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MBase: Representing Knowledge and Context for the Integration of Mathematical Software Systems
, 2000
"... In this article we describe the data model of the MBase system, a webbased, ..."
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Cited by 41 (11 self)
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In this article we describe the data model of the MBase system, a webbased,
Evaluating general purpose automated theorem proving systems
 Artificial Intelligence
"... A key concern of ATP research is the development of more powerful systems, capable of solving more difficult problems within the same resource limits. In order to build more powerful systems, it is important to understand which systems, and hence which techniques, work well for what types of problem ..."
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Cited by 25 (9 self)
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A key concern of ATP research is the development of more powerful systems, capable of solving more difficult problems within the same resource limits. In order to build more powerful systems, it is important to understand which systems, and hence which techniques, work well for what types of problems. This paper deals with the empirical evaluation of general purpose ATP systems, to determine which systems work well for what types of problems. This requires also dealing with the issues of assigning ATP problems into classes that are reasonably homogeneous with respect to the ATP systems that (attempt to) solve the problems, and assigning ratings to problems based on their difficulty.
Computer algebra meets automated theorem proving: Integrating Maple and pvs
 Theorem Proving in Higher Order Logics (TPHOLs 2001), volume 2152 of LNCS
, 2001
"... ..."
Combining symbolic computation and theorem proving: some problems of Ramanujan
 In A. Bundy (Ed.), Automated Deduction (CADE12
, 1994
"... One way of building more powerful theorem provers is to use techniques from symbolic computation. The challenge problems in this paper are taken from Chapter 2 of Ramanujan 's Notebooks. They were selected because they are nontrivial and require the use of symbolic computation techniques. We have d ..."
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Cited by 11 (3 self)
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One way of building more powerful theorem provers is to use techniques from symbolic computation. The challenge problems in this paper are taken from Chapter 2 of Ramanujan 's Notebooks. They were selected because they are nontrivial and require the use of symbolic computation techniques. We have developed a theorem prover based on the symbolic computation system Mathematica that can prove all the challenge problems completely automatically. The axioms and inference rules for constructing the proofs are also briefly discussed. This research was sponsored in part by the Avionics Laboratory, Wright Research and Development Center, Aeronautical Systems Division (AFSC), U.S. Air Force, WrightPatterson AFB, Ohio 454336543 under Contract F3361590C1465, ARPA Order No. 7597, and in part by National Science Foundation under Contract Number CCR9217549. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official p...
Extensions to Proof Planning for Generating Implied Constraints
 In Proceedings of Calculemus01
, 2001
"... . We describe how proof planning is being extended to generate implied algebraic constraints. This inference problem introduces a number of challenging problems like deciding a termination condition and evaluating constraint utility. We have implemented a number of methods for reasoning about al ..."
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Cited by 11 (7 self)
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. We describe how proof planning is being extended to generate implied algebraic constraints. This inference problem introduces a number of challenging problems like deciding a termination condition and evaluating constraint utility. We have implemented a number of methods for reasoning about algebraic constraints. For example, the eliminate method performs Gaussianlike elimination of variables and terms. We are also reusing proof methods from the PRESS equation solving system like (variable) isolation. 1
Classification of Communication and Cooperation Mechanisms for Logical and Symbolic Computation Systems
, 1996
"... . The combination of logical and symbolic computation systems has recently emerged from prototype extensions of standalone systems to the study of environments allowing interaction among several systems. Communication and cooperation mechanisms of systems performing any kind of mathematical service ..."
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Cited by 10 (4 self)
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. The combination of logical and symbolic computation systems has recently emerged from prototype extensions of standalone systems to the study of environments allowing interaction among several systems. Communication and cooperation mechanisms of systems performing any kind of mathematical service enable to study and solve new classes of problems and to perform efficient computation by distributed specialized packages. The classification of communication and cooperation methods for logical and symbolic computation systems given in this paper provides and surveys different methodologies for combining mathematical services and their characteristics, capabilities, requirements, and differences. The methods are illustrated by recent wellknown examples. We separate the classification into communication and cooperation methods. The former includes all aspects of the physical connection, the flow of mathematical information, the communication language(s) and its encoding, encryption, and ...
Adding the axioms to Axiom: Towards a system of automated reasoning in Aldor
 Computing Laboratory, University of Kent
, 1998
"... A number of combinations of theorem proving and computer algebra systems have been proposed; in this paper we describe another, namely a way to incorporate a logic in the computer algebra system Axiom. We examine the type system of Aldor  the Axiom Library Compiler  and show that with some modif ..."
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Cited by 6 (1 self)
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A number of combinations of theorem proving and computer algebra systems have been proposed; in this paper we describe another, namely a way to incorporate a logic in the computer algebra system Axiom. We examine the type system of Aldor  the Axiom Library Compiler  and show that with some modifications we can use the dependent types of the system to model a logic, under the CurryHoward isomorphism. We give a number of example applications of the logic we construct. 1 Introduction Symbolic mathematical  or computer algebra  systems, such as Axiom [JS92], Maple and Mathematica, are in everyday use by scientists, engineers and indeed mathematicians, because they provide a user with techniques of, say, integration which far exceed those of the person themselves, and make routine many calculations which would have been impossible some years ago. These systems are, moreover, taught as standard tools within many university undergraduate programmes and are used in support of both ac...
Nontrivial Symbolic Computations in Proof Planning
 In Proc. of FroCoS 2000, LNCS 1794
, 2000
"... We discuss a pragmatic approach to integrate computer algebra into proof planning. It is based on the idea to separate computation and verification and can thereby exploit the fact that many elaborate symbolic computations are trivially checked. In proof planning the separation is realized by using ..."
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Cited by 6 (3 self)
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We discuss a pragmatic approach to integrate computer algebra into proof planning. It is based on the idea to separate computation and verification and can thereby exploit the fact that many elaborate symbolic computations are trivially checked. In proof planning the separation is realized by using a powerful computer algebra system during the planning process to do nontrivial symbolic computations. Results of these computations are checked during the refinement of a proof plan to a calculus level proof using a small, selfimplemented, system that gives us protocol information on its calculation. This protocol can be easily expanded into a checkable lowlevel calculus proof ensuring the correctness of the computation. We demonstrate our approach with the concrete implementation in the Omega system.
An Open Environment for Doing Mathematics
 Proceedings of 1st International IMACS Conference on Applications of Computer Algebra
, 1995
"... There are several possible approaches to integrate theorem provers (TP) and computer algebra systems (CAS). On one hand classical CAS usually offer a straightforward programming language with adhoc implementations of rewriting. One approach towards introducing theorem proving in CAS is an extension ..."
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Cited by 4 (0 self)
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There are several possible approaches to integrate theorem provers (TP) and computer algebra systems (CAS). On one hand classical CAS usually offer a straightforward programming language with adhoc implementations of rewriting. One approach towards introducing theorem proving in CAS is an extension of Analytica [Clarke & Zhao 92], a Mathematica package to prove theorems in elementary analysis which solves an extensive collection of nontrivial mathematical problems. On the other hand some classical TP were extended by techniques of symbolic computing, e.g. Otter allows to call external algorithms out of proofs. Specialized prover packages have been developed which are capable to perform symbolic mathematical computations. However, there are no environments integrating theorem provers and computer algebra systems which consistently provide the inference capabilities of the first and the powerful arithmetic of the latter systems. Another aspect is the integration of several systems in a ...