Temporalized logics and automata for time granularity

Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym: TPLP Category: Paper for Special Issue (Verification and Computational Logic) Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September 200

Anti-alignments in conformance checking: the dark side of process models

Conformance checking techniques asses the suitability of a process model in representing an underlying process, observed through a collection of real executions. These techniques suffer from the wellknown state space explosion problem, hence handling process models exhibiting large or even infinite state spaces remains a challenge. One important metric in conformance checking is to asses the precision of the model with respect to the observed executions, i.e., characterize the ability of the model to produce behavior unrelated to the one observed. By avoiding the computation of the full state space of a model, current techniques only provide estimations of the precision metric, which in some situations tend to be very optimistic, thus hiding real problems a process model may have. In this paper we present the notion of antialignment as a concept to help unveiling traces in the model that may deviate significantly from the observed behavior. Using anti-alignments, current estimations can be improved, e.g., in precision checking. We show how to express the problem of finding anti-alignments as the satisfiability of a Boolean formula, and provide a tool which can deal with large models efficiently.Peer ReviewedPostprint (author's final draft

Learning Linear Temporal Properties

We present two novel algorithms for learning formulas in Linear Temporal Logic (LTL) from examples. The first learning algorithm reduces the learning task to a series of satisfiability problems in propositional Boolean logic and produces a smallest LTL formula (in terms of the number of subformulas) that is consistent with the given data. Our second learning algorithm, on the other hand, combines the SAT-based learning algorithm with classical algorithms for learning decision trees. The result is a learning algorithm that scales to real-world scenarios with hundreds of examples, but can no longer guarantee to produce minimal consistent LTL formulas. We compare both learning algorithms and demonstrate their performance on a wide range of synthetic benchmarks. Additionally, we illustrate their usefulness on the task of understanding executions of a leader election protocol

Inductive Logic Programming in Databases: from Datalog to DL+log

In this paper we address an issue that has been brought to the attention of the database community with the advent of the Semantic Web, i.e. the issue of how ontologies (and semantics conveyed by them) can help solving typical database problems, through a better understanding of KR aspects related to databases. In particular, we investigate this issue from the ILP perspective by considering two database problems, (i) the definition of views and (ii) the definition of constraints, for a database whose schema is represented also by means of an ontology. Both can be reformulated as ILP problems and can benefit from the expressive and deductive power of the KR framework DL+log. We illustrate the application scenarios by means of examples. Keywords: Inductive Logic Programming, Relational Databases, Ontologies, Description Logics, Hybrid Knowledge Representation and Reasoning Systems. Note: To appear in Theory and Practice of Logic Programming (TPLP).Comment: 30 pages, 3 figures, 2 tables

Mining structured Petri nets for the visualization of process behavior

Visualization is essential for understanding the models obtained by process mining. Clear and efficient visual representations make the embedded information more accessible and analyzable. This work presents a novel approach for generating process models with structural properties that induce visually friendly layouts. Rather than generating a single model that captures all behaviors, a set of Petri net models is delivered, each one covering a subset of traces of the log. The models are mined by extracting slices of labelled transition systems with specific properties from the complete state space produced by the process logs. In most cases, few Petri nets are sufficient to cover a significant part of the behavior produced by the log.Peer ReviewedPostprint (author's final draft