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In Boolean games, each agent controls a set of Boolean variables and has a goal represented by a propositional formula. We study inference problems in Boolean games assuming the presence of a PRINCIPAL who has the ability to control the agents and impose taxation schemes. Previous work used taxation schemes to guide a game towards certain equilibria. We present algorithms that show how taxation schemes can also be used to infer agents' goals. We present experimental results to demonstrate the efficacy our algorithms. We also consider goal inference when only limited information is available in response to a query.
In some agent designs like inverse reinforcement learning an agent needs to learn its own reward function. Learning the reward function and optimising for it are typically two different processes, usually performed at different stages. We consider a continual (``one life'') learning approach where the agent both learns the reward function and optimises for it at the same time. We show that this comes with a number of pitfalls, such as deliberately manipulating the learning process in one direction, refusing to learn, ``learning'' facts already known to the agent, and making decisions that are strictly dominated (for all relevant reward functions). We formally introduce two desirable properties: the first is `unriggability', which prevents the agent from steering the learning process in the direction of a reward function that is easier to optimise. The second is `uninfluenceability', whereby the reward-function learning process operates by learning facts about the environment. We show that an uninfluenceable process is automatically unriggable, and if the set of possible environments is sufficiently large, the converse is true too.
Analogical transfer consists in leveraging a measure of similarity between two situations to predict the amount of similarity between their outcomes. Acquiring a suitable similarity measure for analogical transfer may be difficult, especially when the data is sparse or when the domain knowledge is incomplete. To alleviate this problem, this paper presents a dataset complexity measure that can be used either to select an optimal similarity measure, or if the similarity measure is given, to perform analogical transfer: among the potential outcomes of a new situation, the most plausible is the one which minimizes the dataset complexity.
Ontology-mediated query answering (OMQA) is a promising approach to data access and integration that has been actively studied in the knowledge representation and database communities for more than a decade. The vast majority of work on OMQA focuses on conjunctive queries, whereas more expressive queries that feature counting or other forms of aggregation remain largely unexplored. In this paper, we introduce a general form of counting query, relate it to previous proposals, and study the complexity of answering such queries in the presence of DL-Lite ontologies. As it follows from existing work that query answering is intractable and often of high complexity, we consider some practically relevant restrictions, for which we establish improved complexity bounds.
Previous research has claimed dynamic epistemic logic (DEL) to be a suitable formalism for representing essential aspects of a Theory of Mind (ToM) for an autonomous agent. This includes the ability of the formalism to represent the reasoning involved in false-belief tasks of arbitrary order, and hence for autonomous agents based on the formalism to become able to pass such tests. This paper provides evidence for the claims by documenting the implementation of a DEL-based reasoning system on a humanoid robot. Our implementation allows the robot to perform cognitive perspective-taking, in particular to reason about the first- and higher-order beliefs of other agents. We demonstrate how this allows the robot to pass a quite general class of false-belief tasks involving human agents. Additionally, as is briefly illustrated, it allows the robot to proactively provide human agents with relevant information in situations where a system without ToM-abilities would fail. The symbolic grounding problem of turning robotic sensor input into logical action descriptions in DEL is achieved via a perception system based on deep neural networks.
We consider the setting of asynchronous opinion diffusion with majority threshold: given a social network with each agent assigned to one opinion, an agent will update its opinion if more than half of its neighbors agree on a different opinion. The stabilized final outcome highly depends on the sequence in which agents update their opinion. We are interested in optimistic sequences---sequences that maximize the spread of a chosen opinion. We complement known results for two opinions where optimistic sequences can be computed in time and length linear in the number of agents. We analyze upper and lower bounds on the length of optimistic sequences, showing quadratic bounds in the general and linear bounds in the acyclic case. Moreover, we show that in networks with more than two opinions determining a spread-maximizing sequence becomes intractable; surprisingly, already with three opinions the intractability results hold in highly restricted cases, e.g., when each agent has at most three neighbors, when looking for a short sequence, or when we aim for approximate solutions.
Spectrum-based Fault Localization (SFL) approaches aim to efficiently localize faulty components from examining program behavior. This is done by collecting the execution patterns of various combinations of components and the corresponding outcomes into a spectrum. Efficient fault localization depends heavily on the quality of the spectra. Previous approaches, including the current state-of-the-art Density- Diversity-Uniqueness (DDU) approach, attempt to generate “good” test-suites by improving certain structural properties of the spectra. In this work, we propose a different approach, Multiverse Analysis, that considers multiple hypothetical universes, each corresponding to a scenario where one of the components is assumed to be faulty, to generate a spectrum that attempts to reduce the expected worst-case wasted effort over all the universes. Our experiments show that the Multiverse Analysis not just improves the efficiency of fault localization but also achieves better coverage and generates smaller test-suites over DDU, the current state-of-the-art technique. On average, our approach reduces the developer effort over DDU by over 16% for more than 92% of the instances. Further, the improvements over DDU are indeed statistically significant on the paired Wilcoxon Signed-rank test.
In deductive module extraction, we determine a small subset of an ontology for a given vocabulary that preserves all logical entailments that can be expressed in that vocabulary. While in the literature stronger module notions have been discussed, we argue that for applications in ontology analysis and ontology reuse, deductive modules, which are decidable and potentially smaller, are often sufficient. We present methods based on uniform interpolation for extracting different variants of deductive modules, satisfying properties such as completeness, minimality and robustness under replacements, the latter being particularly relevant for ontology reuse. An evaluation of our implementation shows that the modules computed by our method are often significantly smaller than those computed by existing methods.
In a large-scale knowledge graph (KG), an entity is often described by a large number of triple-structured facts. Many applications require abridged versions of entity descriptions, called entity summaries. Existing solutions to entity summarization are mainly unsupervised. In this paper, we present a supervised approach NEST that is based on our novel neural model to jointly encode graph structure and text in KGs and generate high-quality diversified summaries. Since it is costly to obtain manually labeled summaries for training, our supervision is weak as we train with programmatically labeled data which may contain noise but is free of manual work. Evaluation results show that our approach significantly outperforms the state of the art on two public benchmarks.
In this paper we focus on a less usual way to represent Boolean functions, namely on representations by switch-lists. Given a truth table representation of a Boolean function f the switch-list representation (SLR) of f is a list of Boolean vectors from the truth table which have a different function value than the preceding Boolean vector in the truth table. The main aim of this paper is to include the language SL of all SLR in the Knowledge Compilation Map [Darwiche and Marquis, 2002] and to argue, that SL may in certain situations constitute a reasonable choice for a target language in knowledge compilation. First we compare SL with a number of standard representation languages (such as CNF, DNF, and OBDD) with respect to their relative succinctness. As a by-product of this analysis we also give a short proof of a long standing open question from [Darwiche and Marquis, 2002], namely the incomparability of MODS (models) and PI (prime implicates) languages. Next we analyze which standard transformations and queries (those considered in [Darwiche and Marquis, 2002] can be performed in poly-time with respect to the size of the input SLR. We show that this collection is quite broad and the combination of poly-time transformations and queries is quite unique.
Counting answers to a query is an operation supported by virtually all database management systems. In this paper we focus on counting answers over a Knowledge Base (KB), which may be viewed as a database enriched with background knowledge about the domain under consideration. In particular, we place our work in the context of Ontology-Mediated Query Answering/Ontology-based Data Access (OMQA/OBDA), where the language used for the ontology is a member of the DL-Lite family and the data is a (usually virtual) set of assertions. We study the data complexity of query answering, for different members of the DL-Lite family that include number restrictions, and for variants of conjunctive queries with counting that differ with respect to their shape (connected, branching, rooted). We improve upon existing results by providing PTIME and coNP lower bounds, and upper bounds in PTIME and LOGSPACE. For the LOGSPACE case, we have devised a novel query rewriting technique into first-order logic with counting.
In this paper, we present a learning-based approach to determining acceptance of arguments under several abstract argumentation semantics. More specifically, we propose an argumentation graph neural network (AGNN) that learns a message-passing algorithm to predict the likelihood of an argument being accepted. The experimental results demonstrate that the AGNN can almost perfectly predict the acceptability under different semantics and scales well for larger argumentation frameworks. Furthermore, analysing the behaviour of the message-passing algorithm shows that the AGNN learns to adhere to basic principles of argument semantics as identified in the literature, and can thus be trained to predict extensions under the different semantics – we show how the latter can be done for multi-extension semantics by using AGNNs to guide a basic search. We publish our code at https://github.com/DennisCraandijk/DL-Abstract-Argumentation.
We consider an agent that operates with two models of the environment: one that captures expected behaviors and one that captures additional exceptional behaviors. We study the problem of synthesizing agent strategies that enforce a goal against environments operating as expected while also making a best effort against exceptional environment behaviors. We formalize these concepts in the context of linear-temporal logic, and give an algorithm for solving this problem. We also show that there is no trade-off between enforcing the goal under the expected environment specification and making a best-effort for it under the exceptional one.
Description logics are well-known logical formalisms for knowledge representation. We propose to enrich knowledge bases (KBs) with dynamic axioms that specify how the satisfaction of statements from the KBs evolves when the interpretation is decomposed or recomposed, providing a natural means to predict the evolution of interpretations. Our dynamic axioms borrow logical connectives from separation logics, well-known specification languages to verify programs with dynamic data structures. In the paper, we focus on ALC and EL augmented with dynamic axioms, or to their subclass of positive dynamic axioms. The knowledge base consistency problem in the presence of dynamic axioms is investigated, leading to interesting complexity results, among which the problem for EL with positive dynamic axioms is tractable, whereas EL with dynamic axioms is undecidable.
Answer Set Programming (ASP) is a well-known formalism for Knowledge Representation and Reasoning, successfully employed to solve many AI problems, also thanks to the availability of efficient implementations. Traditionally, ASP systems are based on the ground&solve approach, where the grounding transforms a general input program into its propositional counterpart, whose stable models are then computed by the solver using the CDCL algorithm. This approach suffers an intrinsic limitation: the grounding of one or few constraints may be unaffordable from a computational point of view; a problem known as grounding bottleneck. In this paper, we develop an innovative approach for evaluating ASP programs, where some of the constraints of the input program are not grounded but automatically translated into propagators of the CDCL algorithm that work on partial interpretations. We implemented the new approach on top of the solver WASP and carried out an experimental analysis on different benchmarks. Results show that our approach consistently outperforms state-of-the-art ASP systems by overcoming the grounding bottleneck.
We propose a logic of directions for points (LD) over 2D Euclidean space, which formalises primary direction relations east (E), west (W), and indeterminate east/west (Iew), north (N), south (S) and indeterminate north/south (Ins). We provide a sound and complete axiomatisation of it, and prove that its satisfiability problem is NP-complete.
Strategy representation and reasoning has recently received much attention in artificial intelligence. Impartial combinatorial games (ICGs) are a type of elementary and fundamental games in game theory. One of the challenging problems of ICGs is to construct winning strategies, particularly, generalized winning strategies for possibly infinitely many instances of ICGs. In this paper, we investigate synthesizing generalized winning strategies for ICGs. To this end, we first propose a logical framework to formalize ICGs based on the linear integer arithmetic fragment of numeric part of PDDL. We then propose an approach to generating the winning formula that exactly captures the states in which the player can force to win. Furthermore, we compute winning strategies for ICGs based on the winning formula. Experimental results on several games demonstrate the effectiveness of our approach.
We revisit the notion of i-extension, i.e., the adaption of the fundamental notion of extension to the case of incomplete Abstract Argumentation Frameworks. We show that the definition of i-extension raises some concerns in the "possible" variant, e.g., it allows even conflicting arguments to be collectively considered as members of an (i-)extension. Thus, we introduce the alternative notion of i*-extension overcoming the highlighted problems, and provide a thorough complexity characterization of the corresponding verification problem. Interestingly, we show that the revisitation not only has beneficial effects for the semantics, but also for the complexity: under various semantics, the verification problem under the possible perspective moves from NP-complete to P.
The chase is a famous algorithmic procedure in database theory with numerous applications in ontology-mediated query answering. We consider static analysis of the chase termination problem, which asks, given set of TGDs, whether the chase terminates on all input databases. The problem was recently shown to be undecidable by Gogacz et al. for sets of rules containing only ternary predicates. In this work, we show that undecidability occurs already for sets of single-head TGD over binary vocabularies. This question is relevant since many real-world ontologies, e.g., those from the Horn fragment of the popular OWL, are of this shape.
Constraint satisfaction problems (CSPs) are an important formal framework for the uniform treatment of various prominent AI tasks, e.g., coloring or scheduling problems. Solving CSPs is, in general, known to be NP-complete and fixed-parameter intractable when parameterized by their constraint scopes. We give a characterization of those classes of CSPs for which the problem becomes fixed-parameter tractable. Our characterization significantly increases the utility of the CSP framework by making it possible to decide the fixed-parameter tractability of problems via their CSP formulations. We further extend our characterization to the evaluation of unions of conjunctive queries, a fundamental problem in databases. Furthermore, we provide some new insight on the frontier of PTIME solvability of CSPs. In particular, we observe that bounded fractional hypertree width is more general than bounded hypertree width only for classes that exhibit a certain type of exponential growth. The presented work resolves a long-standing open problem and yields powerful new tools for complexity research in AI and database theory.
We propose a generalisation of liquid democracy in which a voter can either vote directly on the issues at stake, delegate her vote to another voter, or express complex delegations to a set of trusted voters. By requiring a ranking of desirable delegations and a backup vote from each voter, we are able to put forward and compare four algorithms to solve delegation cycles and obtain a final collective decision.
The Resource-Constrained Project Scheduling Problem (RCPSP) and its extension via activity modes (MRCPSP) are well-established scheduling frameworks that have found numerous applications in a broad range of settings related to artificial intelligence. Unsurprisingly, the problem of finding a suitable schedule in these frameworks is known to be NP-complete; however, aside from a few results for special cases, we have lacked an in-depth and comprehensive understanding of the complexity of the problems from the viewpoint of natural restrictions of the considered instances. In the first part of our paper, we develop new algorithms and give hardness-proofs in order to obtain a detailed complexity map of (M)RCPSP that settles the complexity of all 1024 considered variants of the problem defined in terms of explicit restrictions of natural parameters of instances. In the second part, we turn to implicit structural restrictions defined in terms of the complexity of interactions between individual activities. In particular, we show that if the treewidth of a graph which captures such interactions is bounded by a constant, then we can solve MRCPSP in polynomial time.
A prominent application of knowledge graph (KG) is document enrichment. Existing methods identify mentions of entities in a background KG and enrich documents with entity types and direct relations. We compute an entity relation subgraph (ERG) that can more expressively represent indirect relations among a set of mentioned entities. To find compact, representative, and relevant ERGs for effective enrichment, we propose an efficient best-first search algorithm to solve a new combinatorial optimization problem that achieves a trade-off between representativeness and compactness, and then we exploit ontological knowledge to rank ERGs by entity-based document-KG and intra-KG relevance. Extensive experiments and user studies show the promising performance of our approach.
We present NeurASP, a simple extension of answer set programs by embracing neural networks. By treating the neural network output as the probability distribution over atomic facts in answer set programs, NeurASP provides a simple and effective way to integrate sub-symbolic and symbolic computation. We demonstrate how NeurASP can make use of a pre-trained neural network in symbolic computation and how it can improve the neural network's perception result by applying symbolic reasoning in answer set programming. Also, NeurASP can make use of ASP rules to train a neural network better so that a neural network not only learns from implicit correlations from the data but also from the explicit complex semantic constraints expressed by the rules.
We study how belief merging operators can be considered as maximum likelihood estimators, i.e., we assume that there exists a (unknown) true state of the world and that each agent participating in the merging process receives a noisy signal of it, characterized by a noise model. The objective is then to aggregate the agents' belief bases to make the best possible guess about the true state of the world. In this paper, some logical connections between the rationality postulates for belief merging (IC postulates) and simple conditions over the noise model under consideration are exhibited. These results provide a new justification for IC merging postulates. We also provide results for two specific natural noise models: the world swap noise and the atom swap noise, by identifying distance-based merging operators that are maximum likelihood estimators for these two noise models.