Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal solution is an NP-hard problem in general; yet, when restricted over classes of instances whose constraint interactions can be modelled via (nearly-)acyclic g...

This paper introduces a probabilistic description logic that adds probabilistic inclusions to the popular logic ALC, and derives inference algorithms for inference in the logic. The probabilistic logic, referred to as CRALC (“credal” ALC), combines the usual acyclicity condition with a Markov condition; in this context, inference is equated with calculation of (bounds on) posterior probability ...

We develop a new approach to cluster algebras based on the notion of an upper cluster algebra, defined as an intersection of Laurent polynomial rings. Strengthening the Laurent phenomenon established in [6], we show that, under an assumption of “acyclicity”, a cluster algebra coincides with its “upper” counterpart, and is finitely generated; in this case, we also describe its defining ideal, an...

This paper disentangles the topological assumptions of classical results (e.g., Walker (1977)) on existence of maximal elements from rationality conditions. It is known from the social choice literature that under the standard topological conditions—with no other restrictions on preferences—there is an element such that the upper section of strict preference at that element is minimal in terms ...

We give a clear picture of the tractability/intractability frontier for quantified constraint satisfaction problems (QCSPs) under structural restrictions. On the negative side, we prove that checking QCSP satisfiability remains PSPACE-hard for all known structural properties more general than bounded treewidth and for the incomparable hypergraph acyclicity. Moreover, if the domain is not fixed,...

The disjunctive skolem chase is a sound and complete (albeit non-terminating) algorithm that can be used to solve conjunctive query answering over DL ontologies and programs with disjunctive existential rules. Even though acyclicity notions can be used to ensure chase termination for a large subset of real-world knowledge bases, the complexity of reasoning over acyclic theories still remains hi...

A new correctness criterion for discriminating Proof Nets among Proof Structures of Multiplicative Linear Logic with MIX rule is provided. This criterion is inspired by an original interpretation of Proof Structures as distributed systems, and logical formulae as processes. The computation inside a system corresponds to the logical ow of information inside a proof, that is, roughly, a distribut...

We define a notion of total acyclicity for complexes of flat quasi-coherent sheaves over a semi-separated noetherian scheme, generalising complete flat resolutions over a ring. By studying these complexes as objects of the pure derived category of flat sheaves we extend several results about totally acyclic complexes of projective modules to schemes; for example, we prove that a scheme is Goren...

We study access to temporal data with TEL, a temporal extension of the tractable description logic EL. Our aim is to establish a clear computational complexity landscape for the atomic query answering problem, in terms of both data and combined complexity. Atomic queries in full TEL turn out to be undecidable even in data complexity. Motivated by the negative result, we identify well-behaved ye...

We develop a new approach to cluster algebras based on the notion of an upper cluster algebra, defined as an intersection of Laurent polynomial rings. Strengthening the Laurent phenomenon established in [6], we show that, under an assumption of “acyclicity”, a cluster algebra coincides with its “upper” counterpart, and is finitely generated; in this case, we also describe its defining ideal, an...