1,721,482 research outputs found
Complexity results for preference aggregation over (m)CP-nets: Pareto and majority voting
No full textAggregating preferences over combinatorial domains has many applications in artificial intelligence (AI). Given the inherent exponential nature of preferences over combinatorial domains, compact representation languages are needed to represent them, and (m)CP-nets are among the most studied ones. Sequential and global voting are two different ways of aggregating preferences represented via CP-nets. In sequential voting, agents' preferences are aggregated feature-by-feature. For this reason, sequential voting may exhibit voting paradoxes, i.e., the possibility to select sub-optimal outcomes when preferences have specific feature dependencies. To avoid paradoxes in sequential voting, one has often assumed the (quite) restrictive constraint of O-legality, which imposes a shared common topological order among all the agents' CP-nets. On the contrary, in global voting, CP-nets are considered as a whole during the preference aggregation process. For this reason, global voting is immune from the voting paradoxes of sequential voting, and hence there is no need to impose restrictions over the CP-nets' structure when preferences are aggregated via global voting. Sequential voting over O-legal CP-nets received much attention, and O-legality of CP-nets has often been required in other studies. On the other hand, global voting over non-O-legal CP-nets has not carefully been analyzed, despite it was explicitly stated in the literature that a theoretical comparison between global and sequential voting was highly promising and a precise complexity analysis for global voting has been asked for multiple times. In quite a few works, only very partial results on the complexity of global voting over CP-nets have been given. In this paper, we start to fill this gap by carrying out a thorough computational complexity analysis of global voting tasks, for Pareto and majority voting, over not necessarily O-legal acyclic binary polynomially connected (m)CP-nets. We show that all these problems belong to various levels of the polynomial hierarchy, and some of them are even in P or LOGSPACE. Our results are a notable achievement, given that the previously known upper bound for most of these problems was the complexity class EXPTIME. We provide various exact complexity results showing tight lower bounds and matching upper bounds for problems that (up to now) did not have any explicit non-obvious lower bound
A novel characterization of the complexity class Θ^P_k based on counting and comparison
No full textThe complexity class Θ^P_2, which is the class of languages recognizable by deterministic Turing machines in polynomial time with at most logarithmic many calls to an NP oracle, received extensive attention in the literature. Its complete problems can be characterized by different specific tasks, such as deciding whether the optimum solution of an NP problem is unique, or whether it is in some sense “odd” (e.g., whether its size is an odd number). In this paper, we introduce a new characterization of this class and its generalization Θ^P_k to the k-th level of the polynomial hierarchy. We show that problems in Θ^P_k are also those whose solution involves deciding, for two given sets A and B of instances of two Σ^P_{k−1}-complete (or Π^P_{k−1}-complete) problems, whether the number of “yes”-instances in A is greater than those in B. Moreover, based on this new characterization, we provide a novel sufficient condition for Θ^P_k-hardness. We also define the general problem Comp-Valid_k, which is proven here Θ^P_{k+1}-complete. Comp-Valid_k is the problem of deciding, given two sets A and B of quantified Boolean formulas with at most k alternating quantifiers, whether the number of valid formulas in A is greater than those in B. Notably, the problem Comp-Sat of deciding whether a set contains more satisfiable Boolean formulas than another set, which is a particular case of Comp-Valid_1, demonstrates itself as a very intuitive Θ^P_2-complete problem. Nonetheless, to our knowledge, it eluded its formal definition to date. In fact, given its strict adherence to the count-and-compare semantics here introduced, Comp-Valid_k is among the most suitable tools to prove Θ^P_k-hardness of problems involving the counting and comparison of the number of “yes”-instances in two sets. We support this by showing that the Θ^P_2-hardness of the Max voting scheme over mCP-nets is easily obtained via the new characterization of Θ^P_k introduced in this paper
Complexity of Inconsistency-Tolerant Query Answering in Datalog+/- under Cardinality-Based Repairs
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Explanations for Ontology-Mediated Query Answering in Description Logics
Full text linkOntology-mediated query answering is a paradigm that seeks to exploit the semantic knowledge expressed in terms of ontologies to improve query answers over incomplete data sources. In this paper, we focus on description logic ontologies, and study the
problem of explaining why an ontology-mediated query is entailed
from a given data source. Specifically, we view explanations as minimal sets of assertions from an ABox, which satisfy the ontologymediated query. Based on such explanations, we study a variety of
problems taken from the recent literature on explanations (studied
for existential rules), such as recognizing all minimal explanations.
Our results establish tight connections between intractable explanation problems and variants of propositional satisfiability problems.
We provide insights on the inherent computational difficulty of deriving explanations for ontology-mediated querie
Representing Uncertain Concepts in Rough Description Logics via Contextual Indiscernibility Relations
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