Discovering Declarative Process Models from Event Logs through Temporal Logic Query Checking

Käesolev magistritöö keskendub protsessile seatud piirangute avastamisele sündmuste logist, mida saab väljendada temporaalloogika abil. Piirangute avastamise meetodina kasutame temporaalloogika päringute kontrollimist sündmuste logi vastu. Temporaalloogika päring on modaalloogika avaldis, mis sisaldab muutujaid, mis võtavad oma väärtuse automaarpropositsioonide hulgast. Temporaalloogika päring käivitatakse vastu olekumasinat, mis on konstrueeritud sündmuste logi järgi. Päringu tulemuseks on kõik temporaalloogika avaldised, kus muutujad on asendatud kõikvõimalike automaarpropositsioonidega, mis muudavad avaldise tõeseks antud olekumasinas. See meetod ei vaja protsessi piirangute avastamiseks negatiivseid näiteid (protsessi juhtumid, mis ei tohi aset leida) sündmuste logis nagu osa avaldatuid meetodeid vajab. See meetod samuti laiendab võimalike avastatavate piirangute hulka võrreldes olemas olevate meetoditega.This thesis will focus on the discovery of temporal logic constraints from an event log. The constraints are the description of the behavior of a business process. We will use Temporal Logic Query Checking for this purpose. A temporal logic query is a type of modal logic expression containing one or more placeholders that are checked against a transition system. The transition system is built from an event log. The result lists all possible activities that can replace the placeholders to satisfy the constraints described by the query in the log. This approach does not require (as many other approaches in the literature) negative examples as (additional) input and it provides the possibility of discovering a wider range of constraints to describe the process with respect to the existing approaches

On relating CTL to Datalog

CTL is the dominant temporal specification language in practice mainly due to the fact that it admits model checking in linear time. Logic programming and the database query language Datalog are often used as an implementation platform for logic languages. In this paper we present the exact relation between CTL and Datalog and moreover we build on this relation and known efficient algorithms for CTL to obtain efficient algorithms for fragments of stratified Datalog. The contributions of this paper are: a) We embed CTL into STD which is a proper fragment of stratified Datalog. Moreover we show that STD expresses exactly CTL -- we prove that by embedding STD into CTL. Both embeddings are linear. b) CTL can also be embedded to fragments of Datalog without negation. We define a fragment of Datalog with the successor build-in predicate that we call TDS and we embed CTL into TDS in linear time. We build on the above relations to answer open problems of stratified Datalog. We prove that query evaluation is linear and that containment and satisfiability problems are both decidable. The results presented in this paper are the first for fragments of stratified Datalog that are more general than those containing only unary EDBs.Comment: 34 pages, 1 figure (file .eps

Flow Logic

Flow networks have attracted a lot of research in computer science. Indeed, many questions in numerous application areas can be reduced to questions about flow networks. Many of these applications would benefit from a framework in which one can formally reason about properties of flow networks that go beyond their maximal flow. We introduce Flow Logics: modal logics that treat flow functions as explicit first-order objects and enable the specification of rich properties of flow networks. The syntax of our logic BFL* (Branching Flow Logic) is similar to the syntax of the temporal logic CTL*, except that atomic assertions may be flow propositions, like $> \gamma$ or $\geq \gamma$, for $\gamma \in \mathbb{N}$, which refer to the value of the flow in a vertex, and that first-order quantification can be applied both to paths and to flow functions. We present an exhaustive study of the theoretical and practical aspects of BFL*, as well as extensions and fragments of it. Our extensions include flow quantifications that range over non-integral flow functions or over maximal flow functions, path quantification that ranges over paths along which non-zero flow travels, past operators, and first-order quantification of flow values. We focus on the model-checking problem and show that it is PSPACE-complete, as it is for CTL*. Handling of flow quantifiers, however, increases the complexity in terms of the network to ${\rm P}^{\rm NP}$, even for the LFL and BFL fragments, which are the flow-counterparts of LTL and CTL. We are still able to point to a useful fragment of BFL* for which the model-checking problem can be solved in polynomial time. Finally, we introduce and study the query-checking problem for BFL*, where under-specified BFL* formulas are used for network exploration