ABSTRACT. We introduce an extension of Description Logics (DL), appropriate for modelling and reasoning about deontic notions. DLs represent a family of logical systems, most of them corresponding to a specific fragment of first-order logic, developed to reason about taxonomies and ontologies. Starting from defeasible ALC, an extension of the DL ALC which allows us to model and reason about defeasible information (rules that admit exceptions), we show how to modify the semantics in order to also represent and manage conditional obligations and permissions, and we present the correspondent, and easily implementable, decision procedures. Also, we define a semantics combining reasoning about expectations and reasoning about norms, pairing it with corresponding decision procedures.

ABSTRACT. Reasoning in presence of multiple viewpoints or approximate concepts is a long-standing challenge for knowledge representation formalisms. In this paper, we introduce $\mathcal{ALC}^{\lhd\Box}$, a description logic extending the classical $\mathcal{ALC}$ with two pairs of concept constructors that allow us to talk about objects that ``on some/all accounts, are acknowledged to be $C$'' (with $\lhd C$ and $\Box C$, respectively), as well as ``on some/all accounts, are compatible with being $C$'' (with the duals $\rhd C$ and $\Diamond C$, respectively). Semantically, a function equips each element of the domain with a family of \emph{neighbourhoods}, subsets of the domain that represent multiple, possibly imprecise, or even conflicting, accounts on that element. We show that $\mathcal{ALC}^{\lhd\Box}$ concept satisfiability under a knowledge base is reducible in polynomial-time to the same problem for $\mathcal{ALC}$, hence obtaining an $textsc{ExpTime}$-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) $textsc{ExpTime}$ upper bound is preserved, by providing reductions to $\mathcal{ALC}$, $\mathcal{ALCHI}$, or the two-variable guarded fragment $\mathsf{GF}^2$.

ABSTRACT. Standpoint extensions of KR formalisms have been recently introduced to incorporate multi-perspective modelling and reasoning capabilities. In such modal extensions, the integration of conceptual modelling and perspective annotations can be more or less tight, with monodic standpoint extensions striking a good balance as they enable advanced modelling while preserving good reasoning complexities. This extended abstract reports on a paper published in KR'25 where we consider the very expressive description logics SHOIQBs and SROIQBs, which subsume the popular W3C-standardized OWL 1 and OWL 2 ontology languages, and show that they allow for monodic standpoint extensions without any increase of standard reasoning complexity. We do this by first proving the result for the extension of C2 - the counting two-variable fragment of first-order logic - by monodic standpoints and then by showing how to handle role chain axioms. At the core of our treatise is a polytime translation of formulae in said formalism into standpoint-free C2, requiring elaborate model-theoretic arguments. By virtue of this translation, the NExpTime-complete complexity of checking satisfiability in C2 carries over to our formalism. As our formalism subsumes monodic S5 over C2, our result also significantly advances the state of the art in research on first-order modal logics. We prove that NExpTime-hardness already occurs in much less expressive DLs as long as they feature both nominals and monodic standpoints. We also show that, with inverses, functionality, and nominals present, minimally lifting the monodicity restriction leads to undecidability.

ABSTRACT. This extended abstract summarizes our KR’26 paper, where we explore the use of answer set programming (ASP) and its extension with quantifiers, ASP(Q), for inconsistency-tolerant querying of prioritized data. We consider the variants of three well-known semantics (AR, brave and IAR) that use three notions of optimal repairs (Pareto-, globally- and completion-optimal), and for which query answering is in the first or second level of the polynomial hierarchy for a large class of logical theories. Notably, this paper presents the first implementation of globally-optimal repair-based semantics, as well as the first implementation of the grounded semantics, which is a tractable under-approximation of all these optimal repair-based semantics. Our experimental evaluation sheds light on the feasibility of computing answers under globally-optimal repair semantics and the impact of adopting different semantics, approximations, and encodings.

ABSTRACT. We study Two-Variable Fragment of First-Order Logic, FO2, with certain semantic constraints that model hierarchical data. Our first logic extends FO2 with a linear order < and a chain of increasingly coarser equivalence relations E_1 ⊆ E_2 ⊆ ... . We show that its finite satisfiability problem is NExpTime-complete. We also demonstrate that the weaker variant of this logic without linear ordering posesses the exponential model property. Our second main contribution concerns FO2 extended with a chain of total preorders ⪯ 1 ⊆⪯ 2 ⊆ ... . We prove that it likewise admits an NExpTime-complete finite satisfiability problem. However, we show that the complexity increases to EXPSPACE-complete once access to the successor relations of the preorders is allowed.

ABSTRACT. This extended abstract summarizes our recent contribution, currently under double-blind review at IJCAI'26, in which we ask: Within a class of existential rules that supports decidable query entailment, do the usual abstract classes become concrete? We answer in the negative for classes based upon the termination of all classical chase variants and for the bts class. This explains the necessity of diverse, class-specific techniques for proving chase termination, as query entailment offers no systematic tool for this purpose.