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First Order Logic in Practice
 In Proc. FTP
, 1997
"... Now, although interactive provers may require manual guidance, it's desirable to provide quite high levels of automation so that the user avoids the tedious filling in of trivial details. Indeed, the most effective recent systems such as PVS do provide quite powerful automation for special theories ..."
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Now, although interactive provers may require manual guidance, it's desirable to provide quite high levels of automation so that the user avoids the tedious filling in of trivial details. Indeed, the most effective recent systems such as PVS do provide quite powerful automation for special theories felt to be particularly important in practice, e.g. linear arithmetic and propositional tautology checking. But what about the automation of pure, typically first order, logic? There have been attempts since at least SAM [4] to harness automation of pure logic in interactive systems. Yet a common view today is that automation of theories like linear arithmetic is far more significant in practice.
Structuring Deduction by Using Abstractions
 International Symposium on Abstraction, Reformulation, and Approximation (SARA98
, 1998
"... During the last decade a variety of industrial strength formal methods has emerged and has been applied to industrial test cases to demonstrate their adequacy and scalability. Formal techniques require a sufficient tool support especially when dealing with proof obligations. The size and the complex ..."
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During the last decade a variety of industrial strength formal methods has emerged and has been applied to industrial test cases to demonstrate their adequacy and scalability. Formal techniques require a sufficient tool support especially when dealing with proof obligations. The size and the complexity of the arising problems demand for techniques to structure the deduction. In this paper we present techniques to realize a general divideandconquer approach in the framework of proof planning. In order to tackle different subgoals by different proof methods we propose the use of the colorcalculus as an underlying constraint mechanism to resolve possible threats. 1 Introduction The application of formal methods in an industrial setting (cf. [6]) results in an increased complexity of the specification and the correspondent verification. While various techniques have been developed to decompose specifications of large systems into modules of reasonable size (e.g. enrichment, parameteri...
A short survey of automated reasoning
"... Abstract. This paper surveys the field of automated reasoning, giving some historical background and outlining a few of the main current research themes. We particularly emphasize the points of contact and the contrasts with computer algebra. We finish with a discussion of the main applications so f ..."
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Abstract. This paper surveys the field of automated reasoning, giving some historical background and outlining a few of the main current research themes. We particularly emphasize the points of contact and the contrasts with computer algebra. We finish with a discussion of the main applications so far. 1 Historical introduction The idea of reducing reasoning to mechanical calculation is an old dream [75]. Hobbes [55] made explicit the analogy in the slogan ‘Reason [...] is nothing but Reckoning’. This parallel was developed by Leibniz, who envisaged a ‘characteristica universalis’ (universal language) and a ‘calculus ratiocinator ’ (calculus of reasoning). His idea was that disputes of all kinds, not merely mathematical ones, could be settled if the parties translated their dispute into the characteristica and then simply calculated. Leibniz even made some steps towards realizing this lofty goal, but his work was largely forgotten. The characteristica universalis The dream of a truly universal language in Leibniz’s sense remains unrealized and probably unrealizable. But over the last few centuries a language that is at least adequate for
HOL Light Tutorial (for version 2.20). http://www.cl.cam.ac.uk/ jrh13/hollight/tutorial 220.pdf
"... The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, ..."
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The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, aimed at teaching basic use of the system quickly by means of a graded set of examples. Some readers may find it easier to absorb; those who do not are referred after all to the standard manual. “Shouldn’t we read the instructions?”
Proceedings of the CADE14 Workshop on Strategies in Automated Deduction
, 1997
"... After introducing the basic notions of reflective logic and internal strategies, we discuss in detail how reflection can be systematically exploited to design a strategy language internal to a reflective logic in the concrete case of rewriting logic and Maude; and we illustrate the advantages of thi ..."
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After introducing the basic notions of reflective logic and internal strategies, we discuss in detail how reflection can be systematically exploited to design a strategy language internal to a reflective logic in the concrete case of rewriting logic and Maude; and we illustrate the advantages of this new approach to strategies by showing how the rules of inference for KnuthBendix completion can be given strategies corresponding to completion procedures in a completely modular way, not requiring any change whatsoever to the inference rules themselves.