Description Logics of Context with Rigid Roles Revisited

Decidable Description Logics of Context with Rigid Roles

To represent and reason about contextualized knowledge often two-dimensional Description Logics (DLs) are employed, where one DL is used to describe contexts (or possible worlds) and the other DL is used to describe the objects, i.e. the relational structure of the specific contexts. Previous approaches for DLs of context that combined pairs of DLs resulted in undecidability in those cases wher...

The Complexity of Temporal Description Logics with Rigid Roles and Restricted TBoxes: In Quest of Saving a Troublesome Marriage

Decidable Contextualized DLs with Rigid Roles

Description logics (DLs) of context can be employed to represent and reason about contextualized knowledge, which naturally occurs in practice [5,4,7,9,8]. Consider, for instance, the rôles played by a person in different contexts. The person Bob, who works for the company Siemens, plays the rôle of an employee of Siemens in the work context, whereas he might play the rôle of a customer of Siem...

Decidability of Circumscribed Description Logics Revisited

We revisit non-monotonic description logics based on circumscription (with preferences) and prove several decidability results for their satisfiability problem. In particular, we consider circumscribed description logics without the finite model property (DL-LiteF andALCFI) and with fixed roles (DL-LiteF and a fragment of DL-LiteR), improving upon previous decidability results that are limited ...

Consequence-based Reasoning for Description Logics with Disjunction, Inverse Roles, and Nominals

We present a consequence-based calculus for the SHOI description logic. Known consequence-based reasoning procedures are either restricted to logics without nominals (e.g. SRIQ), or to Horn logics (e.g. Horn-SROIQ). In line with existing approaches, our algorithm uses context structures to assist in the derivation of clauses, which are generated by inference rules such as (hyper)resolution. The...