Proof and Model Generation with Disconnection Tableaux

Letz, Reinhold; Stenz, Gernot

doi:10.1007/3-540-45653-8_10

Cited by 28 publications

(19 citation statements)

References 12 publications

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“…The Disconnection Tableau Calculus calculus has been developed by Billon [Bil96] and Letz and Stenz [LS01,Ste02]. In order to define development of a disconnection tableau, we need the notions of links, paths and tableaux:…”

Section: The Disconnection Tableau Calculusmentioning

confidence: 99%

“…There are calculi which arrange instances in a tree or a tableau, integrating an implicit satisfiability check. This approach is used by the disconnection tableau calculus [Bil96,LS01,Ste02], as well as by Baumgartner's FDPLL [Bau00] and the model evolution calculus [BT03]. Other procedures separate instance generation and satisfiability test.…”

Section: Introductionmentioning

confidence: 99%

“…For a comprehensive description, we refer to Letz and Stenz [LS01,Ste02] for DCC, Ganzinger and Korovin [GK03] for SInst-Gen, and Hooker et al [HRCR02] for PPI.…”

Section: Introducing the Calculimentioning

confidence: 99%

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Comparing Instance Generation Methods for Automated Reasoning

Jacobs

Waldmann

2005

Lecture Notes in Computer Science

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Abstract. The clause linking technique of Lee and Plaisted proves the unsatisfiability of a set of first-order clauses by generating a sufficiently large set of instances of these clauses that can be shown to be propositionally unsatisfiable. In recent years, this approach has been refined in several directions, leading to both tableau-based methods, such as the Disconnection Tableau Calculus, and saturation-based methods, such as Primal Partial Instantiation and Resolution-based Instance Generation. We investigate the relationship between these calculi and answer the question to what extent refutation or consistency proofs in one calculus can be simulated in another one.

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Section: The Disconnection Tableau Calculusmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Comparing Instance Generation Methods for Automated Reasoning

Jacobs

Waldmann

2005

Lecture Notes in Computer Science

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“…Instantiation-based methods can be divided into two major categories: (i) finegrained interleaving of instantiation with efficient propositional inference rules, and (ii) modular combination of instantiation and propositional reasoning. Examples from the first category include the disconnection calculus (DCTP) [8,24], which combines instance generation with an efficient tableau data structure, and the model evolution calculus (ME) [6], which interleaves instance generation with DPLL style reasoning. Both DCTP and ME methods have advanced implementations DCTP [33] and Darwin [3], respectively.…”

mentioning

confidence: 99%

Instantiation-Based Automated Reasoning: From Theory to Practice

Korovin

2009

Automated Deduction – CADE-22

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Instantiation-based automated reasoning aims at combining the efficiency of propositional SAT and SMT technologies with the expressiveness of firstorder logic. Propositional SAT and SMT solvers are probably the most successful reasoners applied to real-world problems, due to extremely efficient propositional methods and optimized implementations. However, the expressiveness of firstorder logic is essential in many applications ranging from formal verification of software and hardware to knowledge representation and querying. Therefore, there is a growing demand to integrate efficient propositional and more generally ground reasoning modulo theories into first-order reasoning.The basic idea behind instantiation-based reasoning is to interleave smart generation of instances of first-order formulae with propositional type reasoning. Instantiation-based methods can be divided into two major categories: (i) finegrained interleaving of instantiation with efficient propositional inference rules, and (ii) modular combination of instantiation and propositional reasoning. Examples from the first category include the disconnection calculus (DCTP) [8,24], which combines instance generation with an efficient tableau data structure, and the model evolution calculus (ME) [6], which interleaves instance generation with DPLL style reasoning. Both DCTP and ME methods have advanced implementations DCTP [33] and Darwin [3], respectively.Our approach to instantiation-based reasoning [15,21] falls into the second category, where propositional reasoning is integrated in a modular fashion and was inspired by work on hyper-linking and its extensions (see [23,31,18]). The main advantage of the modular combination is that it allows one to use off-theshelf SAT/SMT solvers in the context of first-order reasoning. One of our main goals was to develop a flexible theoretical framework, called Inst-Gen, for modular combination of instantiation with propositional reasoning and more generally with ground reasoning modulo theories. This framework provides methods for proving completeness of instantiation calculi, powerful redundancy elimination criteria and flexible saturation strategies. All these ingredients are crucial for developing reasoning systems which can be used in practical applications. We also show that most of the powerful machinery developed in the resolution-based framework can be suitably adapted for the Inst-Gen method.Based on these theoretical results we have developed and implemented an automated reasoning system, called iProver [22]. iProver features state-of-theart implementation techniques such as unification and simplification indexes;Supported by The Royal Society

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“…In our case, we encode tableau proofs, because we suspect that SAT solver will be able to direct its search better in that case. We can also compare our recent work with recent papers on instantiationbased theorem proving, which either try to use a SAT solver to create a first order model [6], or else try to use DPLL-like methods directly on first order clauses [3,5,14,19,2]. Those are completely different approaches.…”

Section: Resultsmentioning

confidence: 99%

Encoding First Order Proofs in SAT

Deshane

Jablonski

et al.

Automated Deduction – CADE-21

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Abstract. We present a method for proving rigid first order theorems by encoding them as propositional satisfiability problems. We encode the existence of a first order connection tableau and the satisfiability of unification constraints. Then the first order theorem is rigidly unsatisfiable if and only if the encoding is propositionally satisfiable. We have implemented this method in our theorem prover CHEWTPTP, and present experimental results. This method can be useful for general first order problems, by continually adding more instances of each clause.

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Proof and Model Generation with Disconnection Tableaux

Cited by 28 publications

References 12 publications

Comparing Instance Generation Methods for Automated Reasoning

Comparing Instance Generation Methods for Automated Reasoning

Instantiation-Based Automated Reasoning: From Theory to Practice

Encoding First Order Proofs in SAT

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