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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 ..."
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Cited by 16 (8 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.
Experiments with an Agentoriented Reasoning System
 In In Proc. of KI 2001, volume 2174 of LNAI
, 2001
"... Abstract. This paper discusses experiments with an agent oriented approach to automated and interactive reasoning. The approach combines ideas from two subfields of AI (theorem proving/proof planning and multiagent systems) and makes use of state of the art distribution techniques to decentralise a ..."
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Cited by 12 (8 self)
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Abstract. This paper discusses experiments with an agent oriented approach to automated and interactive reasoning. The approach combines ideas from two subfields of AI (theorem proving/proof planning and multiagent systems) and makes use of state of the art distribution techniques to decentralise and spread its reasoning agents over the internet. It particularly supports cooperative proofs between reasoning systems which are strong in different application areas, e.g., higherorder and firstorder theorem provers and computer algebra systems. 1
The Design and Implementation of a Compositional CompetitionCooperation Parallel ATP System
 Proceedings of the 2nd International Workshop on the Implementation of Logics, number MPII20012006 in MaxPlanckInstitut für Informatik, Research Report
, 2001
"... Key concerns in the development of more powerful ATP systems are to provide breadth of coverage – an ability to solve a large range of problems, and to provide greater depth of coverage – an ability to solve more difficult problems, within the same resource limits. This work describes the design and ..."
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Cited by 7 (1 self)
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Key concerns in the development of more powerful ATP systems are to provide breadth of coverage – an ability to solve a large range of problems, and to provide greater depth of coverage – an ability to solve more difficult problems, within the same resource limits. This work describes the design and implementation of CSSCPA, a compositional competitioncooperation parallel ATP System. CSSCPA combines existing high performance ATP systems in a framework that allows them to work independently, but also allows communication of intermediate results. The performance data shows that CSSPCA has high breadth and depth of coverage. 1
Ten Years of Parallel Theorem Proving: A Perspective
 Dept. of Comp. Sci., Univ. of Iowa
, 1999
"... this paper, we have extended our analysis to the impact of the parallelization approaches on the control of search. We observed that approaches with parallelism at the term level may replace the search plan by lowlevel datadriven forms of concurrency, or produce strategycompliant parallelizations ..."
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Cited by 1 (0 self)
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this paper, we have extended our analysis to the impact of the parallelization approaches on the control of search. We observed that approaches with parallelism at the term level may replace the search plan by lowlevel datadriven forms of concurrency, or produce strategycompliant parallelizations. It seems that the potential problem is a loss of control for the former, and an excess of control for the latter. Datadriven concurrency may be appropriate for ground computations that are guaranteed to converge (e.g., computing a congruence closure for ground completion), but may represent a counterproductive loss of control in general theorem proving, where the essence, from a practical point of view, is not saturation (i.e., do all the steps, with the order being a secondary issue), but effective search (i.e., find a good order to do the steps in order to avoid doing them all). Strategycompliant parallelizations, on the other hand, may be too conservative: they avoid the risk of mixing search with parallelism, but they renounce using parallelism to try to generate better searches.
Theorem Proving with the Inverse Method for Linear Logic
, 2004
"... Linear logic presents a unified framework for describing and reasoning about stateful systems. Because of its view of hypotheses as resources, it supports such phenomena as concurrency, external and internal choice, and state transitions that are common in such domains as protocol verification, conc ..."
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Linear logic presents a unified framework for describing and reasoning about stateful systems. Because of its view of hypotheses as resources, it supports such phenomena as concurrency, external and internal choice, and state transitions that are common in such domains as protocol verification, concurrent computation, process calculi and games. It accomplishes this unifying view by providing logical connectives whose behaviour is closely tied to the collection of resources, which is free of structural phenomena such as weakening (allowing more resources than necessary) or contraction (using a resource more than once). The usual (nonlinear) logic is embedded in this substructural framework by means of an exponential modal operator. The interaction of the rules for multiplicative, additive and exponential connectives gives rise to a wide and expressive array of behaviours. Various approaches have been taken to produce automated reasoning systems for fragments of linear logic, usually in the form of logic programming engines; but, due to the lack of the full complement of linear connectives, uses of such systems have an idiomatic commitment, for example as serializations or in continuationpassingstyle. This thesis addresses the need for automated reasoning for the complete set of operators for first order intuitionistic linear logic (i.e., ⊗, 1, ❜, &, ⊤, ⊕, 0,!, ∀, ∃), which removes the need for such idiomatic constructions and allows direct logical expression. The particular theorem proving technique used is the inverse method, which performs forward
Symbolic Negotiation with Linear Logic
 In Proceedings of the 4 th Int. Workshop on Computational Logic in MultiAgent Systems, CLIMA IV, Fort Lauderdale
, 2004
"... Negotiation over resources and multiagent planning are important issues in multiagent systems research. It has been demonstrated [19] how symbolic negotiation and distributed planning together could be formalised as distributed Linear Logic (LL) theorem proving. LL has been chosen mainly becau ..."
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Negotiation over resources and multiagent planning are important issues in multiagent systems research. It has been demonstrated [19] how symbolic negotiation and distributed planning together could be formalised as distributed Linear Logic (LL) theorem proving. LL has been chosen mainly because of its expressive power for representation of resources and its computationoriented nature. This paper extends the previous work by taking advantage of a richer fragment of LL and introducing two sorts of nondeterministic choices into negotiation. This allows agents to reason and negotiate under certain degree of uncertainty.