Abstract: 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.
Abstract: 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.
Abstract: 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.