On the computational cost of disjunctive logic programming: Propositional case

Eiter, Thomas; Gottlob, Georg

doi:10.1007/bf01536399

Cited by 279 publications

(327 citation statements)

References 39 publications

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“…every) consistent answer set S of B ∪H satisfies O ⊆ S is P 2 -complete (resp. P 2 -complete) (Eiter and Gottlob 1995). Hence, the result holds.…”

Section: Deciding Whether a Given Hypothesis Is A Solution Of Brave Imentioning

confidence: 53%

“…In this case, two different types of inferences, brave inference and cautious inference, are considered in nonmonotonic logics (McDermott 1982) and disjunctive logic programs (Eiter and Gottlob 1995). Under the minimal model semantics, a formula F is a consequence of brave inference in a theory T if F is true in some minimal model of T .…”

Section: Brave Inference and Cautious Inferencementioning

confidence: 99%

“…This is a task of the extended GCWA and is known P 2 -complete (Eiter and Gottlob 1995), so that the verification problem is P 2 -complete. In case of cautious induction, H becomes a solution iff B ∧ H |= O iff B ∧ H ∧ ¬O is inconsistent.…”

Section: Deciding Whether a Given Hypothesis Is A Solution Of Brave Imentioning

confidence: 99%

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Brave induction: a logical framework for learning from incomplete information

Sakama

Inoue

2009

Mach Learn

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This paper introduces a novel logical framework for concept-learning called brave induction. Brave induction uses brave inference for induction and is useful for learning from incomplete information. Brave induction is weaker than explanatory induction which is normally used in inductive logic programming, and is stronger than learning from satisfiability, a general setting of concept-learning in clausal logic. We first investigate formal properties of brave induction, then develop an algorithm for computing hypotheses in full clausal theories. Next we extend the framework to induction in nonmonotonic logic programs. We analyze computational complexity of decision problems for induction on propositional theories. Further, we provide examples of problem solving by brave induction in systems biology, requirement engineering, and multiagent negotiation.

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“…every) consistent answer set S of B ∪H satisfies O ⊆ S is P 2 -complete (resp. P 2 -complete) (Eiter and Gottlob 1995). Hence, the result holds.…”

Section: Deciding Whether a Given Hypothesis Is A Solution Of Brave Imentioning

confidence: 53%

Section: Brave Inference and Cautious Inferencementioning

confidence: 99%

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Brave induction: a logical framework for learning from incomplete information

Sakama

Inoue

2009

Mach Learn

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“…The more difficult checking part of our encoding also uses metaprogramming, but combined with a saturation technique that exploits the minimality criterion of answer sets for disjunctive programs, which is e.g. used in [3] to show Σ P 2 -hardness of disjunctive logic programs under the ASP semantics. The rest of this paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Computing Fuzzy Answer Sets Using dlvhex

2007

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Abstract. Fuzzy answer set programming has been introduced as a framework that successfully combines the concepts of answer set programming and fuzzy logic. In this paper, we show how the fuzzy answer set semantics can be mapped onto the semantics for HEX-programs, which are nonmonotonic logic programs under the answer set semantics that support the use of external function calls. By using the DLVHEX reasoning engine, we so devise a vehicle for effectively computing fuzzy answer sets.

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“…The latter is quite well understood, and detailed pictures of the complexity for ASP and major extensions are given in [4,5,10,13,35,42], for ground (propositional) and non-ground programs (with variables, but without function symbols, i.e., the Datalog case); see [8] for a survey. Consistency checking of non-ground (disjunctive) ASP programs has complexity NEXP NP , i.e., non-deterministic exponential time with an oracle for NP, and thus provides a powerful host for problem solving.…”

mentioning

confidence: 99%

Complexity results for answer set programming with bounded predicate arities and implications

Eiter

Faber

Fink

et al. 2007

Ann Math Artif Intell

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Answer set programming is a declarative programming paradigm rooted in logic programming and non-monotonic reasoning. This formalism has become a host for expressing knowledge representation problems, which reinforces the interest in efficient methods for computing answer sets of a logic program. The complexity of various reasoning tasks for general answer set programming has been amply studied and is understood quite well. In this paper, we present a language fragment in which the arities of predicates are bounded by a constant. Subsequently, we analyze the complexity of various reasoning tasks and computational problems for this fragment, comprising answer set existence, brave and cautious reasoning, and strong equivalence. Generally speaking, it turns out that the complexity drops significantly with respect to the full non-ground language, but is still harder than for the respective ground or propositional languages. These results have several implications, most importantly for solver implementations: Virtually all currently available solvers have exponential (in the size of the input) space requirements even for programs with bounded predicate arities, while our results indicate that for those programs polynomial space should be sufficient. This can be seen as a manifestation of the "grounding bottleneck" (meaning that programs are first instantiated and then solved) from which answer set programming solvers currently suffer. As a final contribution, we provide a sketch of a method that can avoid the exponential space requirement for programs with bounded predicate arities.

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On the computational cost of disjunctive logic programming: Propositional case

Cited by 279 publications

References 39 publications

Brave induction: a logical framework for learning from incomplete information

Brave induction: a logical framework for learning from incomplete information

Computing Fuzzy Answer Sets Using dlvhex

Complexity results for answer set programming with bounded predicate arities and implications

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