arXiv subjects

Marco Montali

Publications and source records attributed to Marco Montali.

At least 19 recordsLinked to original sources

arXiv2026

Time to Reason: Scalable Neurosymbolic Learning for LTLf via Fuzzy Semantics

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.

cs.AI↗

arXiv2026

First-Order Temporal Logic Tensor Networks

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.

cs.AI↗

arXiv2026

Monitoring Data-aware Temporal Properties (Extended Version)

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.

cs.AI↗

arXiv2026

On the Hybrid Nature of ABPMS Process Frames and its Implications on Automated Process Discovery

A core component of any AI-Augmented Business Process Management System (ABPMS) is the process frame, which gives the system process-awareness and defines its maximal behavioral boundaries. Compared to traditional process models, the process frame should, in principle, provide a somewhat more permissive representation of the managed processes, such that the (semi) autonomous behavior of an ABPMS, referred to as framed autonomy, could emerge. In addition, the process frame is not limited to a single linguistic or symbolic formalism and may incorporate heterogeneous knowledge ranging from predefined procedures to common sense rules and best practices. In this paper, we first conceptualize the ABPMS process frame as a hybrid business process representation, consisting of semi-concurrently executed procedural and declarative process models, extending the open-world assumption of the declarative paradigm also to procedural models. The latter allows any set of (non-conflicting) models of either type to be combined for execution, but complicates the automated discovery of these models from event data. Existing approaches for procedural models are particularly affected due to their reliance on observing directly-follows relations between pairs of activities. In search of an alternative, we present an in-depth analysis of how different procedural behaviors manifest as sets of discovered Declare constraints, each corresponding to a specific type of eventually-follows relation. This reveals behavioral overlaps between declarative and procedural models, while also laying the foundation for developing corresponding process (frame) discovery techniques.

cs.AI↗

arXiv2026

Formal Foundations of Agentic Business Process Management

Just like traditional BPM systems, agentic BPM systems are built around a specification of the process under consideration. Their distinguishing feature, however, is that the execution of the process is driven by multiple autonomous decision-makers, referred to as agents. Since such agents cannot be fully controlled, the process specification is augmented with explicit objectives, or goals, assigned to the participating agents. Agents then pursue these goals, at least to the best of their efforts, under suitable assumptions on the behavior of others, by adopting appropriate strategies. Centrally, the organization enacting the process can use these specifications to provide guardrails on the decision-making capabilities of agents at the strategy level. This paper sets up the mathematical foundations of such systems in three key settings and analyzes four foundational problems of agentic BPM.

cs.AI↗

arXiv2026

Agentic Business Process Management: A Research Manifesto

This paper presents a manifesto that articulates the conceptual foundations of Agentic Business Process Management (APM), an extension of Business Process Management (BPM) for governing autonomous agents executing processes in organizations. From a management perspective, APM represents a paradigm shift from the traditional process view of the business process, driven by the realization of process awareness and an agent-oriented abstraction, where software and human agents act as primary functional entities that perceive, reason, and act within explicit process frames. This perspective marks a shift from traditional, automation-oriented BPM toward systems in which autonomy is constrained, aligned, and made operational through process awareness. We introduce the core abstractions and architectural elements required to realize APM systems and elaborate on four key capabilities that such APM agents must support: framed autonomy, explainability, conversational actionability, and self-modification. These capabilities jointly ensure that agents' goals are aligned with organizational goals and that agents behave in a framed yet proactive manner in pursuing those goals. We discuss the extent to which the capabilities can be realized and identify research challenges whose resolution requires further advances in BPM, AI, and multi-agent systems. The manifesto thus serves as a roadmap for bridging these communities and for guiding the development of APM systems in practice.

cs.AI↗

arXiv2026

Detecting Dynamic Relationships in Object-Centric Event Logs

Object-centric process mining examines how processes interact with multiple co-evolving objects, and has gained great interest in recent years. However, object-centric event logs (OCELs) leave object relationships underspecified in several respects, especially if relationships are dynamic, i.e., they change over time. In this paper, we identify and formally define for the first time assumptions that allow to represent and manipulate dynamic relationships in OCELs in a semantically unambiguous way. We evaluate existing logs to show that our assumptions are often satisfied, ensuring full transparency of relationship semantics.

cs.DB↗

arXiv2025

Time and Relations into Focus: Ontological Foundations of Object-Centric Event Data

Object-centric process mining is a new branch of process mining where events are associated with multiple objects, and where object-to-object interactions are essential to understand the process dynamics. Traditional event data models, also called case-centric, are unable to cope with the complexity introduced by these more refined relationships. Several models have been made to move from case-centric to Object-Centric Event Data (OCED), trying to retain simplicity as much as possible. Still, these suffer from inherent ambiguities, and lack a comprehensive support of essential dimensions related to time and (dynamic) relations. In this work, we propose to fill this gap by leveraging a well-founded ontology of events and bringing ontological foundations to OCED, with a three-step approach. First, we start from key open issues reported in the literature regarding current OCED metamodels, and witness their ambiguity and expressiveness limitations on illustrative and representative examples proposed therein. Second, we consider the OCED Core Model, currently proposed as the basis for defining a new standard for object-centric event data, and we enhance it by grounding it on a lightweight version of UFO-B called gUFO, a well-known foundational ontology tailored to the representation of objects, events, time, and their (dynamic) relations. This results in a new metamodel, which we call gOCED. The third contribution then shows how gOCED at once covers the features of existing metamodels preserving their simplicity, and extends them with the essential features needed to overcome the ambiguity and expressiveness issues reported in the literature.

cs.DB↗

arXiv2025

T-ILR: a Neurosymbolic Integration for LTLf

State-of-the-art approaches for integrating symbolic knowledge with deep learning architectures have demonstrated promising results in static domains. However, methods to handle temporal logic specifications remain underexplored. The only existing approach relies on an explicit representation of a finite-state automaton corresponding to the temporal specification. Instead, we aim at proposing a neurosymbolic framework designed to incorporate temporal logic specifications, expressed in Linear Temporal Logic over finite traces (LTLf), directly into deep learning architectures for sequence-based tasks. We extend the Iterative Local Refinement (ILR) neurosymbolic algorithm, leveraging the recent introduction of fuzzy LTLf interpretations. We name this proposed method Temporal Iterative Local Refinement (T-ILR). We assess T-ILR on an existing benchmark for temporal neurosymbolic architectures, consisting of the classification of image sequences in the presence of temporal knowledge. The results demonstrate improved accuracy and computational efficiency compared to the state-of-the-art method.

cs.AI↗

arXiv2025

To bind or not to bind? Discovering Stable Relationships in Object-centric Processes (Extended Version)

Object-centric process mining investigates the intertwined behavior of multiple objects in business processes. From object-centric event logs, object-centric Petri nets (OCPN) can be discovered to replay the behavior of processes accessing different object types. Although they indicate how objects flow through the process and co-occur in events, OCPNs remain underspecified about the relationships of objects. Hence, they are not able to represent synchronization, i.e. executing objects only according to their intended relationships, and fail to identify violating executions. Existing formal modeling approaches, such as object-centric Petri nets with identifiers (OPID), represent object identities and relationships to synchronize them correctly. However, OPID discovery has not yet been studied. This paper uses explicit data models to bridge the gap between OCPNs and formal OPIDs. We identify the implicit assumptions of stable many-to-one relationships in object-centric event logs, which implies synchronization of related objects. To formally underpin this observation, we combine OCPNs with explicit stable many-to-one relationships in a rigorous mapping from OCPNs to OPIDs explicitly capturing the intended stable relationships and the synchronization of related objects. We prove that the original OCPNs and the resulting OPIDs coincide for those executions that satisfy the intended relationships. Moreover, we provide an implementation of the mapping from OCPN to OPID under stable relationships.

cs.LO↗

arXiv2025

Efficient Conformance Checking of Rich Data-Aware Declare Specifications (Extended)

Despite growing interest in process analysis and mining for data-aware specifications, alignment-based conformance checking for declarative process models has focused on pure control-flow specifications, or mild data-aware extensions limited to numerical data and variable-to-constant comparisons. This is not surprising: finding alignments is computationally hard, even more so in the presence of data dependencies. In this paper, we challenge this problem in the case where the reference model is captured using data-aware Declare with general data types and data conditions. We show that, unexpectedly, it is possible to compute data-aware optimal alignments in this rich setting, enjoying at once efficiency and expressiveness. This is achieved by carefully combining the two best-known approaches to deal with control flow and data dependencies when computing alignments, namely A* search and SMT solving. Specifically, we introduce a novel algorithmic technique that efficiently explores the search space, generating descendant states through the application of repair actions aiming at incrementally resolving constraint violations. We prove the correctness of our algorithm and experimentally show its efficiency. The evaluation witnesses that our approach matches or surpasses the performance of the state of the art while also supporting significantly more expressive data dependencies, showcasing its potential to support real-world applications.

cs.DB↗

arXiv2025

Object-centric Processes with Structured Data and Exact Synchronization (Extended Version)

Real-world processes often involve interdependent objects that also carry data values, such as integers, reals, or strings. However, existing process formalisms fall short to combine key modeling features, such as tracking object identities, supporting complex datatypes, handling dependencies among them, and object-aware synchronization. Object-centric Petri nets with identifiers (OPIDs) partially address these needs but treat objects as unstructured identifiers (e.g., order and item IDs), overlooking the rich semantics of complex data values (e.g., item prices or other attributes). To overcome these limitations, we introduce data-aware OPIDs (DOPIDs), a framework that strictly extends OPIDs by incorporating structured data manipulation capabilities, and full synchronization mechanisms. In spite of the expressiveness of the model, we show that it can be made operational: Specifically, we define a novel conformance checking approach leveraging satisfiability modulo theories (SMT) to compute data-aware object-centric alignments.

cs.MA↗

arXiv2025

From Sound Workflow Nets to LTLf Declarative Specifications by Casting Three Spells

In process management, effective behavior modeling is essential for understanding execution dynamics and identifying potential issues. Two complementary paradigms have emerged in the pursuit of this objective: the imperative approach, representing all allowed runs of a system in a graph-based model, and the declarative one, specifying the rules that a run must not violate in a constraint-based specification. Extensive studies have been conducted on the synergy and comparisons of the two paradigms. To date, though, whether a declarative specification could be systematically derived from an imperative model such that the original behavior was fully preserved (and if so, how) remained an unanswered question. In this paper, we propose a three-fold contribution. (1) We introduce a systematic approach to synthesize declarative process specifications from safe and sound Workflow nets. (2) We prove behavioral equivalence of the input net with the output specification, alongside related guarantees. (3) We experimentally demonstrate the scalability and compactness of our encoding through tests conducted with synthetic and real-world testbeds.

cs.LO↗

arXiv2025

Generating Counterfactual Explanations Under Temporal Constraints

Counterfactual explanations are one of the prominent eXplainable Artificial Intelligence (XAI) techniques, and suggest changes to input data that could alter predictions, leading to more favourable outcomes. Existing counterfactual methods do not readily apply to temporal domains, such as that of process mining, where data take the form of traces of activities that must obey to temporal background knowledge expressing which dynamics are possible and which not. Specifically, counterfactuals generated off-the-shelf may violate the background knowledge, leading to inconsistent explanations. This work tackles this challenge by introducing a novel approach for generating temporally constrained counterfactuals, guaranteed to comply by design with background knowledge expressed in Linear Temporal Logic on process traces (LTLp). We do so by infusing automata-theoretic techniques for LTLp inside a genetic algorithm for counterfactual generation. The empirical evaluation shows that the generated counterfactuals are temporally meaningful and more interpretable for applications involving temporal dependencies.

cs.AI↗

arXiv2024

Towards a Simple and Extensible Standard for Object-Centric Event Data (OCED) -- Core Model, Design Space, and Lessons Learned

Process mining is shifting towards use cases that explicitly leverage the relations between data objects and events under the term of object-centric process mining. Realizing this shift and generally simplifying the exchange and transformation of data between source systems and process mining solutions requires a standardized data format for such object-centric event data (OCED). This report summarizes the activities and results for identifying requirements and challenges for a community-supported standard for OCED. (1) We present a proposal for a core model for object-centric event data that underlies all known use cases. (2) We detail the limitations of the core model wrt. a broad range of use cases and discuss how to overcome them through conventions, usage patterns, and extensions of OCED, exhausting the design-space for an OCED data model and the inherent trade-offs in representing object-centric event data. (3) These insights are backed by five independent OCED implementations which are presented alongside a series of lessons learned in academic and industrial case studies. The results of this report provide guidance to the community to start adopting and building new process mining use cases and solutions around the reliable concepts for object-centric event data, and to engage in a structured process for standardizing OCED based on the known OCED design space.

cs.DB↗

arXiv2024

Conformance Checking of Fuzzy Logs against Declarative Temporal Specifications

Traditional conformance checking tasks assume that event data provide a faithful and complete representation of the actual process executions. This assumption has been recently questioned: more and more often events are not traced explicitly, but are instead indirectly obtained as the result of event recognition pipelines, and thus inherently come with uncertainty. In this work, differently from the typical probabilistic interpretation of uncertainty, we consider the relevant case where uncertainty refers to which activity is actually conducted, under a fuzzy semantics. In this novel setting, we consider the problem of checking whether fuzzy event data conform with declarative temporal rules specified as Declare patterns or, more generally, as formulae of linear temporal logic over finite traces (LTLf). This requires to relax the assumption that at each instant only one activity is executed, and to correspondingly redefine boolean operators of the logic with a fuzzy semantics. Specifically, we provide a threefold contribution. First, we define a fuzzy counterpart of LTLf tailored to our purpose. Second, we cast conformance checking over fuzzy logs as a verification problem in this logic. Third, we provide a proof-of-concept, efficient implementation based on the PyTorch Python library, suited to check conformance of multiple fuzzy traces at once.

cs.AI↗

arXiv2024

Depth-Bounded Epistemic Planning

We propose a novel algorithm for epistemic planning based on dynamic epistemic logic (DEL). The novelty is that we limit the depth of reasoning of the planning agent to an upper bound b, meaning that the planning agent can only reason about higher-order knowledge to at most (modal) depth b. We then compute a plan requiring the lowest reasoning depth by iteratively incrementing the value of b. The algorithm relies at its core on a new type of "canonical" b-bisimulation contraction that guarantees unique minimal models by construction. This yields smaller states wrt. standard bisimulation contractions, and enables to efficiently check for visited states. We show soundness and completeness of our planning algorithm, under suitable bounds on reasoning depth, and that, for a bound b, it runs in (b+1)-EXPTIME. We implement the algorithm in a novel epistemic planner, DAEDALUS, and compare it to the EFP 2.0 planner on several benchmarks from the literature, showing effective performance improvements.

cs.AI↗

arXiv2023

Object-Centric Conformance Alignments with Synchronization (Extended Version)

Real-world processes operate on objects that are inter-dependent. To accurately reflect the nature of such processes, object-centric process mining techniques are needed, notably conformance checking. However, while the object-centric perspective has recently gained traction, few concrete process mining techniques have been presented so far. Moreover, existing approaches are severely limited in their abilities to keep track of object identity and object dependencies. Consequently, serious problems in logs remain undetected. In this paper, we present a new formalism that combines the key modelling features of two existing approaches, in particular the ability of object-centric Petri nets to capture one-to-many relations and the one of Petri nets with identifiers to compare and synchronize objects based on their identity. We call the resulting formalism 'object-centric Petri nets with identifiers', and define alignments and the conformance checking task for this setting. We propose a conformance checking approach for such nets based on an encoding in satisfiability modulo theories (SMT), and illustrate how it can be effectively used to overcome shortcomings of earlier work. To assess its practicality, we perform an evaluation on data from the literature.

cs.LO↗