Completeness Results for Recursive Data Bases

Completeness results for metrized rings and lattices

The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...

Performing Inferences over Recursive Data Bases

The research reported in this paper presents a solution to an open problem which arises in systems that use recursive production rules to represent knowledge. The problem can be stated as follows: "Given a recursive definition, how can we derive an equivalent non-recursive program with well-defined termination conditions". Our solution uses connection graphs to first detect occurrences of recur...

Completeness Results for Circumscription

We inv estigate the model theory of the notion of circumscription, and find completeness theorems that provide a partial converse to a result of McCarthy. We show that the circumscriptive theorems are precisely the truths of the minimal models, in the case of various classes of theories, and for various versions of circumscription. We also present an example of commonsense reasoning in which fi...

Completeness results for graph isomorphism

On completeness results for predicate

In this paper we deal with generic expansions of first-order predicate logics of some left-continuous t-norms with a countable set of truth-constants. Besides already known results for the case of Lukasiewicz logic, we obtain new conservativeness and completenesss results for some other expansions. Namely, we prove that the expansions of predicate Product, Gödel and Nilpotent Minimum logics wit...