78 research outputs found
On the Relationship between Quantified Reflective Logic and Quantified Default Logic
Reflective Logic and Default Logic are both generalized so as to allow universally quantified
variables to cross modal scopes whereby the Barcan formula and its converse hold. This is done by
representing both the fixed-point equation for Reflective Logic and the fixed-point equation for Default both as
necessary equivalences in the Modal Quantificational Logic Z. and then inserting universal quantifiers before
the defaults. The two resulting systems, called Quantified Reflective Logic and Quantified Default Logic, are
then compared by deriving metatheorems of Z that express their relationships. The main result is to show that
every solution to the equivalence for Quantified Default Logic is a strongly grounded solution to the
equivalence for Quantified Reflective Logic. It is further shown that Quantified Reflective Logic and
Quantified Default Logic have exactly the same solutions when no default has an entailment condition
Epistemic Foundation of Stable Model Semantics
Stable model semantics has become a very popular approach for the management
of negation in logic programming. This approach relies mainly on the closed
world assumption to complete the available knowledge and its formulation has
its basis in the so-called Gelfond-Lifschitz transformation.
The primary goal of this work is to present an alternative and
epistemic-based characterization of stable model semantics, to the
Gelfond-Lifschitz transformation. In particular, we show that stable model
semantics can be defined entirely as an extension of the Kripke-Kleene
semantics. Indeed, we show that the closed world assumption can be seen as an
additional source of `falsehood' to be added cumulatively to the Kripke-Kleene
semantics. Our approach is purely algebraic and can abstract from the
particular formalism of choice as it is based on monotone operators (under the
knowledge order) over bilattices only.Comment: 41 pages. To appear in Theory and Practice of Logic Programming
(TPLP
Epistemic Equilibrium Logic
International audienceWe add epistemic modal operators to the language of here-and-there logic and define epistemic here-and-there models.We then successively define epistemic equilibrium models and autoepistemic equilibrium models. The former are obtained from here-and-there models by the standard minimisation of truth of Pearce’s equilibrium logic; they provide an epistemic extension of that logic. The latter are obtained from the former by maximising the set of epistemic possibilities; they provide a new semantics for Gelfond’s epistemic specifications. For both definitions we characterise strong equivalence by means of logical equivalence in epistemic here-and-there logic
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