La logique modale des modèles d'équilibre

@article{Cerro2012LaLM,
  title={La logique modale des mod{\`e}les d'{\'e}quilibre},
  author={Luis Fari{\~n}as del Cerro and Andreas Herzig},
  journal={Rev. d'Intelligence Artif.},
  year={2012},
  volume={26},
  pages={85-102}
}
Here-an-there models and equilibrium models were investigated as a semantical framework for answer ensemble programming by Pearce, Cabalar, Lifschitz, Ferraris and oth- ers. The semantics of equilibrium logic is indirect in that the notion of satisfiability is defined in terms of satisfiability in the logic of here-and-there. We here give a direct semantics of equi- librium logic, stated in terms of a modal language into which the language of equilibrium logic can be embedded. 

Figures from this paper

References

SHOWING 1-10 OF 20 REFERENCES
The Modal Logic of Equilibrium Models
TLDR
Here-and-there models and equilibrium models were investigated as a semantical framework for answer set programming by Pearce, Cabalar, Lifschitz, Ferraris and others are investigated in terms of a modal language into which the language of equilibrium logic can be embedded.
A Tableau Calculus for Equilibrium Entailment
We apply tableau methods to the problem of computing entailment in the nonmonotonic system of equilibrium logic, a generalisation of the inference relation associated with the stable model and answer
A New Logical Characterisation of Stable Models and Answer Sets
TLDR
This paper relates inference in extended logic programming with nonclassical, nonmonotonic logics with equilibrium logic, and shows that on logic programs equilibrium logic coincides with the inference operation associated with the stable model and answer set semantics of Gelfond and Lifschitz.
Minimal Logic Programs
TLDR
This work proposes a method consisting in the generation of the set of prime implicates of the original theory, starting from its set of countermodels (in the logic of Here-and-There), in a similar vein to the Quine-McCluskey method forminimisation of boolean functions.
Possibilistic Stable Models
TLDR
This work defines a new framework to use notions from possibility theory to extend the stable model semantics by taking into account a certainty level, expressed in terms of necessity measure, on each rule of a normal logic program.
A New Perspective on Stable Models
TLDR
A new definition of a stable model is proposed, which covers many constructs used in answer set programming (including disjunctive rules, choice rules and conditional literals) and is based on a syntactic transformation, which turns a logic program into a formula of second-order logic that is similar to the formula familiar from the definition of circumscription.
Propositional theories are strongly equivalent to logic programs
TLDR
Any theory can always be reexpressed as a strongly equivalent disjunctive logic program, possibly with negation in the head, under the answer sets semantics.
Modal logic
TLDR
This paper shows how the tree or tableau method provides a simple and easily comprehensible decision procedure for systems such as K, T, S4 and S5 and how the formal techniques of modal logic can be used to analyse several informal problems involving modal concepts, including cases combining modality with quantification.
Possibilistic uncertainty handling for answer set programming
TLDR
This work uses possibility theory to extend the non monotonic semantics of stable models for logic programs with default negation by means of a possibility distribution, and defines a clear semantics of such programs by introducing what is a possibilistic stable model.
Strongly equivalent logic programs
TLDR
The main theorem shows that the verification of strong equivalence can be accomplished by cheching the equivalence of formulas in a monotonic logic, called the logic of here-and-there, which is intermediate between classical logic and intuitionistic logic.
...
...