Theory of linear and integer programming
Theory of linear and integer programming
Theoretical Computer Science
Satisfiability in many-valued sentential logic is NP-complete
Theoretical Computer Science
The mixed integer linear bilevel programming problem
Operations Research
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Stability analysis and design of fuzzy control systems
Fuzzy Sets and Systems
Theoretical Computer Science
Complexity results for disjunctive logic programming and application to nonmonotonic logics
ILPS '93 Proceedings of the 1993 international symposium on Logic programming
The complexity of logic-based abduction
Journal of the ACM (JACM)
Fuzzy relation equations and causal reasoning
Fuzzy Sets and Systems - Special issue: fuzzy relations, part 2
What are fuzzy rules and how to use them
Fuzzy Sets and Systems - Special issue dedicated to the memory of Professor Arnold Kaufmann
ACM Transactions on Database Systems (TODS)
Abduction from logic program: semantics and complexity
Theoretical Computer Science
Annotated fuzzy logic programs
Fuzzy Sets and Systems
Strongly equivalent logic programs
ACM Transactions on Computational Logic (TOCL) - Special issue devoted to Robert A. Kowalski
Fril- Fuzzy and Evidential Reasoning in Artificial Intelligence
Fril- Fuzzy and Evidential Reasoning in Artificial Intelligence
Knowledge Representation, Reasoning, and Declarative Problem Solving
Knowledge Representation, Reasoning, and Declarative Problem Solving
Possibility Theory, Probability Theory and Multiple-Valued Logics: A Clarification
Annals of Mathematics and Artificial Intelligence
Finiteness in Infinite-Valued Σukasiewicz Logic
Journal of Logic, Language and Information
A Multi-adjoint Logic Approach to Abductive Reasoning
Proceedings of the 17th International Conference on Logic Programming
Hybrid Probabilistic Logic Programs as Residuated Logic Programs
JELIA '00 Proceedings of the European Workshop on Logics in Artificial Intelligence
LPNMR '01 Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning
A New Logical Characterisation of Stable Models and Answer Sets
NMELP '96 Selected papers from the Non-Monotonic Extensions of Logic Programming
Hypersequent and the Proof Theory of Intuitionistic Fuzzy Logic
Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic
Two Connections Between Linear Logic and Lukasiewicz Logics
KGC '97 Proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory
Multi-adjoint Logic Programming with Continuous Semantics
LPNMR '01 Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning
Abductive reasoning and measures of similitude in the presence of fuzzy rules
Fuzzy Sets and Systems - Special issue: Preference modelling and applications
Extending Answer Sets for Logic Programming Agents
Annals of Mathematics and Artificial Intelligence
ASSAT: computing answer sets of a logic program by SAT solvers
Artificial Intelligence - Special issue on nonmonotonic reasoning
Possibilistic uncertainty handling for answer set programming
Annals of Mathematics and Artificial Intelligence
Annals of Mathematics and Artificial Intelligence
An introduction to fuzzy answer set programming
Annals of Mathematics and Artificial Intelligence
Compiling Fuzzy Answer Set Programs to Fuzzy Propositional Theories
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
Quantified Equilibrium Logic and Foundations for Answer Set Programs
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
Resolution method for mixed integer bi-level linear problems based on decomposition technique
Journal of Global Optimization
General Fuzzy Answer Set Programs
WILF '09 Proceedings of the 8th International Workshop on Fuzzy Logic and Applications
ICLP '09 Proceedings of the 25th International Conference on Logic Programming
Mixed-integer programming methods for finding Nash equilibria
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Pure Nash equilibria: hard and easy games
Journal of Artificial Intelligence Research
Answer Sets in a Fuzzy Equilibrium Logic
RR '09 Proceedings of the 3rd International Conference on Web Reasoning and Rule Systems
RR'07 Proceedings of the 1st international conference on Web reasoning and rule systems
Computing fuzzy answer sets using DLVHEX
ICLP'07 Proceedings of the 23rd international conference on Logic programming
Answer sets for propositional theories
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
LPOD answer sets and nash equilibria
ASIAN'04 Proceedings of the 9th Asian Computing Science conference on Advances in Computer Science: dedicated to Jean-Louis Lassez on the Occasion of His 5th Cycle Birthday
Interpolation of fuzzy data: Analytical approach and overview
Fuzzy Sets and Systems
Analysing and extending well-founded and partial stable semantics using partial equilibrium logic
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
International Journal of Approximate Reasoning
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In this article, we introduce fuzzy equilibrium logic as a generalization of both Pearce equilibrium logic and fuzzy answer set programming. The resulting framework combines the capability of equilibrium logic to declaratively specify search problems, with the capability of fuzzy logics to model continuous domains. We show that our fuzzy equilibrium logic is a proper generalization of both Pearce equilibrium logic and fuzzy answer set programming, and we locate the computational complexity of the main reasoning tasks at the second level of the polynomial hierarchy. We then provide a reduction from the problem of finding fuzzy equilibrium logic models to the problem of solving a particular bilevel mixed integer program (biMIP), allowing us to implement reasoners by reusing existing work from the operations research community. To illustrate the usefulness of our framework from a theoretical perspective, we show that a well-known characterization of strong equivalence in Pearce equilibrium logic generalizes to our setting, yielding a practical method to verify whether two fuzzy answer set programs are strongly equivalent. Finally, to illustrate its application potential, we show how fuzzy equilibrium logic can be used to find strong Nash equilibria, even when players have a continuum of strategies at their disposal. As a second application example, we show how to find abductive explanations from Łukasiewicz logic theories.