Semantical considerations on nonmonotonic logic
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Satisfiability in many-valued sentential logic is NP-complete
Theoretical Computer Science
Artificial Intelligence
Equivalences of logic programs
Foundations of deductive databases and logic programming
Foundations of deductive databases and logic programming
On the relationship between circumscription and negation as failure
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Logic programming with strong negation
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Between circumscription and autoepistemic logic
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A study of nonmonotonic reasoning
A study of nonmonotonic reasoning
Extended logic programs as autoepistemic theories
Proceedings of the second international workshop on Logic programming and non-monotonic reasoning
Reflexive autoepistemic logic and logic programming
Proceedings of the second international workshop on Logic programming and non-monotonic reasoning
Minimal knowledge + negation as failure = only knowing (sometimes)
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Handbook of logic in artificial intelligence and logic programming (vol. 3)
Proceedings of the eleventh international conference on Logic programming
Reducing disjunctive to non-disjunctive semantics by shift-operations
Fundamenta Informaticae - Special issue: to the memory of Prof. Helena Rasiowa
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Strongly equivalent logic programs
ACM Transactions on Computational Logic (TOCL) - Special issue devoted to Robert A. Kowalski
Extending and implementing the stable model semantics
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Computers and Intractability: A Guide to the Theory of NP-Completeness
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Knowledge Representation, Reasoning, and Declarative Problem Solving
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Nested expressions in logic programs
Annals of Mathematics and Artificial Intelligence
Fages' Theorem for Programs with Nested Expressions
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ICLP '02 Proceedings of the 18th International Conference on Logic Programming
Testing the Equivalence of Logic Programs under Stable Model Semantics
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
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NMELP '96 Selected papers from the Non-Monotonic Extensions of Logic Programming
A Tableau Calculus for Equilibrium Entailment
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Modal Nonmonotonic Logics Revisited: Efficient Encodings for the Basic Reasoning Tasks
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Lemma and Model Caching in Decision Procedures for Quantified Boolean Formulas
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Solving Advanced Reasoning Tasks Using Quantified Boolean Formulas
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Logic programming with ordered disjunction
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ASSAT: computing answer sets of a logic program by SAT solvers
Eighteenth national conference on Artificial intelligence
Backjumping for quantified Boolean logic satisfiability
Artificial Intelligence
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
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AI Communications
Theory and Practice of Logic Programming
Strong equivalence made easy: nested expressions and weight constraints
Theory and Practice of Logic Programming
Characterization of strongly equivalent logic programs in intermediate logics
Theory and Practice of Logic Programming
Autoepistemic logic and introspective circumscription
TARK '94 Proceedings of the 5th conference on Theoretical aspects of reasoning about knowledge
On Computing Belief Change Operations using Quantified Boolean Formulas
Journal of Logic and Computation
The DLV system for knowledge representation and reasoning
ACM Transactions on Computational Logic (TOCL)
A generalization of the Lin-Zhao theorem
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Annals of Mathematics and Artificial Intelligence
cc{\rm T}: A Tool for Checking Advanced Correspondence Problems in Answer-Set Programming
CIC '06 Proceedings of the 15th International Conference on Computing
Semantical characterizations and complexity of equivalences in answer set programming
ACM Transactions on Computational Logic (TOCL)
Propositional theories are strongly equivalent to logic programs
Theory and Practice of Logic Programming
A common view on strong, uniform, and other notions of equivalence in answer-set programming*
Theory and Practice of Logic Programming
Modular Equivalence for Normal Logic Programs
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
A Solver for QBFs in Nonprenex Form
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Elementary sets for logic programs
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Properties of programs with monotone and convex constraints
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
A reductive semantics for counting and choice in answer set programming
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Hyperequivalence of logic programs with respect to supported models
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Constructing conditional plans by a theorem-prover
Journal of Artificial Intelligence Research
Embedding non-ground logic programs into autoepistemic logic for knowledge-base combination
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
A new perspective on stable models
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
On the equivalence between answer sets and models of completion for nested logic programs
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
On solution correspondences in answer-set programming
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Strong equivalence for logic programs with preferences
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
A model-theoretic counterpart of loop formulas
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
A characterization of strong equivalence for logic programs with variables
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
ICLP'07 Proceedings of the 23rd international conference on Logic programming
Temporal equilibrium logic: a first approach
EUROCAST'07 Proceedings of the 11th international conference on Computer aided systems theory
FoIKS'08 Proceedings of the 5th international conference on Foundations of information and knowledge systems
Towards implementations for advanced equivalence checking in answer-set programming
ICLP'05 Proceedings of the 21st international conference on Logic Programming
Answer sets for propositional theories
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
Testing strong equivalence of datalog programs – implementation and examples
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
SELP – a system for studying strong equivalence between logic programs
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
CMODELS: SAT-based disjunctive answer set solver
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
cc⊤: a correspondence-checking tool for logic programs under the answer-set semantics
JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Reducing propositional theories in equilibrium logic to logic programs
EPIA'05 Proceedings of the 12th Portuguese conference on Progress in Artificial Intelligence
Representing paraconsistent reasoning via quantified propositional logic
Inconsistency Tolerance
Equivalence between extended datalog programs -- a brief survey
Datalog'10 Proceedings of the First international conference on Datalog Reloaded
Forgetting for answer set programs revisited
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Strong equivalence of qualitative optimization problems
Journal of Artificial Intelligence Research
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Equilibrium logic is an approach to non-monotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations are permitted in heads and bodies of rules, as special kinds of theories. In this paper, we present polynomial reductions of the main reasoning tasks associated with equilibrium logic and nested logic programs into quantified propositional logic, an extension of classical propositional logic where quantifications over atomic formulas are permitted. Thus, quantified propositional logic is a fragment of second-order logic, and its formulas are usually referred to as quantified Boolean formulas (QBFs). We provide reductions not only for decision problems, but also for the central semantical concepts of equilibrium logic and nested logic programs. In particular, our encodings map a given decision problem into some QBF such that the latter is valid precisely in case the former holds. The basic tasks we deal with here are the consistency problem, brave reasoning and skeptical reasoning. Additionally, we also provide encodings for testing equivalence of theories or programs under different notions of equivalence, viz. ordinary, strong and uniform equivalence. For all considered reasoning tasks, we analyse their computational complexity and give strict complexity bounds. Hereby, our encodings yield upper bounds in a direct manner. Besides this useful feature, our approach has the following benefits: First, our encodings yield a uniform axiomatisation for a variety of problems in a common language. Second, extant solvers for QBFs can be used as back-end inference engines to realise implementations of the encoded task in a rapid prototyping manner. Third, our axiomatisations also allow us to straightforwardly relate equilibrium logic with circumscription.