Towards Conjunctive Query Answering in Defeasible EL_bot
Vortrag von Maximilian Pensel
In Defeasible Description Logics (DDLs), typical or default information about concepts can be stated in the form of defeasible concept inclusions (DCIs) in a DBox. As opposed to general concept inclusions (GCIs), which are strict in the sense that e.g. "every element of C must be an element of D", defeasible statements are more vague and allow to state that "elements of C are usually elements of D", where the term usually insinuates that DCIs are satisfied individually for elements not satisfying properties contradicting the DCI. In 2017, we have discovered and resolved a severe shortcoming of earlier approaches to define semantics for DDLs rooted in the preferential approach by KLM. We introduce a new kind of canonical model in order to determine consequences in defeasible EL_bot. These so-called typicality models extend classical canonical models by additional concept representatives, which are individually forced to satisfy certain DCIs. Typicality models allow us to reconstruct the consequences obtained by previous approaches and extend them appropriately to alleviate the discovered insufficiency. More recently, we have extended this formalism beyond the reasoning service subsumption, to also be capable of deciding defeasible instance checks.
The natural next step is to strengthen the deductive power of our formalism to enable conjunctive query answering (CQA) in defeasible EL_bot, a reasoning service that, to the best of our knowledge, has not been studied for DDLs. We conjecture that the query rewriting approach by Lutz et al. (2009), allowing the use of classical canonical models to answer conjunctive queries, can be adopted to answer defeasible conjunctive queries by using typicality models, due to their canonical nature.
This endeavour is still in its very early stages and aspects of this talk concerning CQA are preliminary ideas and working theories. Input and feedback from the audience is greatly appreciated.