arXiv subjects

Alessandro Gianola

Publications and source records attributed to Alessandro Gianola.

At least 19 recordsLinked to original sources

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

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↗

arXiv2026

Do It for HER: First-Order Temporal Logic Reward Specification in Reinforcement Learning (Extended Version)

In this work, we propose a novel framework for the logical specification of non-Markovian rewards in Markov Decision Processes (MDPs) with large state spaces. Our approach leverages Linear Temporal Logic Modulo Theories over finite traces (LTLfMT), a more expressive extension of classical temporal logic in which predicates are first-order formulas of arbitrary first-order theories rather than simple Boolean variables. This enhanced expressiveness enables the specification of complex tasks over unstructured and heterogeneous data domains, promoting a unified and reusable framework that eliminates the need for manual predicate encoding. However, the increased expressive power of LTLfMT introduces additional theoretical and computational challenges compared to standard LTLf specifications. We address these challenges from a theoretical standpoint, identifying a fragment of LTLfMT that is tractable but sufficiently expressive for reward specification in an infinite-state-space context. From a practical perspective, we introduce a method based on reward machines and Hindsight Experience Replay (HER) to translate first-order logic specifications and address reward sparsity. We evaluate this approach to a continuous-control setting using Non-Linear Arithmetic Theory, showing that it enables natural specification of complex tasks. Experimental results show how a tailored implementation of HER is fundamental in solving tasks with complex goals.

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↗

arXiv2024

A General Automata Model for First-Order Temporal Logics (Extended Version)

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification language for the verification of complex infinite-state systems is appealing. However, a missing piece, which has proved to be an invaluable tool in dealing with other temporal logics, is an automaton model capable of capturing the logic. In this paper we address this issue, by defining and studying such a model, which we call first-order automaton. We define this very general class of automata, and the corresponding notion of regular first-order language, showing their closure under most common language-theoretic operations. We show how they can capture any FOLTL formula over any signature and theory, and provide sufficient conditions for the semi-decidability of their non-emptiness problem. Then, to show the usefulness of the formalism, we prove the decidability of monodic FOLTL, a classic result known in the literature, with a simpler and direct proof.

cs.LO↗

arXiv2024

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↗

arXiv2023

Linear-Time Verification of Data-Aware Processes Modulo Theories via Covers and Automata (Extended Version)

The need to model and analyse dynamic systems operating over complex data is ubiquitous in AI and neighboring areas, in particular business process management. Analysing such data-aware systems is a notoriously difficult problem, as they are intrinsically infinite-state. Existing approaches work for specific datatypes, and/or limit themselves to the verification of safety properties. In this paper, we lift both such limitations, studying for the first time linear-time verification for so-called data-aware processes modulo theories (DMTs), from the foundational and practical point of view. The DMT model is very general, as it supports processes operating over variables that can store arbitrary types of data, ranging over infinite domains and equipped with domain-specific predicates. Specifically, we provide four contributions. First, we devise a semi-decision procedure for linear-time verification of DMTs, which works for a very large class of datatypes obeying to mild model-theoretic assumptions. The procedure relies on a unique combination of automata-theoretic and cover computation techniques to respectively deal with linear-time properties and datatypes. Second, we identify an abstract, semantic property that guarantees the existence of a faithful finite-state abstraction of the original system, and show that our method becomes a decision procedure in this case. Third, we identify concrete, checkable classes of systems that satisfy this property, generalising several results in the literature. Finally, we present an implementation and a first experimental evaluation.

cs.LO↗

arXiv2023

Relational Action Bases: Formalization, Effective Safety Verification, and Invariants (Extended Version)

Modeling and verification of dynamic systems operating over a relational representation of states are increasingly investigated problems in AI, Business Process Management, and Database Theory. To make these systems amenable to verification, the amount of information stored in each relational state needs to be bounded, or restrictions are imposed on the preconditions and effects of actions. We introduce the general framework of relational action bases (RABs), which generalizes existing models by lifting both these restrictions: unbounded relational states can be evolved through actions that can quantify both existentially and universally over the data, and that can exploit numerical datatypes with arithmetic predicates. We then study parameterized safety of RABs via (approximated) SMT-based backward search, singling out essential meta-properties of the resulting procedure, and showing how it can be realized by an off-the-shelf combination of existing verification modules of the state-of-the-art MCMT model checker. We demonstrate the effectiveness of this approach on a benchmark of data-aware business processes. Finally, we show how universal invariants can be exploited to make this procedure fully correct.

cs.AI↗

arXiv2023

Decidable Fragments of LTLf Modulo Theories (Extended Version)

We study Linear Temporal Logic Modulo Theories over Finite Traces (LTLfMT), a recently introduced extension of LTL over finite traces (LTLf) where propositions are replaced by first-order formulas and where first-order variables referring to different time points can be compared. In general, LTLfMT was shown to be semi-decidable for any decidable first-order theory (e.g., linear arithmetics), with a tableau-based semi-decision procedure. In this paper we present a sound and complete pruning rule for the LTLfMT tableau. We show that for any LTLfMT formula that satisfies an abstract, semantic condition, that we call finite memory, the tableau augmented with the new rule is also guaranteed to terminate. Last but not least, this technique allows us to establish novel decidability results for the satisfiability of several fragments of LTLfMT, as well as to give new decidability proofs for classes that are already known.

cs.AI↗

arXiv2022

Span(Graph): a Canonical Feedback Algebra of Open Transition Systems

We show that Span(Graph)*, an algebra for open transition systems introduced by Katis, Sabadini and Walters, satisfies a universal property. By itself, this is a justification of the canonicity of this model of concurrency. However, the universal property is itself of interest, being a formal demonstration of the relationship between feedback and state. Indeed, feedback categories, also originally proposed by Katis, Sabadini and Walters, are a weakening of traced monoidal categories, with various applications in computer science. A state bootstrapping technique, which has appeared in several different contexts, yields free such categories. We show that Span(Graph)* arises in this way, being the free feedback category over Span(Set). Given that the latter can be seen as an algebra of predicates, the algebra of open transition systems thus arises - roughly speaking - as the result of bootstrapping state to that algebra. Finally, we generalize feedback categories endowing state spaces with extra structure: this extends the framework from mere transition systems to automata with initial and final states.

math.CT↗

arXiv2022

Conformance Checking with Uncertainty via SMT (Extended Version)

Logs of real-life processes often feature uncertainty pertaining the recorded timestamps, data values, and/or events. We consider the problem of checking conformance of uncertain logs against data-aware reference processes. Specifically, we show how to solve it via SMT encodings, lifting previous work on data-aware SMT-based conformance checking to this more sophisticated setting. Our approach is modular, in that it homogeneously accommodates for different types of uncertainty. Moreover, using appropriate cost functions, different conformance checking tasks can be addressed. We show the correctness of our approach and witness feasibility through a proof-of-concept implementation.

cs.AI↗

arXiv2022

Linear Temporal Logic Modulo Theories over Finite Traces (Extended Version)

This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic, called LTLf Modulo Theories (LTLfMT), is semi-decidable. Nevertheless, its high expressiveness comes useful in a number of use cases, such as model-checking of data-aware processes and data-aware planning. Despite the general undecidability of these problems, being able to solve satisfiable instances is a compromise worth studying. After motivating and describing such use cases, we provide a sound and complete semi-decision procedure for LTLfMT based on the SMT encoding of a one-pass tree-shaped tableau system. The algorithm is implemented in the BLACK satisfiability checking tool, and an experimental evaluation shows the feasibility of the approach on novel benchmarks.

cs.LO↗

arXiv2022

General Interpolation and Strong Amalgamation for Contiguous Arrays

Interpolation is an essential tool in software verification, where first-order theories are used to constrain datatypes manipulated by programs. In this paper, we introduce the datatype theory of contiguous arrays with maxdiff, where arrays are completely defined in their allocation memory and for which maxdiff returns the max index where they differ. This theory is strictly more expressive than the array theories previously studied. By showing via an algebraic analysis that its models strongly amalgamate, we prove that this theory admits quantifier-free interpolants and, notably, that interpolation transfers to theory combinations. Finally, we provide an algorithm that significantly improves the ones for related array theories: it relies on a polysize reduction to general interpolation in linear arithmetics, thus avoiding impractical full terms instantiations and unbounded loops.

cs.LO↗

arXiv2022

Uniform Interpolants in EUF: Algorithms using DAG-representations

The concept of uniform interpolant for a quantifier-free formula from a given formula with a list of symbols, while well-known in the logic literature, has been unknown to the formal methods and automated reasoning community for a long time. This concept is precisely defined. Two algorithms for computing quantifier-free uniform interpolants in the theory of equality over uninterpreted symbols (EUF) endowed with a list of symbols to be eliminated are proposed. The first algorithm is non-deterministic and generates a uniform interpolant expressed as a disjunction of conjunctions of literals, whereas the second algorithm gives a compact representation of a uniform interpolant as a conjunction of Horn clauses. Both algorithms exploit efficient dedicated DAG representations of terms. Correctness and completeness proofs are supplied, using arguments combining rewrite techniques with model theory.

cs.LO↗

arXiv2021

SMT-Based Safety Verification of Data-Aware Processes under Ontologies (Extended Version)

In the context of verification of data-aware processes (DAPs), a formal approach based on satisfiability modulo theories (SMT) has been considered to verify parameterised safety properties of so-called artifact-centric systems. This approach requires a combination of model-theoretic notions and algorithmic techniques based on backward reachability. We introduce here a variant of one of the most investigated models in this spectrum, namely simple artifact systems (SASs), where, instead of managing a database, we operate over a description logic (DL) ontology expressed in (a slight extension of) RDFS. This DL, enjoying suitable model-theoretic properties, allows us to define DL-based SASs to which backward reachability can still be applied, leading to decidability in PSPACE of the corresponding safety problems.

cs.AI↗

arXiv2021

CoCoMoT: Conformance Checking of Multi-Perspective Processes via SMT (Extended Version)

Conformance checking is a key process mining task for comparing the expected behavior captured in a process model and the actual behavior recorded in a log. While this problem has been extensively studied for pure control-flow processes, conformance checking with multi-perspective processes is still at its infancy. In this paper, we attack this challenging problem by considering processes that combine the data and control-flow dimensions. In particular, we adopt data Petri nets (DPNs) as the underlying reference formalism, and show how solid, well-established automated reasoning techniques can be effectively employed for computing conformance metrics and data-aware alignments. We do so by introducing the CoCoMoT (Computing Conformance Modulo Theories) framework, with a fourfold contribution. First, we show how SAT-based encodings studied in the pure control-flow setting can be lifted to our data-aware case, using SMT as the underlying formal and algorithmic framework. Second, we introduce a novel preprocessing technique based on a notion of property-preserving clustering, to speed up the computation of conformance checking outputs. Third, we provide a proof-of-concept implementation that uses a state-of-the-art SMT solver and report on preliminary experiments. Finally, we discuss how CoCoMoT directly lends itself to a number of further tasks, like multi- and anti-alignments, log analysis by clustering, and model repair.

cs.AI↗