Trichotomies in the Complexity of Minimal Inference

Durand, Arnaud; Hermann, Miki; Nordh, Gustav

doi:10.1007/s00224-011-9320-0

Cited by 5 publications

(2 citation statements)

References 28 publications

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“…e.g. the recent papers (Durand, Hermann, and Nordh 2012;Thomas 2012;Bonatti, Lutz, and Wolter 2009) or the survey (Thomas and Vollmer 2010) -considerably less is known about the complexity of theorem proving in these logics. This is despite the fact that a number of quite different formalisms have been introduced for circumscription and minimal entailment (Olivetti 1992;Niemelä 1996;Bonatti and Olivetti 2002;Grimm and Hitzler 2009;Giordano et al 2013).…”

Section: Introductionmentioning

confidence: 99%

Tableau vs. Sequent Calculi for Minimal Entailment

Beyersdorff¹,

Chew²

2014

Preprint

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In this paper we compare two proof systems for minimal entailment: a tableau system OTAB and a sequent calculus MLK , both developed by Olivetti (1992). Our main result shows that OTAB-proofs can be efficiently translated into MLK -proofs, i.e., MLK psimulates OTAB . The simulation is technically very involved and answers an open question posed by Olivetti (1992) on the relation between the two calculi. We also show that the two systems are exponentially separated, i.e., there are formulas which have polynomialsize MLK -proofs, but require exponential-size OTABproofs. * Supported by a grant from the John Templeton Foundation.† Supported by a Doctoral Training Grant from EPSRC.

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Section: Introductionmentioning

confidence: 99%

Tableau vs. Sequent Calculi for Minimal Entailment

Beyersdorff¹,

Chew²

2014

Preprint

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“…the recent articles [7,14,29]). In particular, deciding circumscriptive inference is harder than for propositional logic as it is complete for Π of proof systems and determine whether proofs can be efficiently translated between different formalisms.…”

Section: Introductionmentioning

confidence: 99%

The Complexity of Theorem Proving in Circumscription and Minimal Entailment

Beyersdorff

Chew

2014

Automated Reasoning

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Abstract. We provide the first comprehensive proof-complexity analysis of different proof systems for propositional circumscription. In particular, we investigate two sequent-style calculi: MLK defined by Olivetti [28] and CIRC introduced by Bonatti and Olivetti [8], and the tableaux calculus NTAB suggested by Niemelä [26]. In our analysis we obtain exponential lower bounds for the proof size in NTAB and CIRC and show a polynomial simulation of CIRC by MLK . This yields a chain NTAB

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Minimal Inference Problem Over Finite Domains: The Landscape of Complexity

Wrona

2017

Logic Programming and Nonmonotonic Reasoning

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Trichotomies in the Complexity of Minimal Inference

Cited by 5 publications

References 28 publications

Tableau vs. Sequent Calculi for Minimal Entailment

Tableau vs. Sequent Calculi for Minimal Entailment

The Complexity of Theorem Proving in Circumscription and Minimal Entailment

Minimal Inference Problem Over Finite Domains: The Landscape of Complexity

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