A Pitch Rich with Width-Witchcraft – Model-Theoretic Criteria for Decidable Query Entailment
Decidability of inferencing is commonly considered a very important property of logic-based knowledge representation formalisms, required for the algorithmization and automation of reasoning. Yet, oftentimes, the corresponding (un)decidability arguments are idiosyncratic and do not shed much light on the underlying principles governing the divide.
In my talk, I will review generic model-theoretic criteria for decidability of querying in fragments of first-order logic. I will describe a general framework by means of which decidability of query entailment can be established based on the existence of countermodels with certain structural properties. These properties depend on the ontology and query language used and range from finite domain over forest-like shape to width-finiteness employing width notions like treewidth and cliquewidth.