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

Implementing Default and Autoepistemic Logics via the Logic of GK

The logic of knowledge and justified assumptions, also known as logic of grounded knowledge (GK), was proposed by Lin and Shoham as a general logic for nonmonotonic reasoning. To date, it has been used to embed in it default logic (propositional case), autoepistemic logic, Turner's logic of universal causation, and general logic programming under stable model semantics. Besides showing the generality of GK as a logic for nonmonotonic reasoning, these embeddings shed light on the relationships among these other logics. In this paper, for the first time, we show how the logic of GK can be embedded into disjunctive logic programming in a polynomial but non-modular translation with new variables. The result can then be used to compute the extension/expansion semantics of default logic, autoepistemic logic and Turner's logic of universal causation by disjunctive ASP solvers such as claspD(-2), DLV, GNT and cmodels.Comment: Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014

Revision in networks of ontologies

euzenat2015aInternational audienceNetworks of ontologies are made of a collection of logic theories, called ontologies, related by alignments. They arise naturally in distributed contexts in which theories are developed and maintained independently, such as the semantic web. In networks of ontologies, inconsistency can come from two different sources: local inconsistency in a particular ontology or alignment, and global inconsistency between them. Belief revision is well-defined for dealing with ontologies; we investigate how it can apply to networks of ontologies. We formulate revision postulates for alignments and networks of ontologies based on an abstraction of existing semantics of networks of ontologies. We show that revision operators cannot be simply based on local revision operators on both ontologies and alignments. We adapt the partial meet revision framework to networks of ontologies and show that it indeed satisfies the revision postulates. Finally, we consider strategies based on network characteristics for designing concrete revision operators

Priority-Based Conflict Resolution in Inconsistent Relational Databases

We study here the impact of priorities on conflict resolution in inconsistent relational databases. We extend the framework of repairs and consistent query answers. We propose a set of postulates that an extended framework should satisfy and consider two instantiations of the framework: (locally preferred) l-repairs and (globally preferred) g-repairs. We study the relationships between them and the impact each notion of repair has on the computational complexity of repair checking and consistent query answers