Out of the joint work of Johan van Benthem and the Hungarian group round Hajnal Andréka, István Németi and Ildikó Sain and their PhD students, two approaches for taming a logic evolved. With taming a logic we mean changing the logic in such a way that it becomes decidable. For first order logic, they took a semantic route using relativisation of models, and a syntactic route focusing on guarded...

Bayesian knowledge bases (BKBs) are a gen­ eralization of Bayes networks and weighted proof graphs (WAODAGs), that allow cycles in the causal graph. Reasoning in BKBs re­ quires finding the most probable inferences consistent with the evidence. The cost­ sharing heuristic for finding least-cost ex­ planations in WAODAGs was presented and shown to be effective by Charniak and Hu­ sain. However, ...

Among others we will see that the equational theory of ! dimensional rep-resentable polyadic equality algebras (RPEA ! 's) is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is nite schema-axiomatizable (and hence the equational theory of this class is nite schema-axi...