Neighbourhood Description Logics for Multiperspective Reasoning

Reasoning in the presence of multiple viewpoints or approximate concepts is a long-standing challenge for knowledge representation formalisms. In this paper, we introduce AℒC□, a description logic extending the classical AℒC with two pairs of concept constructors that allow us to talk about objects that “on some/all accounts, are acknowledged to be C” (with C and □C, respectively), as well as “on all/some accounts, are compatible with being C” (with the duals C and ♢C, respectively). Semantically, a function equips each element of the domain with a family of neighbourhoods, subsets of the domain that represent multiple, possibly imprecise, or even conflicting, accounts on that element. We show that AℒC□ concept satisfiability with respect to a knowledge base is reducible in polynomial-time to the same problem for AℒC, hence obtaining an ExpTime-completeness result. Moreover, we investigate additional conditions on the neighbourhood function, so to capture natural constraints that can be imposed on the accounts of an object: existence, consistency, partial consistency, correctness, and partial correctness. In all these cases, we show that the (tight) ExpTime upper bound is preserved, by providing reductions to AℒC, AℒCℋℐ, or the two-variable guarded fragment GF2