Verification of multi-agent systems requires the ability to check meticulous topological properties when it comes to agents that can move through space in continuous time. This demands a logic with sufficient expressiveness to capture these dynamics. MuTGL logic has interesting properties for expressing entangled space-time properties. However, this logic lacks the expressivity needed to analyse reachability within specific distance bounds, or to track the length or the cost of communication chains: these are fundamental for decentralized monitoring, or graph-theoretic analysis of distributed protocols, where algorithmic complexities often relates with the system's communication graph diameter. We then introduce an extension of muTGL, including a new operator called the space horizon. This addition allows us to bound the distance of communication chains, hence enhancing the logic's expressiveness. We show that this operator allows to encode modalities from other logics, such as reachability or escaping which were not available in vanilla muTGL, while allowing a deeper entanglement of spatial and temporal properties. We provide a centralized offline monitoring algorithm for this logic and illustrate it on several examples on simulations of Consensus-Based Bundle Algorithms, distributed protocols for task allocation.
Spatio-Temporal Logic with Graph Operators (STL-GO) extends Signal Temporal Logic (STL) to multi-agent systems via graph operators that count neighboring agents satisfying a property, together with multi-agent quantifiers. While Boolean semantics for STL-GO are well-defined, quantitative semantics have not yet been developed and existing quantitative semantics for spatio-temporal logics such as STREL cannot capture the counting constraints in STL-GO's graph operators. We develop quantitative semantics for STL-GO as a layered algebraic construction that separates temporal aggregation from graph-operator aggregation (governed by an abstract accumulator with a monotone fold and readout). We prove that soundness and completeness reduce to monotonicity conditions on these components. We implement the framework and evaluate it on two multi-agent environments: a 2D bounded region with stochastic Dubins-car dynamics and a 3D Earth-satellite system, under four semantic instantiations (Boolean, min-max, signed-deficit, and a hybrid), demonstrating the tradeoffs between accumulator choices and reporting scalability in the number of agents and time horizon.
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.
Dynamic systems in AI are often complex and heterogeneous, so that an internal specification is not accessible and verification techniques such as model checking are not applicable. Monitoring is in such cases an attractive alternative, as it evaluates desirable properties along traces generated by an unknown dynamic system. In this work, we consider anticipatory monitoring of linear-time properties enriched with an arbitrary SMT theory over finite traces (LTLfMT). Anticipatory monitoring in this setting is highly challenging, as the monitoring state depends on both the trace prefix seen so far and all its possible finite continuations. Under reasonable assumptions on the background theory, we present and formally prove the correctness of a novel foundational framework for monitoring properties in an expressive fragment of LTLfMT. The framework combines automata-theoretic methods to handle the temporal aspects of the logic, with automated reasoning techniques to address the first-order dimension. Moreover, we identify for the first time decidable fragments of this monitoring problem that are practically relevant as they combine linear arithmetic with uninterpreted functions, which covers e.g. data-aware business processes and dynamic systems operating over a read-only database. Feasibility is witnessed by a prototype implementation and preliminary evaluation.