3. Tableau Model Elimination

Baumgartner, Peter

doi:10.1007/10692875_3

Cited by 2 publications

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“…Those inferences determine the unifiers σ 1 , σ 2 and σ 3 which are subsequent approximations of the simultaneous T -unifier of the three connections. We have θ = σ 1 σ 2 σ 3 for σ 1 …”

Section: Proposition 43 Suppose That the T -Unification Problem Is mentioning

confidence: 99%

“…The background reasoner is consulted whenever the meaning of special built-ins must be considered. There is a number of results for building in theories [1,20,6,3]. Those results form a general framework for building in theories.…”

Section: Introductionmentioning

confidence: 99%

“…Many improvements of resolution have been shown as special kinds of theory resolution in [22]. For a treatment of the lifting to the full first-order calculus see [1] or [19]. Another approach considering theories given by classes of models has been presented by Hans-Jürgen Bürckert [6].…”

Section: Introductionmentioning

confidence: 99%

“…One way to achieve this behavior is the integration of different calculi. This led to so called hybrid reasoning [22,1,10,20] which means the integration of a general purpose foreground reasoner with a specialized background reasoner. A typical task of a background reasoner is to perform special purpose inference rules according to a built-in theory.…”

mentioning

confidence: 99%

“…For this purpose we use a generic approach described in [20]. This more detailed view on built-in theories is not covered by the known general approaches [1,3,6,20] for building in theories into theorem provers. The approach is demonstrated by its application to the target calculi of the algebraic translation [9] of multi-modal and extended multi-modal [7] logic to first-order logic.…”

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confidence: 99%

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Theorem proving with built-in hybrid theories

Petermann

2004

LLP

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Abstract. A growing number of applications of automated reasoning exhibits the necessity of flexible deduction systems. A deduction system should be able to execute inference rules which are appropriate to the given problem. One way to achieve this behavior is the integration of different calculi. This led to so called hybrid reasoning [22,1,10,20] which means the integration of a general purpose foreground reasoner with a specialized background reasoner. A typical task of a background reasoner is to perform special purpose inference rules according to a built-in theory. The aim of this paper is to go a step further, i.e. to treat the background reasoner as a hybrid system itself. The paper formulates sufficient criteria for the construction of complete calculi which enable reasoning under hybrid theories combined from sub-theories. For this purpose we use a generic approach described in [20]. This more detailed view on built-in theories is not covered by the known general approaches [1,3,6,20] for building in theories into theorem provers. The approach is demonstrated by its application to the target calculi of the algebraic translation [9] of multi-modal and extended multi-modal [7] logic to first-order logic.

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Section: Proposition 43 Suppose That the T -Unification Problem Is mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Theorem proving with built-in hybrid theories

Petermann

2004

LLP

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Connection Calculus Theorem Proving with Multiple Built-in Theories

Petermann

2000

Journal of Symbolic Computation

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Gradually more applications of automated reasoning are discovered. This development has the consequence that deduction systems need to be increasingly flexible. They should exhibit a behavior appropriate to a given problem. One way to achieve this behavior is the integration of different systems or calculi. This leads to the so-called hybrid reasoning (Stickel, 1985;Frisch, 1991;Baumgartner, 1992;Petermann, 1993a) which describes the integration of a general purpose foreground reasoner with one specialized theory reasoner. The aim of this paper is to go a step further, i.e. to treat the theory reasoner as a hybrid system itself. The framework proposed below is suitable for building multiple theories into theorem provers. Those theories can be given syntactically but also semantically. Here, semantical reasoning is understood as reasoning, or rather computing, under a theory given by a class of models, whereas syntactical reasoning means reasoning under a theory given by first-order axioms. The presented approach is a generalization of previous attempts of combining syntactical reasoning under the empty theory with semantical reasoning (Bürckert, 1994;Baumgartner and Stolzenburg, 1995), of combining different theories given syntactically (Petermann, 1997) or just theory (or hybrid) reasoning. The paper formulates sufficient criteria for the construction of complete calculi which enable reasoning under hybrid theories combined from sub-theories given semantically and those given syntactically and briefly reports experimental work.

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3. Tableau Model Elimination

Cited by 2 publications

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Theorem proving with built-in hybrid theories

Theorem proving with built-in hybrid theories

Connection Calculus Theorem Proving with Multiple Built-in Theories

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