On the restricted equivalence for subclasses of propositional logic

Flögel, Andreas; Büning, Hans Kleine; Lettmann, Theodor

doi:10.1051/ita/1993270403271

Cited by 4 publications

(8 citation statements)

References 7 publications

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“…Thus, in terms of the knowledge base application, the new variable z can be thought of as being internal to the knowledge base and invisible to the user. Flögel et al [17] showed that deciding the equivalence of such extended Horn formulas is co-NP-complete. This is bad news as it shows that the extended version is too expressive and therefore intractable 5 .…”

Section: Contributions Of This Papermentioning

confidence: 99%

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On Approximate Horn Formula Minimization

Bhattacharya

DasGupta

Mubayi

et al. 2010

Automata, Languages and Programming

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The minimization problem for Horn formulas is to find a Horn formula equivalent to a given Horn formula, using a minimum number of clauses. A 2 log 1−ǫ (n) -inapproximability result is proven, which is the first inapproximability result for this problem. We also consider several other versions of Horn minimization. The more general version which allows for the introduction of new variables is known to be too difficult as its equivalence problem is co-NP-complete. Therefore, we propose a variant called Steinerminimization, which allows for the introduction of new variables in a restricted manner. Steiner-minimization of Horn formulas is shown to be MAX-SNP-hard. In the positive direction, a o(n), namely, O(n log log n/(log n) 1/4 )-approximation algorithm is given for the Steiner-minimization of definite Horn formulas. The algorithm is based on a new result in algorithmic extremal graph theory, on partitioning bipartite graphs into complete bipartite graphs, which may be of independent interest. Inapproximability results and approximation algorithms are also given for restricted versions of Horn minimization, where only clauses present in the original formula may be used.

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Section: Contributions Of This Papermentioning

confidence: 99%

“…Thus the following result of [17] suggests that general extensions of Horn formulas are too general for applications.…”

Section: Definition 1 (Generalized Equivalence)mentioning

confidence: 99%

On Approximate Horn Formula Minimization

Bhattacharya

DasGupta

Mubayi

et al. 2010

Automata, Languages and Programming

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“…They are satisfied by the same partial models that do not evaluate z. Excluding variables from the comparison is restricted equivalence [FKL93].…”

Section: Common Equivalencementioning

confidence: 99%

“…Forgetting and introducing variables have something in common: they both change the alphabet of the formula while retaining some of its consequences. This is formalized by restricted equivalence [FKL93], the equality of the consequences on a given subset of variables. When this subset comprises all variables, restricted equivalence is regular equivalence.…”

Section: Introductionmentioning

confidence: 99%

Common equivalence and size after forgetting

Liberatore¹

2020

Preprint

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Forgetting variables from a propositional formula may increase its size. Introducing new variables is a way to shorten it. Both operations can be expressed in terms of common equivalence, a weakened version of equivalence. In turn, common equivalence can be expressed in terms of forgetting. An algorithm for forgetting and checking common equivalence in polynomial space is given for the Horn case; it is polynomialtime for the subclass of single-head formulae. Minimizing after forgetting is polynomialtime if the formula is also acyclic and variables cannot be introduced, NP-hard when they can.

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“…Observe that for ontologies formulated as general TBoxes in description logics, the computational complexity of deciding Σ-entailment is by at least one exponential harder than the deduction problem, e.g., it is 2ExpTime-complete for expressive description logics such as ALC, ALCQ, and ALCQI [6,12] and ExpTime-complete for EL itself [13]. Moreover, even in such simple formalisms as acyclic propositional Horn Logic Σ-entailment is co-NP-complete [5].…”

Section: Introductionmentioning

confidence: 99%

The Logical Difference Problem for Description Logic Terminologies

Konev

Walther

Wolter

Lecture Notes in Computer Science

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Abstract. We consider the problem of computing the logical difference between distinct versions of description logic terminologies. For the lightweight description logic EL, we present a tractable algorithm which, given two terminologies and a signature, outputs a set of concepts, which can be regarded as the logical difference between the two terminologies. In particular, it decides whether they imply the same concept implications in the signature. A prototype implementation CEX of this algorithm is presented and experimental results based on distinct versions of Snomed ct, the Systematized Nomenclature of Medicine, Clinical Terms, are discussed. Finally, results regarding the relation to uniform interpolants and possible extensions to more expressive description logics are presented.

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On the restricted equivalence for subclasses of propositional logic

Cited by 4 publications

References 7 publications

On Approximate Horn Formula Minimization

On Approximate Horn Formula Minimization

Common equivalence and size after forgetting

The Logical Difference Problem for Description Logic Terminologies

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