A logic for reasoning with inconsistency

Distance-Based Repairs of Databases

“…We denote this by D |= S IC. Common definitions for S are the standard two-valued semantics, the minimal Herbrand model semantics, the stable model semantics [20], Kleene's three-valued semantics [24], or any other multiple-valued semantics [23]. A semantics S defines, for a set Γ of formulas in L, the S-models of Γ , i.e., a set mod S (Γ ) of valuations that satisfy all the formulas in Γ .…”

Query Answering in Inconsistent Databases

“…Following [8], we show here how to generate a consistent first-order theory with a non-classical semantics. We use Annotated Predicate Calculus (APC) [67].…”

“…Several papers by Lozinskii, Kifer, Arieli and Avron [9,67,81] studied the problem of making inferences from a possibly inconsistent, propositional or first-order, knowledge base. The basic idea is to infer the classical consequences of all maximal consistent subsets of the knowledge base [81] or all most consistent models of the knowledge base [9,67] (where the order on models is defined on the basis of atom annotations drawing values from a lattice or a bi-lattice).…”

“…The basic idea is to infer the classical consequences of all maximal consistent subsets of the knowledge base [81] or all most consistent models of the knowledge base [9,67] (where the order on models is defined on the basis of atom annotations drawing values from a lattice or a bi-lattice). This provides a non-monotonic consequence relation but the special role of the integrity constraints (whose truth cannot be given up) is not captured.…”

“…Also, no computational mechanisms for answering first-order (or aggregation) queries are proposed, neither are computational complexity issues addressed. In section 4, we described how the approach of Kifer and Lozinskii [67] can be adapted to the task of computing consistent query answers.…”