Automated mining of formal specifications is vital for verifying real-time systems. However, existing passive learning approaches remain restricted to deterministic specifications or limited fragments of Timed Regular Expressions (TRE). To our knowledge, this paper presents the first framework to tackle \emph{precise} passive learning for an expressive timed logic, \emph{Metric Interval Temporal Logic} (MITL) without relying on predefined templates or restricted logic fragments. Our approach formally reduces the timed learning problem into a scalable untimed one. By identifying quantitative timing differences between positive and negative traces, we synthesise precise timed constraints and inject them as new Boolean atomic propositions. This embeds timing into the alphabet, delegating the complex formula evaluation to highly optimised, off-the-shelf untimed LTL tools. Crucially, our framework is complete, guaranteeing a separating specification can always be found. We evaluate our implementation across several benchmarks, demonstrating the effectiveness of our approach.
Air traffic control procedures are executed through spoken exchanges between controllers and pilots. These interactions are essential to the safety of air transportation: failures in their execution can create severe operational hazards, as evidenced by past fatal accidents. Assessing whether an instruction has been followed requires relating what was said to the aircraft concerned, its state, and the obligations that pilots must meet. We present a runtime verification framework that monitors such procedures by checking controller-pilot exchanges, surveillance data, and onboard observations. The framework parses radio communications into events linked to the entities they concern and merges them with surveillance and onboard observations into a time-stamped trace. The ICAO-derived obligations as formalized as temporal formulas with explicit time bounds and evaluated over execution traces. Every violation is reported along with the breached obligations and the observations that support the verdict. With real traffic, the complete pipeline reaches an F1 of 0.85 against blind human-annotated violations; in 1,495 synthetic situations derived from two public corpora, the monitor logic returns the expected verdict in every case. In two historical accidents reconstructed from official investigation reports, the monitor identifies the same procedural deviations documented by the investigators.
Linear temporal logic is a modal extension of propositional logic that allows one to state how a system should behave over time. Its canonical domain is the booleans, but discretely-valued judgements are of little use in steering softly-valued systems (neural policies, adaptive controllers, sequence models, etc). In such cases, the goal formula's (dis)satisfaction becomes a training signal, and differentiability becomes a prime concern. Candidate differentiable semantics abound, but navigating them is tricky. Implementations, where available, are shallow embeddings, demanding an upfront commitment to a single semantic algebra and its (usually implicit) conduct. The paper casts the reader as a functional programmer asked to come to terms with this predicament, and refusing. Out of that refusal comes an evaluation engine that is algebra-generic and amenable to differentiation, together with an executable specification of the algebras it can accept. Various algebras are implemented and audited for their behavior, both forward and backward. Each algebra turns out to be a choice of which direction to disappoint, and how. Everything described (and more) is part of the PyTorch library telos, to be found at https://github.com/konstantinosKokos/telos.
Riccardo Andreoni, Andrei Buliga, Alessandro Daniele +4cs.AI
Neurosymbolic (NeSy) Artificial Intelligence aims to integrate Deep Learning (DL) architectures with symbolic reasoning. While initial NeSy approaches have targeted mainly symbolic reasoning in propositional and first-order logics, recent works have started to address the construction of neurosymbolic frameworks for Temporal Logics, and in particular for LTLf. These approaches have established temporal NeSy as a promising research direction, laying the foundations for learning under temporal constraints. Nonetheless, they leave many questions unanswered. From a theoretical perspective, several differentiable semantics for interpreting LTLf have been proposed but have not yet been formally and systematically defined within a unified framework. Moreover, existing approaches commonly rely on automata to represent temporal knowledge, resulting in limited scalability. Motivated by this research gap, this paper provides the following contributions: (i) formally defining different fuzzy semantics for LTLf, and systematically analysing theoretical properties regarding equivalences and dualities of temporal operators; (ii) showing how these semantics can be directly integrated within a novel NeSy framework, called DiffLTLf, enabling flexible and scalable learning without relying on the usage of automata; and (iii) introducing a novel evaluation protocol of increased complexity of learning tasks w.r.t. existing benchmarks. Our results show that the choice of fuzzy semantics has a significant impact on predictive performance. Moreover, DiffLTLf achieves performance on par with, and sometimes superior to, state-of-the-art probabilistic approaches while substantially improving scalability. Taken together, these results establish direct fuzzy interpretations as a competitive and scalable alternative to existing temporal NeSy frameworks.
Task guided agents demonstrate strong performance in a wide range of complex tasks. However, most existing task representation algorithms are tailored to specific contexts and struggle to generalize across diverse scenarios. Moreover, they typically depend on gradient signals from reinforcement learning controllers to update their weights, which can degrade both representation quality and learning efficiency. To overcome these limitations, we propose LOTUS, a temporal logic inspired universal task representation framework that can be seamlessly integrated into any RL algorithm to enhance agent performance across diverse task settings. Specifically, we design a novel task representation architecture capable of modeling relationships and extracting task semantics from LTL formulas. We further introduce a more effective update mechanism that treats the LTL encoder as a policy, thereby improving representation capacity. To enhance stability and robustness, LOTUS leverages the bisimulation metric, which provides theoretical guarantees for LTL representation, including behavioral equivalence, optimality fidelity, and trajectory robustness. Experimental results show that LOTUS outperforms most existing methods in learning efficiency, generalization capability, and representation quality. Specifically, LOTUS accelerates convergence over 20% in single-task scenarios, achieves a 15%-45% higher success rate in unseen manipulation tasks, and improves generalization performance over 25% in complex multi-task environments with increased sub-goal depth or conjunctions. The corresponding code, videos, and appendix are available at: https://lotus-website.github.io/.
Hallucinations are a major concern for the integration of artificial intelligence into medicine, although less explored in the realm of medical image processing. Unlike problems in natural text understanding and reasoning therewith, determining whether or not predictions derived from biomedical images and signals is less intuitively clear. This article suggests that topological errors could constitute hallucinations in a way that can be more readily measured and thus regulated. Certain of these properties for certain types of problems, such as biomedical signal segmentation, can be rephrased as linear temporal logic predicates, a number of which can be explicitly enforced using probabilistic graphical models. Our simulations show the potential of these explicitly constrained predicates for the case of automatic surgical phase recognition in robot-assisted hysterectomy, improving accuracy by approximately 10% while removing the vast majority of topological errors, suggesting that mathematical guarantees of correctness can supplement other empirical forms of regulating machine learning in medical image computing and computer-assisted interventions.
Translating natural language instructions into machine-interpretable formal specifications enables robots and autonomous systems to plan, reason, and formally verify their behavior. However, existing translation models typically generate a specification for every input, even when the result is unreliable or fails to capture the user's intent, creating risks in safety-critical applications. Inspired by selective conformal prediction, we propose a selective translation framework that not only generates formal specifications but also determines when they can be trusted. Reliability is scored by two complementary black-box signals, the fidelity of the specification back-translated into natural language and the dispersion of repeated translations under exact semantic equivalence, which fail on different errors and jointly separate incorrect translations more sharply than either alone. Conformal risk control calibrates this score into a decision that accepts a specification or abstains, with a distribution-free bound on the rate at which incorrect specifications are accepted for execution, and a conformal anomaly detector on instruction embeddings screens out-of-distribution inputs before any translation is attempted. The proposed framework is general across formal specification languages, with experiments on Signal Temporal Logic (STL), Linear Temporal Logic (LTL), and geometric Spatio-Temporal Logic (SpaTiaL) demonstrating improved translation reliability, robustness under the evaluated cross-tier shifts, and effective uncertainty-aware abstention. This work establishes a foundation for trustworthy natural language interfaces by enabling AI systems to recognize when generated specifications may not be reliable.
Agentic systems driven by large language models (LLMs) are increasingly deployed in real-world workflows where they act on persistent operational data. Before deployment, these systems need to be verified against business requirements that govern workflow execution and data evolution. However, existing approaches do not provide such system-level guarantees, as they mainly constrain or analyse behaviour at the agent's interface level. We study here the verification of agentic systems comprising a single LLM and a tool orchestration harness over relational operational data. We formalise them as Stateful Tool-Enabled Agentic Deployments (STEADs), give their semantics, define the problem of verifying them against First-Order Computation Tree Logic (FO-CTL) specifications, and show that it is undecidable. We identify sufficient conditions for exact preservation of FO-CTL specifications under a finite-domain restriction, over which verification is PSPACE-complete. The key requirement is that renaming opaque identifiers in the data must correspondingly rename the selected tool calls. We show that LLM-driven agents can violate this condition and introduce a canonical deployment wrapper that guarantees it for arbitrary base agents while preserving already-equivariant behaviour. We prove that computing canonical representations required by this construction is graph-isomorphism-hard. Finally, we illustrate our framework on an LLM agent orchestrating a case-management workflow.
Christoph Weinhuber, Maximilian Prokop, Giuseppe De Giacomo +1cs.AI cs.FL cs.LO
Linear Temporal Logic (LTL) is one of the most widely adopted languages for specifying temporal extended objectives in AI, with applications ranging from reactive synthesis to stochastic planning in Markov decision processes and reinforcement learning. Traditionally, solving any of these problems requires translating the LTL specification to a nondeterministic automata on infinite words and then determinizing it, a step that is notoriously difficult in theory and in practice. Recent work has introduced LTLf+, which lifts the finite-trace logic LTLf to infinite traces. LTLf+ has the same expressive power as LTL, yet it retains most of the crucial advantages of its base logic LTLf. Most reasoning in LTLf+ rests on finite automata on finite words, for which we have not only a canonical minimal representation but also an efficient determinization procedure. In this work we present the first translation from LTL to LTLf+. We first normalize an LTL formula into the syntactic reactivity fragment of the Manna-Pnueli hierarchy, to create the general fragment-based shape of LTLf+. We then present linear translations for each individual component of that fragment. As a consequence of this translation, the expanding body of techniques developed for LTLf+ now becomes available to many AI problems currently formulated in LTL. We further show that this comes at no asymptotic cost, as the pipeline from LTL to automaton via LTLf+ remains doubly exponential.
Yan Huang, Xubing Hao, Xiaojin Li +4cs.LO cs.AI cs.ET
The reliance on unstructured free text for documenting clinical trial protocols creates a significant barrier to automated reasoning, cohort discovery, and trial simulation. The lack of formal structure obscures critical temporal phenotypes, such as dynamic eligibility criteria and event timing constraints. Although Temporal Ensemble Logic (TEL) offers an expressive framework for modeling these elements, manual encoding remains a prohibitive bottleneck. We introduce the CT-TEL workflow: a scalable pipeline leveraging Large Language Models (LLMs) to translate narrative clinical protocols into TEL formulas. We applied CT-TEL to generate logical models for 23 real-world trials from ClinicalTrials.gov. We evaluated translation fidelity via a back-translation approach, using LLMs to convert TEL formulas back into natural language and measuring semantic similarity against source texts. The resulting semantic retention suggests that LLMs may offer a pathway for mapping informal protocols to computable logic, providing preliminary evidence toward scalable clinical trial emulation within the emerging "Symbolic Biomedicine" paradigm championed by the corresponding author.
We introduce VSeek, an agentic framework that transforms long-video question answering (LVQA) from a passive, single-pass perception task into a multi-turn retrieval process. VSeek utilizes a natural language-driven search to identify relevant context within long videos and is post-trained with reinforcement learning (RL) to jointly formulate targeted search queries and reason over retrieved clips for LVQA. While RL post-training has revolutionized reasoning in symbolic domains such as mathematics and code, its application to long-video understanding remains hindered by a lack of verified rewards. To ensure that the retrieved context is relevant, we propose a novel neuro-symbolic approach that bridges open-ended natural language with discrete visual verification. Specifically, complex user queries are compiled into formal temporal logic specifications for systematically decomposing natural language questions into a definitive checklist of required atomic visual primitives, such as key objects and activities, along with their temporal ordering. These systematically derived grounding events provide the critical feedback signal for RL post-training, enabling dense, verifiable rewards based on the successful retrieval of these specific visual elements rather than relying entirely on outcome-only answer accuracy. By explicitly optimizing for this verifiable evidence-seeking behavior, VSeek improves Pass@1 scores by up to 8% and Pass@4 scores by 15% on long-video understanding benchmarks compared to base models. We open-source our code at https://utaustin-swarmlab.github.io/VSeek.
Tool-using LLM agents are usually evaluated by final-answer correctness or LLM judges. Neither captures how an answer was produced. In safety-critical settings, the procedure itself is part of correctness. In this paper, we introduce AgentLTL, a language derived from First-Order Linear Temporal Logic (FO-LTL) that expresses procedural rules over agent traces. It yields a deterministic, judge-free compliance score. In this framework, a single specification drives two usages. The first is harnessing: the constraints score completed traces, or gate tool calls by checking each prefix online, before execution. The second is finetuning: the score serves as a dense reward. On a benchmark spanning ordering, branching, iteration, and grounding, block-and-warn harnessing improves compliance on five of seven models. Finetuning with the same reward yields +38 and +17.5 percentage point gains in accuracy and compliance on held-out patterns, including unseen tool-name aliases. These findings are consistent with the model acquiring procedural structure rather than memorizing surface tool names and procedures.
Marco Aruta, Francesco Improta, Vadim Malvone +2cs.MA cs.AI
A rigorous formalization of system requirements is a fundamental prerequisite for the verification of Multi-Agent Systems (MAS). However, writing correct formal specifications is well known as an error-prone, time-consuming, and expertise-intensive task. This difficulty is further accentuated in MAS, where requirements must capture strategic abilities and temporal objectives. At present, there is no established methodology for deriving MAS specifications from natural language. We present a framework for translating Natural Language descriptions of strategic requirements into well-formed ATL/ATL* formulas using Large Language Models (LLMs). Since no available dataset supports supervised learning for the NL-to-ATL/ATL* translation task, we create and curate a novel expert-validated dataset, employed for training and evaluating fine-tuned models. On a held-out test set, evaluated under the LLM judge that best agrees with expert annotations, in-domain fine-tuning of small open-weight models (3 - 7B parameters) matches strong few-shot proprietary API baselines. Our best fine-tuned system reaches 0.84 semantic accuracy, statistically on par with 0.86 for the strongest few-shot proprietary baseline, while keeping requirements on-premises. We further find that judge reliability is inverse to generator strength. The open-weight Llama-3.3-70B tracks human verdicts most closely, whereas the strongest proprietary models are the least reliable judges, over-rejecting faithful paraphrases of the reference. To assess the practical applicability of the generated specifications, we embed our tool to an existing strategic logics model checker, enabling non-expert users to specify strategic properties in natural language.
Luca Boscarato, Ivan Donadello, Alessandro Artale +2cs.AI cs.LG cs.LO
Most of the existing neuro-symbolic AI methods focus on the scenario of static knowledge where objects do not change according to a temporal dimension. Temporal neuro-symbolic works are still under explored and are mainly developed for time-interval logic or propositional linear temporal logic. There is a lack of models studying linear temporal logics with predicates that deal with objects whose properties and relations change through the time. We present First-Order Temporal Logic Tensor Networks (FOT-LTN) that is an extension of Logic Tensor Networks (LTN) that fills this gap by considering a linear-temporal dimension. In particular, FOT-LTN joins the syntax of First-Order Linear Temporal Logic with the fuzzy (and real-valued) semantics of LTN obtaining a framework that supports both temporal operators and quantifiers and is totally differentiable. A first evaluation regards a temporal knowledge graph completion task on two synthetic datasets showing better performance of FOT-LTN with respect to dedicated (purely neural) methods.
Enabling robots to follow natural language commands to complete zero-shot long-horizon tasks remains challenging. It requires extracting implicit temporal and logical constraints from natural language commands and executing multiple sub-tasks accordingly. Recent zero-shot object navigation methods use vision-language models (VLMs) to guide frontier-based exploration in unknown environments, but they are limited to single-target tasks. Real-world commands such as "Clean either the chair or the couch, then turn on the tv." require navigating to multiple targets in a temporally constrained order, which no existing zero-shot system can handle. We present ViTL, a framework that addresses this gap at two levels. At the task level, we use a large language model (LLM) to compile natural language commands into Linear Temporal Logic (LTL) formulas, which are then converted into Deterministic Finite Automata~(DFA) that coordinate multi-channel value maps and trigger dynamic replanning when new objects are detected. At the navigation level, we introduce directional score: rather than producing a direction-agnostic value across the entire field of view, we label frontier directions on the observation image and extract per-direction scores from the VLM. Experiments on Habitat-Matterport 3D (HM3D) show that the full framework enables zero-shot long-horizon completion of natural language navigation tasks with temporal constraints, and that directional score improves single-target navigation accuracy and efficiency over the baseline.
Achraf Hsain, Sultan Almuhammadics.AI cs.CR cs.GT cs.LG cs.MA
Shielded reinforcement learning is typically presented as a runtime safety mechanism that compiles temporal-logic specifications into automata restricting an agent's actions. We argue this is the wrong product. The same automata-theoretic machinery -- specification compilation, product game construction, attractor computation, and winning-region extraction -- is better read as a design-time analytical instrument whose outputs are structural insights about a system rather than runtime constraints on a deployed agent. We instantiate this through a constrained two-player safety game for network defense. The two specifications are enforced asymmetrically: the defender specification defines the unsafe region of the game, whereas the attacker specification restricts the adversary's legal actions during attractor computation. Solving the game yields a defensibility verdict -- a formal certificate that a topology-specification pair is or is not defensible -- with the associated winning region and shield. Beyond the binary verdict, we derive topology-level metrics from the attractor structure and combine them with post-convergence behavior from shield-constrained adversarial multi-agent reinforcement learning. Together these form a defensibility fingerprint capturing both a network's formal safety properties and its operational behavior under adaptive play. A what-if analysis shows that formal defensibility and operational effectiveness capture distinct aspects of security: small architectural changes can produce large shifts in operational outcomes while leaving formal safety margins nearly unchanged. Shield synthesis is thus most valuable not as a deployment mechanism for safe agents, but as a framework for answering architectural questions about whether, where, and how a system can be defended. The defensibility verdict is the output, not the safe policy.
Ashkan Ansarifard, Matteo Mancanelli, Elena Umili +1cs.AI cs.FL
In this work we study offline reinforcement learning (RL) under temporally extended task constraints expressed in Linear Temporal Logic over finite traces (LTLf). Recently, transformer-based approaches such as Trajectory Transformers and Decision Transformers have been adopted to address RL as a sequence modeling problem. However, these methods optimize purely for reward and do not account for high-level temporal requirements. Here, we introduce a neurosymbolic framework that injects LTLf background knowledge into such transformer-based RL policies. Our approach compiles LTLf formulas into deterministic finite automata (DFAs) and integrates them into the learning process through a differentiable representation and a logic-based loss function. In particular, we derive differentiable satisfaction signals from DFA progression and use them as a regularization term during training. The resulting method is architecture-agnostic across different models. We evaluate the proposed framework on navigation environments with specification suites covering combinations of safety and reachability temporal properties. Experimental results show that incorporating background knowledge not only improves constraint satisfaction, but also maintains competitive return compared to vanilla baselines.
Yunhao Yang, Neel P. Bhatt, Kevin Wang +3cs.RO cs.AI
Reusable robot skills are becoming the basic units through which embodied agents turn open-ended instructions into long-horizon physical behavior. We argue that, while foundation models have collapsed the cost of creating these skills, the cost of trusting them has not. Existing skill-evolution loops refine skills through execution feedback, unit tests, environment reward, or LLM self-critique, but these signals provide only trace-level evidence: they show that a skill worked on sampled executions, not that skill-induced plans satisfy temporal safety contracts under untested conditions. We introduce VASO, a framework for verification-guided self-evolution of LLM-generated robot skill contracts. In VASO, each skill is represented as a semantic contract with two coupled interfaces: a formal interface that aligns robot states, observations, and control commands with logical propositions for model checking, and a planner-facing interface that guides executable behavior generation. A model checker first filters logically inconsistent skill contracts, then verifies plans induced by the skill against global and local temporal specifications. When verification fails, VASO translates the counterexample trace into a textual gradient that updates the reusable skill contract while keeping foundation-model weights frozen. On Clearpath Jackal and PX4 quadcopter tasks, VASO reaches 97.2% formal-specification compliance using fewer than 100 optimization samples, outperforming execution-feedback, prompt-optimization, and fine-tuning baselines. To our knowledge, VASO is the first framework that closes the loop between formal verification and self-evolving LLM-generated skills for physical AI agents: formal counterexamples become optimization feedback for reusable robot skill contracts, rather than merely verifying one-off plans, tuning planner prompts, or fine-tuning model weights.
The TimeLogic Challenge evaluates formal temporal-logic reasoning over video - 16 operators (before, after, until, since, always, co-occur, ordering, ...) in boolean and 4-way multiple-choice form. End-to-end video-language models (VLMs) hover near chance on this task because they treat video as a bag of frames and cannot localize when actions occur. We present TLG (Temporal-Logic Grounding), a three-tier system that (i) reconstructs each video's action timeline from the public source-dataset annotations the benchmark was generated from, parses every question into a temporal-logic program, and executes it deterministically; (ii) falls back to a strong open VLM where no annotation exists; and (iii) routes only the question categories where the VLM is empirically weakest to a frontier reasoning model. TLG raises test accuracy from a 46.9% VLM baseline to 71.37%, a +24.5 absolute gain, reaching within 3 points of the leaderboard top. We report extensive ablations, including three model-based timeline-reconstruction variants that all underperform a holistic VLM, isolating temporal grounding as the irreducible bottleneck and showing that real annotations - not larger models - drive accuracy.
Distributed LLM agent workflows should not be monitored as if they produced a single sequential log. In an asynchronous execution, a decision can only depend on events that are causally visible to the lifeline that makes it: an event that appears earlier in some log may still be unknown locally. We extend the ZipperGen agent-workflow framework with Causal Past Logic (CPL), a small past-time temporal logic for guards in conditionals and while loops. In addition to standard past-time modalities such as previous and since, a guard can inspect the latest causally visible event of another lifeline and selected variables stored there. The formula is a source-level guard: it is evaluated online by the owner lifeline and can influence control flow at runtime. We give a vector-clock monitor with latest-value views and prove that the locally computed monitor value coincides with the denotational semantics of the guard at the current event. Thus runtime verification becomes part of the coordination language itself, rather than a post-hoc check over an execution log.