3 research outputs found
Space Efficiency of Propositional Knowledge Representation Formalisms
We investigate the space efficiency of a Propositional Knowledge
Representation (PKR) formalism. Intuitively, the space efficiency of a
formalism F in representing a certain piece of knowledge A, is the size of the
shortest formula of F that represents A. In this paper we assume that knowledge
is either a set of propositional interpretations (models) or a set of
propositional formulae (theorems). We provide a formal way of talking about the
relative ability of PKR formalisms to compactly represent a set of models or a
set of theorems. We introduce two new compactness measures, the corresponding
classes, and show that the relative space efficiency of a PKR formalism in
representing models/theorems is directly related to such classes. In
particular, we consider formalisms for nonmonotonic reasoning, such as
circumscription and default logic, as well as belief revision operators and the
stable model semantics for logic programs with negation. One interesting result
is that formalisms with the same time complexity do not necessarily belong to
the same space efficiency class
Where Fail-Safe Default Logics Fail
Reiter's original definition of default logic allows for the application of a
default that contradicts a previously applied one. We call failure this
condition. The possibility of generating failures has been in the past
considered as a semantical problem, and variants have been proposed to solve
it. We show that it is instead a computational feature that is needed to encode
some domains into default logic
On the Intertranslatability of Autoepistemic, Default and Priority Logics, and Parallel Circumscription
This paper concentrates on comparing the relative expressive power of five non-monotonic logics that have appeared in the literature. The results o