Results 1 
7 of
7
Certifying solutions to permutation group problems
 In F. Baader, ed, CADE19, LNAI 2741
, 2003
"... Abstract. We describe the integration of permutation group algorithms with proof planning. We consider eight basic questions arising in computational permutation group theory, for which our code provides both answers and a set of certificates enabling a user, or an intelligent software system, to pr ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We describe the integration of permutation group algorithms with proof planning. We consider eight basic questions arising in computational permutation group theory, for which our code provides both answers and a set of certificates enabling a user, or an intelligent software system, to provide a full proof of correctness of the answer. To guarantee correctness we use proof planning techniques, which construct proofs in a humanoriented reasoning style. This gives the human mathematician the necessary insight into the computed solution, as well as making it feasible to check the solution for relatively large groups. 1
Combined reasoning by automated cooperation
 JOURNAL OF APPLIED LOGIC
, 2008
"... Different reasoning systems have different strengths and weaknesses, and often it is useful to combine these systems to gain as much as possible from their strengths and retain as little as possible from their weaknesses. Of particular interest is the integration of firstorder and higherorder tech ..."
Abstract

Cited by 11 (7 self)
 Add to MetaCart
Different reasoning systems have different strengths and weaknesses, and often it is useful to combine these systems to gain as much as possible from their strengths and retain as little as possible from their weaknesses. Of particular interest is the integration of firstorder and higherorder techniques. Firstorder reasoning systems, on the one hand, have reached considerable strength in
some niches, but in many areas of mathematics they still cannot reliably solve relatively simple problems, for example, when
reasoning about sets, relations, or functions. Higherorder reasoning systems, on the other hand, can solve problems of this kind
automatically. But the complexity inherent in their calculi prevents them from solving a whole range of problems. However, while
many problems cannot be solved by any one system alone, they can be solved by a combination of these systems.
We present a general agentbased methodology for integrating different reasoning systems. It provides a generic integration
framework which facilitates the cooperation between diverse reasoners, but can also be refined to enable more efficient, specialist
integrations. We empirically evaluate its usefulness, effectiveness and efficiency by case studies involving the integration of first
order and higherorder automated theorem provers, computer algebra systems, and model generators.
Interfacing to computer algebra via term indexing
 In Proceedings of Calculemus. Elsevier
, 2006
"... this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be found at the ENTCS Macro Home Page. blackrgb0,0,0 0.5 setgray0 0.5 setgray1 ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be found at the ENTCS Macro Home Page. blackrgb0,0,0 0.5 setgray0 0.5 setgray1
On the White Box Integration of Computer Algebra Algorithms into a Deduction System
 Master’s thesis, Universität des Saarlandes
, 2005
"... angefertigt bla bla ..."
Combined Reasoning by Automated Cooperation ⋆
"... Different reasoning systems have different strengths and weaknesses, and often it is useful to combine these systems to gain as much as possible from their strengths and retain as little as possible from their weaknesses. Of particular interest is the integration of firstorder and higherorder tech ..."
Abstract
 Add to MetaCart
(Show Context)
Different reasoning systems have different strengths and weaknesses, and often it is useful to combine these systems to gain as much as possible from their strengths and retain as little as possible from their weaknesses. Of particular interest is the integration of firstorder and higherorder techniques. Firstorder reasoning systems, on the one hand, have reached considerable strength in some niches, but in many areas of mathematics they still cannot reliably solve relatively simple problems, for example, when reasoning about sets, relations, or functions. Higherorder reasoning systems, on the other hand, can solve problems of this kind automatically. But the complexity inherent in their calculi prevents them from solving a whole range of problems. However, while many problems cannot be solved by any one system alone, they can be solved by a combination of these systems. We present a general agentbased methodology for integrating different reasoning systems. It provides a generic integration framework which facilitates the cooperation between diverse reasoners, but can also be refined to enable more efficient, specialist integrations. We empirically evaluate its usefulness, effectiveness and efficiency by case studies involving the integration of firstorder and higherorder automated theorem provers, computer algebra systems, and model generators.
Institute for Computing and Information Sciences,
"... Abstract. We present a prototype of a computer algebra system that is built on top of a proof assistant, HOL Light. This architecture guarantees that one can be certain that the system will make no mistakes. All expressions in the system will have precise semantics, and the proof assistant will chec ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We present a prototype of a computer algebra system that is built on top of a proof assistant, HOL Light. This architecture guarantees that one can be certain that the system will make no mistakes. All expressions in the system will have precise semantics, and the proof assistant will check the correctness of all simplifications according to this semantics. The system actually proves each simplification performed by the computer algebra system. Although our system is built on top of a proof assistant, we designed the user interface to be very close in spirit to the interface of systems like Maple and Mathematica. The system, therefore, allows the user to easily probe the underlying automation of the proof assistant for strengths and weaknesses with respect to the automation of mainstream computer algebra systems. The system that we present is a prototype, but can be straightforwardly scaled up to a practical computer algebra system. 1