Temporal Logic Research Articles

A Framework for Simultaneous Task Allocation and Planning under Uncertainty

We present novel techniques for simultaneous task allocation and planning in multi-robot systems operating under uncertainty. By performing task allocation and planning simultaneously, allocations are informed by individual robot behaviour, creating more efficient team behaviour. We go beyond existing work by planning for task reallocation across the team given a model of partial task satisfaction under potential robot failures and uncertain action outcomes. We model the problem using Markov decision processes, with tasks encoded in co-safe linear temporal logic, and optimise for the expected number of tasks completed by the team. To avoid the inherent complexity of joint models, we propose an alternative model that simultaneously considers task allocation and planning, but in a sequential fashion. We then build a joint policy from the sequential policy obtained from our model, thus allowing for concurrent policy execution. Furthermore, to enable adaptation in the case of robot failures, we consider replanning from failure states and propose an approach to preemptively replan in an anytime fashion, replanning for more probable failure states first. Our method also allows us to quantify the performance of the team by providing an analysis of properties such as the expected number of completed tasks under concurrent policy execution. We implement and extensively evaluate our approach on a range of scenarios. We compare its performance to a state-of-the-art baseline in decoupled task allocation and planning: sequential single-item auctions. Our approach outperforms the baseline in terms of computation time and the number of times replanning is required on robot failure.

Singly exponential translation of alternating weak Büchi automata to unambiguous Büchi automata

We introduce a method for translating an alternating weak Büchi automaton (AWA), which corresponds to a Linear Dynamic Logic (LDL) formula, to an unambiguous Büchi automaton (UBA). Our translations generalize constructions for Linear Temporal Logic (LTL), a less expressive specification language than LDL. In classical constructions, LTL formulas are first translated to alternating very weak Büchi automata (AVAs)—automata that have only singleton strongly connected components (SCCs); these AVAs are then handled by efficient disambiguation procedures. However, general AWAs can have larger SCCs, which complicates disambiguation. Currently, the only available disambiguation procedure has to go through an intermediate construction of nondeterministic Büchi automata (NBAs), which would incur an exponential blow-up of its own. We introduce a translation from general AWAs to UBAs with a singly exponential blow-up, which also immediately provides a singly exponential translation from LDL to UBAs. Interestingly, the complexity of our translation is smaller than the best known disambiguation algorithm for NBAs (broadly (0.53n)n vs. (0.76n)n), while the input of our construction can be exponentially more succinct.

Validating multiple variants of an automotive light system with Alloy 6

This paper reports on the development and validation of a formal model for an automotive adaptive exterior lights system (ELS) with multiple variants in Alloy 6, which is the most recent version of the Alloy lightweight formal specification language that supports mutable relations and temporal logic. We explore different strategies to address variability, one in pure Alloy and another through an annotative language extension. We then show how Alloy and its Analyzer can be used to validate systems of this nature, namely by checking that the reference scenarios are admissible, and to automatically verify whether the established requirements hold. A prototype was developed to translate the provided validation sequences into Alloy and back to further automate the validation process. The resulting ELS model was validated against the provided validation sequences and verified for most of requirements for all variants.

STRONG COMPLETENESS OF A FIRST-ORDER TEMPORAL LOGIC FOR REAL TIME

Abstract Propositional temporal logic over the real number time flow is finitely axiomatisable, but its first-order counterpart is not recursively axiomatisable. We study the logic that combines the propositional axiomatisation with the usual axioms for first-order logic with identity, and develop an alternative “admissible” semantics for it, showing that it is strongly complete for admissible models over the reals. By contrast there is no recursive axiomatisation of the first-order temporal logic of admissible models whose time flow is the integers, or any scattered linear ordering.

Design of a bi-directional methodology for automated assessment of compliance to continuous application of clinical guidelines, and its evaluation in the type 2 diabetes domain.

We introduce a new approach for automated guideline-based-care quality assessment, the bidirectional knowledge-based assessment of compliance (BiKBAC) method, and the DiscovErr system, which implements it. Our methodology compares the guideline's Asbru-based formal representation, including its intentions, with the longitudinal medical record, using a top-down and bottom-up approach. Partial matches are resolved using fuzzy temporal logic. The system was evaluated in the type 2 Diabetes management domain, comparing it to three expert clinicians, including two diabetes experts. The system and the experts commented on the management of 10 patients, randomly selected from 2,000 diabetes patients. On average, each record spanned 5.23 years; the data included 1,584 medical transactions. The system provided 279 comments. The experts made 181 different unique comments. The completeness (recall) of the system was 91% when the gold standard was comments made by at least two of the three experts, and 98%, compared to comments made by all three experts. The experts also assessed all of the 114 medication-therapy-related comments, and a random 35% of the 165 tests-and-monitoring-related comments. The system's correctness (precision) was 81%, compared to comments judged as correct by both diabetes experts, and 91%, compared to comments judged as correct by one diabetes expert and at least as partially correct by the other. 89% of the comments were judged as important by both diabetes experts, 8% were judged as important by one expert, and 3% were judged as less important by both experts. Adding the validated system comments to the experts' comments, the completeness scores of the experts were 75%, 60%, and 55%; the expert correctness scores were respectively 99%, 91%, and 88%. Thus, the system could be ranked first in completeness and second in correctness. We conclude that systems such as DiscovErr can effectively assess the quality of continuous guideline-based care.

Model checking distributed temporal logic

Abstract The distributed temporal logic (DTL) is a logic for reasoning about temporal properties of distributed systems from the local point of view of the system’s agents, which are assumed to execute sequentially and to interact by means of synchronous event sharing. Different versions of DTL have been provided over the years for a number of different applications, reflecting different perspectives on how non-local information can be accessed by each agent. In this paper, we propose an automata-theoretic model checking algorithm for DTL. To this end, we propose a notion of distributed transition system that will be used to specify the system to be verified. The properties that the system should meet are specified in DTL. In order to capture the models of these properties, we propose the notions of generalized distributed Büchi automaton and of distributed Büchi automaton. With these concepts, we are able to adapt results from automata-theoretic approaches to model checking in LTL to the distributed case.

Runtime Verification-Based Safe MARL for Optimized Safety Policy Generation for Multi-Robot Systems

The intelligent warehouse is a modern logistics management system that uses technologies like the Internet of Things, robots, and artificial intelligence to realize automated management and optimize warehousing operations. The multi-robot system (MRS) is an important carrier for implementing an intelligent warehouse, which completes various tasks in the warehouse through cooperation and coordination between robots. As an extension of reinforcement learning and a kind of swarm intelligence, MARL (multi-agent reinforcement learning) can effectively create the multi-robot systems in intelligent warehouses. However, MARL-based multi-robot systems in intelligent warehouses face serious safety issues, such as collisions, conflicts, and congestion. To deal with these issues, this paper proposes a safe MARL method based on runtime verification, i.e., an optimized safety policy-generation framework, for multi-robot systems in intelligent warehouses. The framework consists of three stages. In the first stage, a runtime model SCMG (safety-constrained Markov Game) is defined for the multi-robot system at runtime in the intelligent warehouse. In the second stage, rPATL (probabilistic alternating-time temporal logic with rewards) is used to express safety properties, and SCMG is cyclically verified and refined through runtime verification (RV) to ensure safety. This stage guarantees the safety of robots’ behaviors before training. In the third stage, the verified SCMG guides SCPO (safety-constrained policy optimization) to obtain an optimized safety policy for robots. Finally, a multi-robot warehouse (RWARE) scenario is used for experimental evaluation. The results show that the policy obtained by our framework is safer than existing frameworks and includes a certain degree of optimization.

Deep Learning-Enhanced Sampling-Based Path Planning for LTL Mission Specifications.

The presented paper introduces a novel path planning algorithm designed for generating low-cost trajectories that fulfill mission requirements expressed in Linear Temporal Logic (LTL). The proposed algorithm is particularly effective in environments where cost functions encompass the entire configuration space. A core contribution of this paper is the presentation of a refined approach to sampling-based path planning algorithms that aligns with the specified mission objectives. This enhancement is achieved through a multi-layered framework approach, enabling a simplified discrete abstraction without relying on mesh decomposition. This abstraction is especially beneficial in complex or high-dimensional environments where mesh decomposition is challenging. The discrete abstraction effectively guides the sampling process, influencing the selection of vertices for extension and target points for steering in each iteration. To further improve efficiency, the algorithm incorporates a deep learning-based extension, utilizing training data to accurately model the optimal trajectory distribution between two points. The effectiveness of the proposed method is demonstrated through simulated tests, which highlight its ability to identify low-cost trajectories that meet specific mission criteria. Comparative analyses also confirm the superiority of the proposed method compared to existing methods.

Temporal logics for compartmental models

Abstract This paper introduces two logic frameworks for the study of SIR (Susceptible-Infected-Recovered) and SIRS compartmental epidemic models, one based on Linear Temporal Logic and the other on Computation Tree Logic. We provide a short literature overview on compartmental models and other related works using logics, and then define our logics with their respective axiomatizations, and demonstrate their soundness and completeness proofs.

Mining of extended signal temporal logic specifications with ParetoLib 2.0

Cyber-physical systems are complex environments that combine physical devices (i.e., sensors and actuators) with a software controller. The ubiquity of these systems and dangers associated with their failure require the implementation of mechanisms to monitor, verify and guarantee their correct behaviour. This paper presents ParetoLib 2.0, a Python tool for offline monitoring and specification mining of cyber-physical systems. ParetoLib 2.0 uses signal temporal logic (STL) as the formalism for specifying properties on time series. ParetoLib 2.0 builds upon other tools for evaluating and mining STL expressions, and extends them with new functionalities. ParetoLib 2.0 implements a set of new quantitative operators for trace analysis in STL, a novel mining algorithm and an original graphical user interface. Additionally, the performance is optimised with respect to previous releases of the tool via data-type annotations and multi core support. ParetoLib 2.0 allows the offline verification of STL properties as well as the specification mining of parametric STL templates. Thanks to the implementation of the new quantitative operators for STL, the tool outperforms the expressiveness and capabilities of similar runtime monitors.

Zombie Startups: Time, Labour and Value in Singapore’s Innovative Entrepreneurship ‘Ecosystem’

ABSTRACT Zombie startups – which neither grow nor die, but persistently breakeven and inexplicably refuse to fold – are a staple presence in startup sectors globally. While dominant business discourses dismiss them as aberrantly misguided ventures, I draw on anthropological understandings of the labour of time to show how zombies are integral to the startup sector’s temporal logics. Startup sectors run on the interplay between what scholars have termed ‘the time of investment’ and ‘the time of speculation.’ Following a startup in Singapore through five years of unprofitable operation, my ethnography shows how zombies are produced by and, in turn, contribute to maintaining these temporalities. By connecting the value that successful startups create to the unpaid labour that un-succeeding startups do to maintain the sector’s timescape, the article demonstrates how anthropology’s attentiveness to time can surface new forms of relationality that are emerging with this globally expanding form of entrepreneurship.

Controller synthesis for linear temporal logic and steady-state specifications

Controller synthesis for linear temporal logic and steady-state specifications

Formal Analysis and Detection for ROS2 Communication Security Vulnerability

Robotic systems have been widely used in various industries, so the security of communication between robots and their components has become an issue that needs to be focused on. As a framework for developing robotic systems, the security of ROS2 (Robot Operating System 2) can directly affect the security of the upper-level robotic systems. Therefore, it is a worthwhile research topic to detect and analyze the security of ROS2. In this study, we adopted a formal approach to analyze the security of the communication mechanism of ROS2. First, we used a state transition system to model the potential vulnerabilities of ROS2 based on the ROS2 communication mechanism and the basic process of penetration testing. Secondly, we introduced a CIA model based on the established vulnerability model and used linear temporal logic to define its security properties. Then, we designed and implemented a vulnerability detection tool for ROS2 applications based on the vulnerability model and security properties. Finally, we experimentally tested some ROS2-based applications, and the results show that ROS2 has vulnerabilities without additional protection safeguards.

Metric Temporal Equilibrium Logic over Timed Traces

AbstractIn temporal extensions of answer set programming (ASP) based on linear time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. However, timing constraints are important in many applications like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time temporal equilibrium logic, in which temporal operators are constrained by intervals over natural numbers. The resulting Metric Equilibrium Logic (MEL) provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. To this end, we define a translation of metric formulas into monadic first-order formulas and give a correspondence between their models in MEL and Monadic Quantified Equilibrium Logic, respectively. Interestingly, our translation provides a blue print for implementation in terms of ASP modulo difference constraints.

Finite-step approximately bi-similar symbolic model for switched systems

Obtaining an approximately bi-similar symbolic model for a continuous-state system is a crucial step in symbolic control. Symbolic control aims to design switching logic to achieve temporal logic specifications. Most existing approaches to approximate bi-simulation are developed over infinite time horizons. However, many control tasks are set within finite periods in practical scenarios. Hence, it makes sense to consider the behavior of trajectories within finite-time horizons. Therefore, this paper introduces two new notions: finite-time uniform incremental stability (FUI-stability) and finite-step approximate bi-simulation. Furthermore, a FUI-stability condition for switched system is derived using the multiple incremental Lyapunov-like functions technique. A symbolic model is constructed for switched system by the state space grid technique. Subsequently, a sufficient condition for finite-step approximate bi-simulation between the finite-time uniformly incrementally stable (FUI-stable) switched system and the constructed symbolic model is derived. Finally, the obtained results are illustrated by two numerical examples.

Statistical Verification using Surrogate Models and Conformal Inference and a Comparison with Risk-Aware Verification

Uncertainty in safety-critical cyber-physical systems can be modeled using a finite number of parameters or parameterized input signals. Given a system specification in Signal Temporal Logic (STL), we would like to verify that for all (infinite) values of the model parameters/input signals, the system satisfies its specification. Unfortunately, this problem is undecidable in general. Statistical model checking (SMC) offers a solution by providing guarantees on the correctness of CPS models by statistically reasoning on model simulations. We propose a new approach for statistical verification of CPS models for user-provided distribution on the model parameters. Our technique uses model simulations to learn surrogate models , and uses conformal inference to provide probabilistic guarantees on the satisfaction of a given STL property. Additionally, we can provide prediction intervals containing the quantitative satisfaction values of the given STL property for any user-specified confidence level. We compare this prediction interval with the interval we get using risk estimation procedures. We also propose a refinement procedure based on Gaussian Process (GP)-based surrogate models for obtaining fine-grained probabilistic guarantees over sub-regions in the parameter space. This in turn enables the CPS designer to choose assured validity domains in the parameter space for safety-critical applications. Finally, we demonstrate the efficacy of our technique on several CPS models.

Planning for heterogeneous teams of robots with temporal logic, capability, and resource constraints

This paper presents a comprehensive approach for planning for teams of heterogeneous robots with different capabilities and the transportation of resources. We use Capability Temporal Logic (CaTL), a formal language that helps express tasks involving robots with multiple capabilities with spatial, temporal, and logical constraints. We extend CaTL to also capture resource constraints, where resources can be divisible and indivisible, for instance, sand and bricks, respectively. Robots transport resources using various storage types, such as uniform (shared storage among resources) and compartmental (individual storage per resource). Robots’ resource transportation capacity is defined based on resource type and robot class. Robot and resource dynamics and the CaTL mission are jointly encoded in a Mixed Integer Linear Programming (MILP), which maximizes disjoint robot and resource robustness while minimizing spurious movement of both. We propose a multi-robustness approach for Multi-Class Signal Temporal Logic (mcSTL), allowing for generalized quantitative semantics across multiple predicate classes. Thus, we compute availability robustness scores for robots and resources separately. Finally, we conduct multiple experiments demonstrating functionality and time performance by varying resources and storage types.

Time-Controlled Authentication Strategies for Molecular Information Transfer.

Modern cryptography based on computational complexity theory is mainly constructed with silicon-based circuits. As DNA nanotechnology penetrates the molecular domain, utilizing molecular cryptography for data access protection in the biomolecular domain becomes a unique approach to information security. However, building security devices and strategies with robust security and compatibility is still challenging. Here, this study reports a time-controlled molecular authentication strategy using DNAzyme and DNA strand displacement as the basic framework. A time limit exists for authorization and access, and this spontaneous shutdown design further protects secure access. Multiple hierarchical authentications, temporal Boolean logic authentication, and enzyme authentication strategies are constructed based on DNA networks'good compatibility and programmability. This study gives proof of concept for the detection and protection of bioinformation about single nucleotide variants and miRNA, highlighting their potential in biosensing and security protection.

Learning to Execute Timed-Temporal-Logic Navigation Tasks under Input Constraints in Obstacle-Cluttered Environments

This study focuses on addressing the problem of motion planning within workspaces cluttered with obstacles while considering temporal and input constraints. These specifications can encapsulate intricate high-level objectives involving both temporal and spatial constraints. The existing literature lacks the ability to fulfill time specifications while simultaneously managing input-saturation constraints. The proposed approach introduces a hybrid three-component control algorithm designed to learn the safe execution of a high-level specification expressed as a timed temporal logic formula across predefined regions of interest in the workspace. The first component encompasses a motion controller enabling secure navigation within the minimum allowable time interval dictated by input constraints, facilitating the abstraction of the robot’s motion as a timed transition system between regions of interest. The second component utilizes formal verification and convex optimization techniques to derive an optimal high-level timed plan over the mentioned transition system, ensuring adherence to the agent’s specification. However, the necessary navigation times and associated costs among regions are initially unknown. Consequently, the algorithm’s third component iteratively adjusts the transition system and computes new plans as the agent navigates, acquiring updated information about required time intervals and associated navigation costs. The effectiveness of the proposed scheme is demonstrated through both simulation and experimental studies.

Estimating event probabilities via signal temporal logic and first occurrence distributions

Abstract Estimating the probability of events is a significant challenge in many fields, often requiring a probabilistic model or additional labels and tasks for accurate prediction. However, those methods have limited scalability or unnecessary computational resource consumption due to predicting unrelated values. To address these issues, we propose a novel approach that estimates event probabilities based on the distributions of their first occurrence in the time domain. By using Signal Temporal Logic formulas to describe events and applying an algorithm that estimates complex events’ probabilities through simple event occurrence distributions, this study presents an efficient approach that does not depend on high-precision prediction. We evaluate the performance of our method on simulated scenarios of unmanned aerial vehicle motion and autonomous driving.