dc.description.abstract | This dissertation is about the analysis of systems using temporal logics, focusing on three perspectives: temporal logic monitoring, motion planning with temporal logic specifications, and temporal logic inference from time series data. Temporal logic monitoring checks if all the given simulation traces satisfy a particular temporal logic formula describing a desired or undesired system attribute, such as correctness or safety criteria. This dissertation is about temporal logic monitoring for swarm robotic systems in particular. Motion planning with temporal logic specifications involves designing control inputs for the robotic system, given its dynamic model and a temporal logic formula, in order to satisfy the desired temporal logic specifications. Temporal logic inference from time series data addresses the challenge of learning a temporal logic formula from a given dataset, allowing for the description of data characteristics in an interpretable format. To begin with, we first introduce the Signal Temporal Logic (STL) and Swarm Signal Temporal Logic (SwarmSTL). STL describes behaviors of individual agents, whereas SwarmSTL describes behaviors of robot swarms on the swarm level. SwarmSTL is defined on the generalized moments (GMs) that represent swarm features. For SwarmSTL, we propose a centralized, sampling-based monitoring algorithm as well as a distributed monitoring algorithm for temporal logic monitoring of robot swarms. We use the attribute of GMs being the mean of a polynomial function to design a Generalized Moment Consensus Algorithm (GMCA), allowing each agent to estimate the GMs and track their satisfaction with respect to SwarmSTL formulas. Next, we present the work of distributed motion planning for robot swarms under SwarmSTL specifications. The motion planning problem is formulated as a mixed-integer quadratic programming (MIQP) problem with the SwarmSTL formulas encoded as linear constraints. A distributed branch and bound algorithm (DBB) executed by the agents is proposed to solve the MIQP problem, and the agents can achieve consensus on the optimal trajectory of the generalized moments, from which the agents can compute the trajectories of their own through inverse projection. Finally, we present the work of temporal logic inference from time series data. The inference work can be divided into two categories from the perspective of the methods to find the optimal parameters of the formulas. The first category of temporal logic inference involves SwarmSTL inference from swarm execution traces. The SwarmSTL inference problem is posed as optimizing parameters for given SwarmSTL formula structures such that the inferred SwarmSTL formula can best describe the swarm data. We propose two algorithms for SwarmSTL inference. One is SwarmSTL inference with entire swarm data, and another is SwarmSTL inference via sampling. To overcome the traditional STL inference algorithm's limitations of nonsmooth robustness degrees and low computation efficiency, we propose the second category of temporal logic inference algorithms. We introduce weights into STL and propose a weighted STL (wSTL). An end-to-end differentiable neuro-symbolic model called Signal Temporal lOgic Neural nEtwork (STONE) is developed to learn wSTL formulas, which improves the computation efficiency of learning wSTL formulas. STONE's design is based on the robustness degree, which is a real-valued number reflecting the degree of satisfaction of wSTL formulas over time series data. To better accommodate the design of STONE to the convention of neural networks and its real-world application, novel quantitative semantics based on the notion of truth degree are proposed for wSTL, which generates the development of a signal temporal logic neural network for electroencephalogram (EEG) signal analysis (EEG-STONE) and seizure detection. Although STONE and EEG-STONE can tackle the computation efficiency limitation of traditional signal temporal logic inference algorithms, they can only achieve binary time series classification tasks. To expand their capability to multi-class time series classification, we develop a decision tree-based time series classifier based on EEG-STONE to classify multi-class time series data, where every node in the tree classifier is an EEG-STONE. In addition to the above neuro-symbolic models, we also explore the effectiveness of similar neuro-symbolic models for modeling multivariate point process. A novel framework for modeling temporal point processes called clock logic neural networks (CLNN) which learn weighted clock logic (wCL) formulas as interpretable temporal logic rules by which some events promote or inhibit the occurrence of other events. Unlike conventional approaches of searching for generative rules through expensive combinatorial optimization, we design smooth activation functions for components of wCL formulas that enable a continuous relaxation of the discrete search space and efficient learning of wCL formulas using gradient-based methods. | |