A novel characterization of the complexity class based on counting and comparison

This is the author's accepted versionFinal version available from Elsevier via the DOI in this recordThe complexity class Θ2P, 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 ΘkP to the k-th level of the polynomial hierarchy. We show that problems in ΘkP are also those whose solution involves deciding, for two given sets A and B of instances of two Σk−1P-complete (or Πk−1P-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 ΘkP-hardness. We also define the general problem Comp-Validk, which is proven here Θk+1P-complete. Comp-Validk 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-Valid1, demonstrates itself as a very intuitive Θ2P-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-Validk is among the most suitable tools to prove ΘkP-hardness of problems involving the counting and comparison of the number of “yes”-instances in two sets. We support this by showing that the Θ2P-hardness of the Max voting scheme over mCP-nets is easily obtained via the new characterization of ΘkP introduced in this paper.This work was supported by the UK EPSRC grants EP/J008346/1, EP/L012138/1, and EP/M025268/1, and by The Alan Turing Institute under the EPSRC grant EP/N510129/1. We thank Dominik Peters and the anonymous reviewers for their helpful comments on a preliminary version of the paper

Complexity of Approximate Query Answering under Inconsistency in Datalog+/-

This is the author accepted manuscript. The final version is freely available from IJCAI via the link in this recordSeveral semantics have been proposed to query inconsistent ontological knowledge bases, including the intersection of repairs and the intersection of closed repairs as two approximate inconsistencytolerant semantics. In this paper, we analyze the complexity of conjunctive query answering under these two semantics for a wide range of Datalog± languages. We consider both the standard setting, where errors may only be in the database, and the generalized setting, where also the rules of a Datalog± knowledge base may be erroneous.This work was supported by The Alan Turing Institute under the UK EPSRC grant EP/N510129/1, and by the EPSRC grants EP/R013667/1, EP/L012138/1, and EP/M025268/1

Complexity of Inconsistency-Tolerant Query Answering in Datalog+/- under Cardinality-Based Repairs

This is the author accepted manuscript. The final version is available from Association for the Advancement of Artificial Intelligence (AAAI) via the link in this recordQuerying inconsistent ontological knowledge bases is an important problem in practice, for which several inconsistencytolerant query answering semantics have been proposed, including query answering relative to all repairs, relative to the intersection of repairs, and relative to the intersection of closed repairs. In these semantics, one assumes that the input database is erroneous, and the notion of repair describes a maximally consistent subset of the input database, where different notions of maximality (such as subset and cardinality maximality) are considered. In this paper, we give a precise picture of the computational complexity of inconsistencytolerant (Boolean conjunctive) query answering in a wide range of Datalog± languages under the cardinality-based versions of the above three repair semantics.This work was supported by the Alan Turing Institute under the UK EPSRC grant EP/N510129/1, and by the EPSRC grants EP/R013667/1, EP/L012138/1, and EP/M025268/1

Complexity of Approximate Query Answering under Inconsistency in Datalog+/-

This is the author accepted manuscript. The final version is available from the publisher via the link in this recordSeveral semantics have been proposed to query inconsistent ontological knowledge bases, including the intersection of repairs and the intersection of closed repairs as two approximate inconsistency-tolerant semantics. In this paper, we analyze the complexity of conjunctive query answering under these two semantics for a wide range of Datalog± languages. We consider both the standard setting, where errors may only be in the database, and the generalized setting, where also the rules of a Datalog± knowledge base may be erroneous.This work was supported by The Alan Turing Institute under the UK EPSRC grant EP/N510129/1, and by the EPSRC grants EP/R013667/1, EP/L012138/1, and EP/M025268/1

Few-Shot Out-of-Domain Transfer Learning of Natural Language Explanations in a Label-Abundant Setup

Training a model to provide natural language explanations (NLEs) for its predictions usually requires the acquisition of task-specific NLEs, which is time- and resource-consuming. A potential solution is the few-shot out-of-domain transfer of NLEs from a parent task with many NLEs to a child task. In this work, we examine the setup in which the child task has few NLEs but abundant labels. We establish four few-shot transfer learning methods that cover the possible fine-tuning combinations of the labels and NLEs for the parent and child tasks. We transfer explainability from a large natural language inference dataset (e-SNLI) separately to two child tasks: (1) hard cases of pronoun resolution, where we introduce the small-e-WinoGrande dataset of NLEs on top of the WinoGrande dataset, and (2) commonsense validation (ComVE). Our results demonstrate that the parent task helps with NLE generation and we establish the best methods for this setup

Twenty Years of Student Scholarship: Celebrating the Dalhousie Journal of Legal Studies

In this paper, we propose a novel controllable text-to-image generative adversarial network (ControlGAN), which can effectively synthesise high-quality images and also control parts of the image generation according to natural language descriptions. To achieve this, we introduce a word-level spatial and channel-wise attention-driven generator that can disentangle different visual attributes, and allow the model to focus on generating and manipulating subregions corresponding to the most relevant words. Also, a word-level discriminator is proposed to provide fine-grained supervisory feedback by correlating words with image regions, facilitating training an effective generator which is able to manipulate specific visual attributes without affecting the generation of other content. Furthermore, perceptual loss is adopted to reduce the randomness involved in the image generation, and to encourage the generator to manipulate specific attributes required in the modified text. Extensive experiments on benchmark datasets demonstrate that our method outperforms existing state of the art, and is able to effectively manipulate synthetic images using natural language descriptions. Code is available at https://github.com/mrlibw/ControlGAN.Comment: NeurIPS 201

Query Answer Explanations under Existential Rules

Ontology-mediated query answering is an extensively studied paradigm, which aims at improving query answers with the use of a logical theory. In this paper, we focus on ontology languages based on existential rules, and we carry out a thorough complexity analysis of the problem of explaining query answers in terms of minimal subsets of database facts and related task

1994 Annual Report Town of Middleton, Massachusetts Two Hundred and Sixty-Sixth Municipal Year

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Aggregating 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.Engineering and Physical Sciences Research Council (EPSRC