This note arises from an attempt to give some model-theoretic interpretation of the concept of flatness. It is well-known that a necessary condition for a ring morphism A → B to be faithfully flat, is that any linear system of equations with coefficients from A which has a solution over B, must have already a solution over A. In fact, if we strenghten this condition to any solution over B comes...

FaCT (Fast Classification of Terminologies) is a Description Logic (DL) classifier which has been implemented as a test-bed for a sound and complete tableaux satisfiability/subsumption testing algorithm. FaCT’s novelty lies in its relatively expressive logic and its highly optimised implementation of the tableaux algorithm. iFaCT is an extension of FaCT that supports reasoning with inverse role...

The representation of terminological knowledge may naturally lead to terminological cycles. In addition to descriptive semantics, the meaning of cyclic terminologies can also be captured by xed-point semantics. To gain a more profound understanding of these semantics and to obtain inference algorithms for inconsistency, subsumption , and related inference tasks, this paper provides automata the...

The representation of terminological knowledge may naturally lead to terminological cycles. In addition to descriptive semantics , the meaning of cyclic terminologies can also be captured by xed-point semantics, namely, greatest and least xed-point semantics. To gain a more profound understanding of these semantics and to obtain inference algorithms as well as complexity results for inconsisten...

The existentially closed models of the theory of fields (of arbitrary characteristic) with a given finite number of commuting derivations can be characterized geometrically, in several ways. In each case, the existentially closed models are those models that contain points of certain differential varieties, which are determined by certain ordinary varieties. How can we tell whether a given syst...