Linear Temporal Logic Modulo Theories over Finite Traces

Heyninck, Jesse; Kern-Isberner, Gabriele; Meyer, Thomas

doi:10.24963/ijcai.2022/366

Cited by 9 publications

(22 citation statements)

References 32 publications

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“…We, therefore, design a scalable SAT-Solver working under equational rewriting, thus rewriting a temporal specification into an equivalent and more tractable rewritten temporal specification Φ ′ d . Future works will analyse DECLAREd's time complexity by also considering first-order arithmetic conditions [16]. Experiments on Lydia remarked that the latter does not support adequate rewriting for internal formula minimisation as computing (Φ c,g i ) ↓A i is always slower than Φ ′c i : no algebraic rewriting is considered, as the minimisation steps are only performed while composing the DFA and never at the LTL f level.…”

Section: Discussionmentioning

confidence: 99%

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DECLAREd: A Polytime LTLf Fragment

Bergami

2024

Preprint

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This paper considers a specific fragment of Linear Temporal Logic for Finite traces, DECLAREd, which, to the best of our knowledge, we prove for the first time to be a {polytime} fragment of LTLf. We derive this in terms of the following ancillary results: we propose a set of novel LTLf equivalence rules that, when applied to \LTLf specifications, lead to an equivalent specification which can be computed faster by any existing verified temporal artificial intelligence task. We also introduce the concept of temporal non-simultaneity, prescribing that two activities shall never satisfy the same atom, and temporal short-circuit, that occurs when a specification interpreted in LTL would accept an infinitely long trace while, on LTLf, it can be rewritten so to postulate the absence of certain activity labels. We test these considerations over formal synthesis (Lydia), SAT-Solvers (AALTAF) and formal verification (KnoBAB) tools, where formal verification can be also run on top of a relational database and can be therefore expressed in terms of relational query answering. We show that all these benefit from the aforementioned assumptions, as running their tasks over a rewritten equivalent specification will improve their running times.

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Section: Discussionmentioning

confidence: 99%

“…While LTL f is generally known as a decidable language, most recent research [16] also consider decidable fragments of LTL f also involving first-order logic arithmetic properties. Differently from our proposed characterization, events are not labelled as required when actions need to be ascertained.…”

Section: Ltl F Modulo Theoriesmentioning

confidence: 99%

DECLAREd: A Polytime LTLf Fragment

Bergami

2024

Preprint

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“…Moreover, it is worth investigating in this setting also properties that go beyond safety, such as liveness. In this respect, we intend to exploit the framework proposed in (Geatti, Gianola, and Gigante 2022) for solving satisfiability of Linear Temporal Logic Modulo Theories over Finite Traces (LTLf MT ), which is a first-order extension of LTLf, so as to symbolically represent DL-based processes and express temporal properties over them. This approach is particularly promising because it relies on the use of the efficient BLACK solver Montanari 2019, 2021), which leverages SMT solvers as backend tools.…”

Section: Discussionmentioning

confidence: 99%

SMT Safety Verification of Ontology-Based Processes

Calvanese

Gianola

Mazzullo

et al. 2023

AAAI

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In the context of verification of data-aware processes, a formal approach based on satisfiability modulo theories (SMT) has been considered to verify parameterised safety properties. This approach requires a combination of model-theoretic notions and algorithmic techniques based on backward reachability. We introduce here Ontology-Based Processes, which are 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. We prove that when the DL is expressed in (a slight extension of) RDFS, it enjoys suitable model-theoretic properties, and that by relying on such DL we can define Ontology-Based Processes to which backward reachability can still be applied. Relying on these results we are able to show that in this novel setting, verification of safety properties is decidable in PSPACE.

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“…A procedure for restricted linear-time verification of transition systems operating over databases was also presented by Deutsch, Li, and Vianu (2019), but the verification language is not full LTL, systems need to be hierarchical, and no arithmetic is supported. Related to our work is also a tableau-based semi-decision procedure for satisfiability of LTL f with general SMT constraints (Geatti, Gianola, and Gigante 2022), but no decidability results are given there.…”

Section: Introductionmentioning

confidence: 99%

Linear-Time Verification of Data-Aware Processes Modulo Theories via Covers and Automata

Gianola,

Montali,

Winkler

2024

AAAI

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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 an experimental evaluation over a benchmark of real-world data-aware business processes.

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Linear Temporal Logic Modulo Theories over Finite Traces

Cited by 9 publications

References 32 publications

DECLARE<em>d</em>: A Polytime LTL<sub>f</sub> Fragment

DECLARE<em>d</em>: A Polytime LTL<sub>f</sub> Fragment

SMT Safety Verification of Ontology-Based Processes

Linear-Time Verification of Data-Aware Processes Modulo Theories via Covers and Automata

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