A Logic Approach to Database Dynamic Updating

We introduce a logic-based framework for database updating under constraints. In our framework, the constraints are represented as an instantiated extended logic program. When performing an update, database consistency may be violated. We provide an approach of maintaining database consistency, and study the conditions under which the maintenance process is deterministic. We show that the complexity of the computations and decision problems presented in our framework is in each case polynomial time.

Extended Deductive Databases with Uncertain Information

The paper presents an approach for handling uncertain information in deductive databases using multivalued logics. Uncertainty means that database facts may be assigned logical values other than the conventional ones - true and false. The logical values represent various degrees of truth, which may be combined and propagated by applying the database rules. A corresponding multivalued database semantics is defined. We show that it extends successful conventional semantics as the well-founded semantics, and has a polynomial time data complexity.

Extended Well-Founded Semantics in Bilattices

One of the most used assumptions in logic programming and deductive databases is the so-called Closed World Assumption (CWA), according to which the atoms that cannot be inferred from the programs are considered to be false (i.e. a pessimistic assumption). One of the most successful semantics of conventional logic programs based on the CWA is the well-founded semantics. However, the CWA is not applicable in all circumstances when information is handled. That is, the well-founded semantics, if conventionally defined, would behave inadequately in different cases. The solution we adopt in this paper is to extend the well-founded semantics in order for it to be based also on other assumptions. The basis of (default) negative information in the well-founded semantics is given by the so-called unfounded sets. We extend this concept by considering optimistic, pessimistic, skeptical and paraconsistent assumptions, used to complete missing information from a program. Our semantics, called extended well-founded semantics, expresses also imperfect information considered to be missing/incomplete, uncertain and/or inconsistent, by using bilattices as multivalued logics. We provide a method of computing the extended well-founded semantics and show that Kripke-Kleene semantics is captured by considering a skeptical assumption. We show also that the complexity of the computation of our semantics is polynomial time.