Toward a Paraconsistent Semantics of Database Integrity

alence of the consistency view wrt violation, i.e. wrt negative information, corresponds to the prevalence of normal clauses wrt positive information. However, we have argued that an application-independent semantics of integrity should not be one-sided wrt conditions that entail violation (or, resp., satisfaction) while being less concerned wrt the opposite. Rather, it should be left to the particular requirements of a given application to relax positions, for taking sides wrt weaker or stronger notions of satisfaction or violation of integrity, if necessary. This led to a refinement of our three-valued view, resulting in a non-biased two-valued semantics. The four possible cases that an integrity constraint is either satisfied by each sustained model, or only weakly satisfied by some sustained model, or that it is neither satisfied nor violated, or that it is violated in each sustained model, might even suggest to investigate a four-valued semantics of database integrity. Third, there was a need to clarify the relationships between the traditional the-oremhood and consistency views of integrity [SK] and more recent proposals concerning database integrity in abductive logic programming [KM1] [KKT] [TK]. That need arose in the context of ongoing work on using abductive logic programming for knowledge assimilation in deductive databases [De5, 6]. To repeat, the starting point of this paper was a somehow uneasy feeling wrt the subtle diversity of existing proposals for capturing the meaning of integrity constraints. This paper is not the first in this regard. Similar observations have been made in [Re3]. However, the conclusions drawn in [Re3] lead into a direction which is different from ours. Reiter proposes to make the epistemic meta-level character of integrity constraints explicit by using a first-order calculus enhanced with modal operators. As opposed to that, my goal is to see how far model theory together with abductive logic programming can carry, in terms of relaxing traditional notions of consistency and integrity of databases toward paraconsistency. We expect our findings to be amenable to practical applications such as the federation of heterogeneous databases, where paraconsistency is very likely to occur.