Logic Programming and Autoepistemic Logics: New Relations and Complexity Results

@inproceedings{Schaerf1993LogicPA,
  title={Logic Programming and Autoepistemic Logics: New Relations and Complexity Results},
  author={Marco Schaerf},
  booktitle={AI*IA},
  year={1993}
}
  • M. Schaerf
  • Published in AI*IA 26 October 1993
  • Computer Science
In recent years, many authors have pointed out the strict correlation between non-Horn logic programs and non-monotonic reasoning. As a result, many studies on the relations between various semantics for negation and non-monotonic logics have appeared in the literature. The analysis of these relations helps understanding the properties of the various systems and allows importing analysis from one formalism into another one. In this paper we show a one-to-one mapping between the positivistic… 

Complexity Results for Disjunctive Logic Programming and Application to Nonmonotonic Logics

TLDR
Strong evidence is provided that deciding the existence of an answer set and deciding occurrence of literals in any respectively every answer sets of a nite propositional EDLP are shown to be complete for classes within the polynomial hierarchy.

Negation and minimality in non-horn databases

TLDR
This work generalizes the semantics for negation in logic programs, putting together the constructive nature of the rule-based deductive databases with the syntax-independence of the closed-world reasoning rules.

Negation and Minimality in Disjunctive Databases

A Survey of Complexity Results for Nonmonotonic Logics

On the computational cost of disjunctive logic programming: Propositional case

TLDR
This paper shows that the consistency check is Σ2p-complete for the disjunctive stable model semantics, the iterated closed world assumption, and the perfect model semantics; analogous results are derived for the answer sets semantics of extendeddisjunctive logic programs.

Complexity aspects of various semantics for disjunctive databases

This paper addresses complexity issues for important problems arising with disjunctive databases. In particular, the complexity of inference of a literal and a formula from a propositional

References

SHOWING 1-10 OF 18 REFERENCES

Computing Intersection of Autoepistemic Expansions

TLDR
This paper describes a method that assigns to a modal theory I a propositional theory PI and to amodal-free formula φ another formulaπ in such a manner that φ is in the intersection of all expansions of I if and only if PI ⊢ φ .

Autoepistemic logic

TLDR
It is proven that the problem of existence of stable models is NP-complete and the definition of stratified theories is extended and efficient algorithms for testing whether atheory is stratified are proposed.

Positivism vs minimalism in deductive databases

TLDR
Three formalizations of the Closed World Assumption which accommodate disjunctive informaticn are compared and positivism is compared, in both static and dynamic contexts, showing that positivism an’d minimalism are “non-monotonic”.

The well-founded semantics for general logic programs

TLDR
It is shown that the class of programs possessing a total well-founded model properly includes previously studied classes of "stratified" and "locally stratified" programs, and is compared with other proposals in the literature.

The Polynomial-Time Hierarchy

  • L. Stockmeyer
  • Computer Science, Mathematics
    Theor. Comput. Sci.
  • 1976