Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due to their general nature, they have found applications for studying computational processes, interaction in multi-agent systems, machine learning algorithms and other computer science related phenomena. In the vast majority of applications, a dynamical system consists of the action of a continuous `transition function' on a metric space. In this work, we consider decidable formal systems for reasoning about such structures. Spatial logics can be traced back to the 1940's, but our work follows a more dynamic turn that these logics have taken due to two recent developments: the study of the topological mu-calculus, and the the integration of linear temporal logic with logics based on the Cantor derivative. In this paper, we combine dynamic topological logics based on the Cantor derivative and the `next point in time' operators with an expressively complete fixed point operator to produce a combination of the topological mu-calculus with linear temporal logic. We show that the resulting logics are decidable and have a natural axiomatisation. Moreover, we prove that these logics are complete for interpretations on the Cantor space, the rational numbers, and subspaces thereof.
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Epistemic planning is useful in situations where multiple agents have different knowledge and beliefs about the world, such as in robot-human interaction. One aspect that has been largely neglected in the literature is planning with observations in the presence of false beliefs. This is a particularly challenging problem because it requires belief revision. We introduce a simple specification language for reasoning about actions with knowledge and belief. We demonstrate our approach on well-known false-belief tasks such as the Sally-Anne Task and compare it to other action languages. Our logic leads to an epistemic planning formalism that is expressive enough to model second-order false-belief tasks, yet has the same computational complexity as classical planning.
Assumption-based argumentation (ABA) is a powerful defeasible reasoning formalism which is based on the interplay of assumptions, their contraries, and inference rules. ABA with preferences (ABA+) generalizes the basic model by allowing qualitative comparison between assumptions. The integration of preferences however comes with a cost. In ABA+, the evaluation under two central and well-established semantics---grounded and complete semantics---is not guaranteed to yield an outcome. Moreover, while ABA frameworks without preferences allow for a graph-based representation in Dung-style frameworks, an according instantiation for general ABA+ frameworks has not been established so far. In this work, we tackle both issues: First, we develop a novel abstract argumentation formalism based on set-to-set attacks. We show that our so-called Hyper Argumentation Frameworks (HYPAFs) capture ABA+. Second, we propose relaxed variants of complete and grounded semantics for HYPAFs that yield an extension for all frameworks by design, while still faithfully generalizing the established semantics of Dung-style Argumentation Frameworks. We exploit the newly established correspondence between ABA+ and HYPAFs to obtain variants for grounded and complete ABA+ semantics that are guaranteed to yield an outcome. Finally, we discuss basic properties and provide a complexity analysis. Along the way, we settle the computational complexity of several ABA+ semantics.
This paper studies a stable model semantics for Description Logic (DL) knowledge bases (KBs) and for (possibly cyclic) terminologies, ultimately showing that terminologies under the proposed semantics can be equipped with effective reasoning algorithms. The semantics is derived using Quantified Equilibrium Logic, and---in contrast to the usual semantics of DLs based on classical logic---supports default negation and allows to combine the open-world and the closed-world assumptions in a natural way. Towards understanding the computational properties of this and related formalisms, we show a strong undecidability result that applies not only to KBs under the stable model semantics, but also to the more basic setting of minimal model reasoning. Specifically, we show that concept satisfiability in minimal models of an ALCIO KB is undecidable. We then turn our attention to (possibly cyclic) DL terminologies, where ontological axioms are limited to definitions of concept names in terms of complex concepts. This restriction still yields a very rich setting. We show that standard reasoning problems, like concept satisfiability and subsumption, are ExpTime-complete for terminologies expressed in ALCI under the stable model semantics.
We consider the NP-hard problem of finding a smallest decision tree representing a classification instance in terms of a partially defined Boolean function. Small decision trees are desirable to provide an interpretable model for the given data. We show that the problem is fixed-parameter tractable when parameterized by the rank-width of the incidence graph of the given classification instance. Our algorithm proceeds by dynamic programming using an NLC decomposition obtained from a rank-width decomposition. The key to the algorithm is a succinct representation of partial solutions. This allows us to limit the space and time requirements for each dynamic programming step in terms of the parameter.
The ability to generalise from a small number of examples is a fundamental challenge in machine learning. To tackle this challenge, we introduce an inductive logic programming (ILP) approach that combines negation and predicate invention. Combining these two features allows an ILP system to generalise better by learning rules with universally quantified body-only variables. We implement our idea in NOPI, which can learn normal logic programs with predicate invention, including Datalog programs with stratified negation. Our experimental results on multiple domains show that our approach can improve predictive accuracies and learning times.
Explaining an answer to a Datalog query is an essential task towards Explainable AI, especially nowadays where Datalog plays a critical role in the development of ontology-based applications. A well-established approach for explaining a query answer is the so-called why-provenance, which essentially collects all the subsets of the input database that can be used to obtain that answer via some derivation process, typically represented as a proof tree. It is well known, however, that computing the why-provenance for Datalog queries is computationally expensive, and thus, very few attempts can be found in the literature. The goal of this work is to demonstrate how off-the-shelf SAT solvers can be exploited towards an efficient computation of the why-provenance for Datalog queries. Interestingly, our SAT-based approach allows us to build the why-provenance in an incremental fashion, that is, one explanation at a time, which is much more useful in a practical context than the one-shot computation of the whole set of explanations as done by existing approaches.
We present a novel computational approach to resolving conflicts among norms by nonmonotonic normative reasoning (in constrained I/O logics). Our approach extends standard sequent-based proof systems and makes them more adequate to nonmonotonic reasoning by adding to the sequents annotations that keep track of what is known about the defeasible status of the derived sequents. This makes transparent the reasons according to which norms should be applicable or inapplicable, and accordingly the sequents that make use of such norms are accepted or retracted. We also show that this proof theoretic method has tight links to the semantics of formal argumentation frameworks. The outcome of this paper is thus a threefold characterization result that relates, in the context of nonmonotonic normative reasoning, three traditional ingredients of AI-based reasoning methods: maximally consistent sets of premises (in constrained I/O logics), derived sequents (which are accepted in corresponding annotated sequent calculi), and logical arguments (that belong to the grounded extensions of the induced logical argumentation frameworks).
Query answering for Knowledge Bases (KBs) amounts to extracting information from the various models of a KB, and presenting the user with an object that represents such information. In the vast majority of cases, this object consists of those tuples of constants that satisfy the query expression either in every model (certain answers) or in some model (possible answers). However, similarly to the case of incomplete databases, both these forms of answers are a lossy representation of all the knowledge inferable from the query and the queried KB. In this paper, we illustrate a formal framework to characterize the information that query answers for KBs are able to represent. As a first application of the framework, we study the informativeness of current query answering approaches, including the recently introduced partial answers. We then define a novel notion of answers, allowing repetition of variables across answer tuples. We show that these answers are capable of representing a meaningful form of information, and we also study their data complexity properties.
This paper studies the design and analysis of approximation algorithms for aggregating preferences over combinatorial domains, represented using Conditional Preference Networks (CP-nets). Its focus is on aggregating preferences over so-called swaps, for which optimal solutions in general are already known to be of exponential size. We first analyze a trivial 2-approximation algorithm that simply outputs the best of the given input preferences, and establish a structural condition under which the approximation ratio of this algorithm is improved to 4/3. We then propose a polynomial-time approximation algorithm whose outputs are provably no worse than those of the trivial algorithm, but often substantially better. A family of problem instances is presented for which our improved algorithm produces optimal solutions, while, for any ε, the trivial algorithm cannot attain a (2- ε)-approximation. These results may lead to the first polynomial-time approximation algorithm that solves the CP-net aggregation problem for swaps with an approximation ratio substantially better than 2.
Dung’s Argumentation Framework (AF) has been extended in several directions. Among the numerous proposed extensions, three of them seem to be of particular interest and have correlations between them. These extensions are: constrained AF (CAF), where AF is augmented with (strong) constraints; epistemic AF (EAF), where AF is augmented with epistemic constraints; and incomplete AF (iAF), where arguments and attacks can be uncertain. While the complexity and expressiveness of CAF and iAF have been studied, that of EAF has not been explored so far. In this paper we investigate the complexity and expressivity of EAF. To this end, we first introduce the Labeled CAF (LCAF), a variation of CAF where constraints are defined over the alphabet of labeled arguments. Then, we investigate the complexity of credulous and skeptical reasoning and show that: i) EAF is more expressive than iAF (under preferred semantics), ii) although LCAF is a restriction of EAF where modal operators are not allowed, these frameworks have the same complexity, iii) the results for LCAF close a gap in the characterization of the complexity of CAF. Interestingly, even though EAF has the same complexity as LCAF, it allows modeling domain knowledge in a more natural and easy-to-understand way.
Point clouds have shown significant potential in various domains, including Simultaneous Localization and Mapping (SLAM). However, existing approaches either rely on dense point clouds to achieve high localization accuracy or use generalized descriptors to reduce map size. Unfortunately, these two aspects seem to conflict with each other. To address this limitation, we propose an unified architecture, DeepPointMap, achieving excellent preference on both aspects. We utilize neural network to extract highly representative and sparse neural descriptors from point clouds, enabling memory-efficient map representation and accurate multi-scale localization tasks (e.g., odometry and loop-closure). Moreover, we showcase the versatility of our framework by extending it to more challenging multi-agent collaborative SLAM. The promising results obtained in these scenarios further emphasize the effectiveness and potential of our approach.
Global localization is a challenging task for intelligent robots, as its accuracy directly contributes to the performance of downstream navigation and planning tasks. However, existing literature focus more on the place retrieval and the success rate of localization, with limited attention given to the metrics of position estimation. In this paper, a single-shot global LiDAR localization method is proposed with the ultimate goal of achieving high position accuracy, inspired by the positioning approach of multi-constellation localization systems. Initially, we perform coarse localization using global descriptors and select observation points along with their corresponding coordinates based on the obtained coarse localization results. Coordinates can be acquired from a pre-built map, GNSS, or other devices. Then, a lightweight LiDAR odometry method is designed to estimate the distance between the retrieved data and the observation points. Ultimately, the localization problem is transformed into an optimization problem of solving a system of multiple sphere equations. The experimental results on the KITTI dataset and the self-collected dataset demonstrate that our method achieves an average localization error (including errors in the z-axis) of 0.89 meters. In addition, it achieves retrieval efficiency of 0.357 s per frame on the former dataset and 0.214 s per frame on the latter one. Code and data are available at https://github.com/jlurobot/multi-constellation-localization.
Our work aims at efficiently leveraging ambiguous demonstrations for the training of a reinforcement learning (RL) agent. An ambiguous demonstration can usually be interpreted in multiple ways, which severely hinders the RL agent from learning stably and efficiently. Since an optimal demonstration may also suffer from being ambiguous, previous works that combine RL and learning from demonstration (RLfD works) may not work well. Inspired by how humans handle such situations, we propose to use self-explanation (an agent generates explanations for itself) to recognize valuable high-level relational features as an interpretation of why a successful trajectory is successful. This way, the agent can leverage the explained important relations as guidance for its RL learning. Our main contribution is to propose the Self-Explanation for RL from Demonstrations (SERLfD) framework, which can overcome the limitations of existing RLfD works. Our experimental results show that an RLfD model can be improved by using our SERLfD framework in terms of training stability and performance. To foster further research in self-explanation-guided robot learning, we have made our demonstrations and code publicly accessible at https://github.com/YantianZha/SERLfD. For a deeper understanding of our work, interested readers can refer to our arXiv version at https://arxiv.org/pdf/2110.05286.pdf, including an accompanying appendix.
Due to the inability to receive signals from the Global Navigation Satellite System (GNSS) in extreme conditions, achieving accurate and robust navigation for Unmanned Aerial Vehicles (UAVs) is a challenging task. Recently emerged, vision-based navigation has been a promising and feasible alternative to GNSS-based navigation. However, existing vision-based techniques are inadequate in addressing flight deviation caused by environmental disturbances and inaccurate position predictions in practical settings. In this paper, we present a novel angle robustness navigation paradigm to deal with flight deviation in point-to-point navigation tasks. Additionally, we propose a model that includes the Adaptive Feature Enhance Module, Cross-knowledge Attention-guided Module and Robust Task-oriented Head Module to accurately predict direction angles for high-precision navigation. To evaluate the vision-based navigation methods, we collect a new dataset termed as UAV_AR368. Furthermore, we design the Simulation Flight Testing Instrument (SFTI) using Google Earth to simulate different flight environments, thereby reducing the expenses associated with real flight testing. Experiment results demonstrate that the proposed model outperforms the state-of-the-art by achieving improvements of 26.0% and 45.6% in the success rate of arrival under ideal and disturbed circumstances, respectively.
The utilization of multi-modal sensor data in visual place recognition (VPR) has demonstrated enhanced performance compared to single-modal counterparts. Nonetheless, integrating additional sensors comes with elevated costs and may not be feasible for systems that demand lightweight operation, thereby impacting the practical deployment of VPR. To address this issue, we resort to knowledge distillation, which empowers single-modal students to learn from cross-modal teachers without introducing additional sensors during inference. Despite the notable advancements achieved by current distillation approaches, the exploration of feature relationships remains an under-explored area. In order to tackle the challenge of cross-modal distillation in VPR, we present DistilVPR, a novel distillation pipeline for VPR. We propose leveraging feature relationships from multiple agents, including self-agents and cross-agents for teacher and student neural networks. Furthermore, we integrate various manifolds, characterized by different space curvatures for exploring feature relationships. This approach enhances the diversity of feature relationships, including Euclidean, spherical, and hyperbolic relationship modules, thereby enhancing the overall representational capacity. The experiments demonstrate that our proposed pipeline achieves state-of-the-art performance compared to other distillation baselines. We also conduct necessary ablation studies to show design effectiveness. The code is released at: https://github.com/sijieaaa/DistilVPR
MorphVAE: Advancing Morphological Design of Voxel-Based Soft Robots with Variational Autoencoders
PDF ↗Soft robot design is an intricate field with unique challenges due to its complex and vast search space. In the past literature, evolutionary computation algorithms, including novel probabilistic generative models (PGMs), have shown potential in this realm. However, these methods are sample inefficient and predominantly focus on rigid robots in locomotion tasks, which limit their performance and application in robot design automation. In this work, we propose MorphVAE, an innovative PGM that incorporates a multi-task training scheme and a meticulously crafted sampling technique termed ``continuous natural selection'', aimed at bolstering sample efficiency. This method empowers us to gain insights from assessed samples across diverse tasks and temporal evolutionary stages, while simultaneously maintaining a delicate balance between optimization efficiency and biodiversity. Through extensive experiments in various locomotion and manipulation tasks, we substantiate the efficiency of MorphVAE in generating high-performing and diverse designs, surpassing the performance of competitive baselines.
Hierarchical Planning and Learning for Robots in Stochastic Settings Using Zero-Shot Option Invention
PDF ↗This paper addresses the problem of inventing and using hierarchical representations for stochastic robot-planning problems. Rather than using hand-coded state or action representations as input, it presents new methods for learning how to create a high-level action representation for long-horizon, sparse reward robot planning problems in stochastic settings with unknown dynamics. After training, this system yields a robot-specific but environment independent planning system. Given new problem instances in unseen stochastic environments, it first creates zero-shot options (without any experience on the new environment) with dense pseudo-rewards and then uses them to solve the input problem in a hierarchical planning and refinement process. Theoretical results identify sufficient conditions for completeness of the presented approach. Extensive empirical analysis shows that even in settings that go beyond these sufficient conditions, this approach convincingly outperforms baselines by 2x in terms of solution time with orders of magnitude improvement in solution quality.
Object rearrangement in a multi-room setup should produce a reasonable plan that reduces the agent's overall travel and the number of steps. Recent state-of-the-art methods fail to produce such plans because they rely on explicit exploration for discovering unseen objects due to partial observability and a heuristic planner to sequence the actions for rearrangement. This paper proposes a novel task planner to efficiently plan a sequence of actions to discover unseen objects and rearrange misplaced objects within an untidy house to achieve a desired tidy state. The proposed method introduces several innovative techniques, including (i) a method for discovering unseen objects using commonsense knowledge from large language models, (ii) a collision resolution and buffer prediction method based on Cross-Entropy Method to handle blocked goal and swap cases, (iii) a directed spatial graph-based state space for scalability, and (iv) deep reinforcement learning (RL) for producing an efficient plan to simultaneously discover unseen objects and rearrange the visible misplaced ones to minimize the overall traversal. The paper also presents new metrics and a benchmark dataset called MoPOR to evaluate the effectiveness of the rearrangement planning in a multi-room setting. The experimental results demonstrate that the proposed method effectively addresses the multi-room rearrangement problem.
Visual place recognition (VPR) is a fundamental task for many applications such as robot localization and augmented reality. Recently, the hierarchical VPR methods have received considerable attention due to the trade-off between accuracy and efficiency. They usually first use global features to retrieve the candidate images, then verify the spatial consistency of matched local features for re-ranking. However, the latter typically relies on the RANSAC algorithm for fitting homography, which is time-consuming and non-differentiable. This makes existing methods compromise to train the network only in global feature extraction. Here, we propose a transformer-based deep homography estimation (DHE) network that takes the dense feature map extracted by a backbone network as input and fits homography for fast and learnable geometric verification. Moreover, we design a re-projection error of inliers loss to train the DHE network without additional homography labels, which can also be jointly trained with the backbone network to help it extract the features that are more suitable for local matching. Extensive experiments on benchmark datasets show that our method can outperform several state-of-the-art methods. And it is more than one order of magnitude faster than the mainstream hierarchical VPR methods using RANSAC. The code is released at https://github.com/Lu-Feng/DHE-VPR.