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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)
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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.
On handling distinct objects in the superposition calculus
 In Notes 5th IWIL Workshop
, 2005
"... Abstract. Many domains of reasoning include a set of distinct objects. For generalpurpose automated theorem provers, this property has to be specified explicitly, by including distinctness axioms. Since their number grows quadratically with the number of distinct objects, this results in large and ..."
Abstract

Cited by 8 (7 self)
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Abstract. Many domains of reasoning include a set of distinct objects. For generalpurpose automated theorem provers, this property has to be specified explicitly, by including distinctness axioms. Since their number grows quadratically with the number of distinct objects, this results in large and clumsy specifications, that may affect performance adversely. We show that object distinctness can be handled directly by a modified superpositionbased inference system, including additional inference rules. The new calculus is shown to be sound and complete. A preliminary implementation shows promising results in the theory of arrays. 1
E 0.8x User Manual
, 2004
"... E is an equational theorem prover for full clausal logic, based on superposition and rewriting. In this very preliminary manual we first give a short introduction for impatient new users, and then cover calculus, control, options and input/output of the prover in some more detail. ..."
Abstract
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E is an equational theorem prover for full clausal logic, based on superposition and rewriting. In this very preliminary manual we first give a short introduction for impatient new users, and then cover calculus, control, options and input/output of the prover in some more detail.