integration of disparate provers. The components of a prover may be based on different logics, they may have different domain models, they may use different representations of information and reasoning strategies, and they may have different interaction capabilities. The need for composing complex provers from existing modules, and to add new modules to existing provers is motivated by the desire of not having to build from scratch a new prover for each new problem or variation of an old problem. Multilogic provers are needed in many formalization problems, such as hardware and software verification. Multilogic provers are also needed in complex applications which require embedding of reasoning modules inside other systems. Some examples are: program transformation systems, including synthesis; partial evaluation and compiling; planning systems; intelligent agents; and natural language systems. 2 Thesis objectives Our ultimate goal is to provide a framework and a methodology which will allow users, and not only developers, to construct complex reasoning systems by composing existing modules, or to add new modules to existing systems. These modules and systems might be based on different logics; have different domain models; use different vocabularies and data structures; use different reasoning strategies. The thesis proposal makes two main contributions towards our goal. First, it proposes a formal notation (FBHypersequents) for presenting the syntax and semantics of reasoning theories of Open Mechanized Reasoning Systems (OMRSs) as stated in [Giunchiglia et a/., 1994]. Second, it developes the theory underlying the control component which consists of a set of inference strategies of OMRSs. This development is motivated by an analysis of (logical) consequence relation in general, and especially its possible relations with computational issues. Some of the problems that the thesis proposal addresses are general problem of