Abstract
Abstract
An important advantage of using a formal method of developing software is that one can prove that development steps are correct with respect to their specification. Conducting proofs by hand, however, can be time consuming to the extent that designers have to judge whether a proof of a particular obligation is worth conducting. Even if hand proofs are worth conducting, how do we know that they are correct?
One approach to overcoming this problem is to use an automatic theorem proving system to develop and check our proofs. However, in order to enable present day theorem provers to check proofs, one has to conduct them in much more detail than hand proofs. Carrying out more detailed proofs is of course more time consuming.
This paper describes the use of proof by analogy in an attempt to reduce the time spent on proofs. We develop and implement a proof follower based on analogy and present an example to illustrate its characteristics. The example shows that even when the follower fails to complete a proof, it can provide a hint that enables the user to complete a proof.
- [B+83] Buchanan B. G. et al. Constructing an expert system. In F. Hayes-Roth, D. A. Waterman, and D. B. Lenat, editors,Building Expert Systems, pages 127–167. Addison Wesley, 1983.Google Scholar
- [Bun79] Bundy. A.The Computer Modelling of Mathematical Reasoning. Academic Press, 1979.Google Scholar
- [Bun88] Bundy. A. The use of explicit plans to guide inductive proofs. In R. Lusk and R. Overbeek, editors,9th Conference on Automated Deduction, pages 111–120. Springer-Verlag, 1988.Google Scholar
- [GiH80] Gick M. and Holyoak K. J. Analogical problem solving.Cognitive Psychology, 12, 1980.Google Scholar
- [Hal89] Computational approaches to analogical reasoning: A comparative analysisArtificial Intelligence1989393912010.1016/0004-3702(89)90003-90668.68097993810Google ScholarDigital Library
- [JJL91] mural;A Formal Development Support System1991LondonSpringer Verlag0758.68046Google Scholar
- [Jon90] Jones C. B.Systematic Software Development using VDM. Prentice Hall International, second edition, 1990.Google Scholar
- [Kli71] A paradigm for reasoning by analogyArtificial Intelligence1971214717810.1016/0004-3702(71)90008-70227.68041Google ScholarCross Ref
- [McD79] McDermott J. Learning to use analogies. InProceedings of the International Joint Conference on Artificial Intelligence, pages 568–576, Tokyo, 1979.Google Scholar
- [Mun8l] Analogy as a means of discovery in problem-solving and learningPhD thesis1981Santa CruzUniversity of CaliforniaGoogle Scholar
- [MaW85] The Logical Basis for Computer Programming I1985Reading, MassachusettsAddison Wesley0572.68008Google Scholar
- [Owe90] Owen S.Analogy for Automated Reasoning. Academic Press, 1990.Google Scholar
- [Vad92] Heuristics for ProofsPhD thesis1992Manchester M13 9PL, UKUniversity of ManchesterGoogle Scholar
- [Vad95] Proof by analogy in mural — a more detailed accountFormal Aspects of Computing19957E129Google Scholar
Index Terms
- Proof by analogy in mural
Recommendations
A Formalization and Proof Checker for Isabelle’s Metalogic
AbstractIsabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an ...
A Proof System for a Unified Temporal Logic
Computing and CombinatoricsAbstractTheorem proving is a widely used approach to the verification of computer systems, and its theoretical basis is generally a proof system for formal derivation of logic formulas. In this paper, we propose a proof system for Propositional Projection ...
Completeness and Cut-elimination in the Intuitionistic Theory of Types
In this paper we define a model theory and give a semantic proof of cut-elimination for ICTT, an intuitionistic formulation of Church's theory of types defined by Miller et al. and the basis for the λProlog programming language. Our approach, extending ...
Comments