Fabrizio Riguzzi

Applying inductive logic programming to process mining

The management of business processes has recently received a lot of attention. One of the most interesting problems is the description of a process model in a language that allows the checking of the compliance of a process execution (or trace) to the model. In this paper we propose a language for the representation of process models that is inspired to the SCIFF language and is an extension of clausal logic. A process model is represented in the language as a set of integrity constraints that allow conjunctive formulas as disjuncts in the head. We present an approach for inducing these models from data: we define a subsumption relation for the integrity constraints, we define a refinement operator and we adapt the algorithm ICL to the problem of learning such formulas. The system has been applied to the problem of inducing the model of a sealed bid auction and of the NetBill protocol. The data used for learning and testing were randomly generated from correct models of the processes.

The PITA system: Tabling and answer subsumption for reasoning under uncertainty

Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic Programming (PLP), leading to languages such as the Independent Choice Logic, Logic Programs with Annotated Disjunctions (LPADs), Problog, PRISM and others. These languages share a similar distribution semantics, and methods have been devised to translate programs between these languages. The complexity of computing the probability of queries to these general PLP programs is very high due to the need to combine the probabilities of explanations that may not be exclusive. As one alternative, the PRISM system reduces the complexity of query answering by restricting the form of programs it can evaluate. As an entirely different alternative, Possibilistic Logic Programs adopt a simpler metric of uncertainty than probability. Each of these approaches -- general PLP, restricted PLP, and Possibilistic Logic Programming -- can be useful in different domains depending on the form of uncertainty to be represented, on the form of programs needed to model problems, and on the scale of the problems to be solved. In this paper, we show how the PITA system, which originally supported the general PLP language of LPADs, can also efficiently support restricted PLP and Possibilistic Logic Programs. PITA relies on tabling with answer subsumption and consists of a transformation along with an API for library functions that interface with answer subsumption.

Inducing declarative logic-based models from labeled traces

In this work we propose an approach for the automatic discoveryof logic-based models starting from a set of process executiontraces. The approach is based on a modified Inductive Logic Programmingalgorithm, capable of learning a set of declarative rules. The advantage of using a declarative description is twofold. First, theprocess is represented in an intuitive and easily readable way; second,a family of proof procedures associated to the chosen language can beused to support the monitoring and management of processes (conformancetesting, properties verification and interoperability checking, inparticular). The approach consists in first learning integrity constraints expressedas logical formulas and then translating them into a declarative graphicallanguage named DecSerFlow. We demonstrate the viability of the approach by applying it to a realdataset from a health case process and to an artificial dataset from ane-commerce protocol.

Exploiting Inductive Logic Programming Techniques for Declarative Process Mining

In the last few years, there has been a growing interest in the adoption of declarative paradigms for modeling and verifying process models. These paradigms provide an abstract and human understandable way of specifying constraints that must hold among activities executions rather than focusing on a specific procedural solution. Mining such declarative descriptions is still an open challenge. In this paper, we present a logic-based approach for tackling this problem. It relies on Inductive Logic Programming techniques and, in particular, on a modified version of the Inductive Constraint Logic algorithm. We investigate how, by properly tuning the learning algorithm, the approach can be adopted to mine models expressed in the ConDec notation, a graphical language for the declarative specification of business processes. Then, we sketch how such a mining framework has been concretely implemented as a ProM plug-in called DecMiner. We finally discuss the effectiveness of the approach by means of an example which shows the ability of the language to model concurrent activities and of DecMiner to learn such a model.

A Top Down Interpreter for LPAD and CP-Logic

Logic Programs with Annotated Disjunctions and CP-logic are two different but related languages for expressing probabilistic information in logic programming. The paper presents a top down interpreter for computing the probability of a query from a program in one of these two languages. The algorithm is based on the one available for ProbLog. The performances of the algorithm are compared with those of a Bayesian reasoner and with those of the ProbLog interpreter. On programs that have a small grounding, the Bayesian reasoner is more scalable, but programs with a large grounding require the top down interpreter. The comparison with ProbLog shows that the added expressiveness effectively requires more computation resources.

Checking Compliance of Execution Traces to Business Rules

Complex and flexible business processes are critical not only because they are difficult to handle, but also because they often tend to loose their intelligibility. Verifying compliance of complex and flexible processes becomes therefore a fundamental requirement. We propose a framework for performing compliance checking of process execution traces w.r.t. expressive reactive business rules, tailored to the MXML meta-model. Rules are mapped to Logic Programming, using Prolog to classify execution traces as compliant/non-compliant. We show how different rule templates, inspired by the ConDec language, can be easily specified and then customized in the context of a real industrial case study. We finally describe how the proposed language and its underlying a-posteriori reasoning technique have been concretely implemented as a ProM analysis plug-in.

Extended semantics and inference for the Independent Choice Logic

The Independent Choice Logic (ICL), proposed by Poole, is a language for expressing probabilistic information in logic programming that adopts a distribution semantics: an ICL theory defines a distribution over a set of normal logic programs. The probability of a query is then given by the sum of the probabilities of the programs where the query is true. The ICL semantics requires the theory to be acyclic. This is a strong limitation that rules out many interesting programs. In this paper we present an extension of the ICL semantics that allows theories to be modularly acyclic. Inference with ICL can be performed with the Ailog2 system that computes explanations to queries and then makes them mutually incompatible by means of an iterative algorithm. We propose the system PICL (for Probabilistic inference with ICL) that computes the explanations to queries by means of a modification of SLDNF-resolution and then makes the explanations mutually incompatible by means of Binary Decision Diagrams. PICL and Ailog2 are compared on problems that involve computing the probability of a connection between two nodes in biological graphs and in social networks. Moreover, they are also applied to three games of dice. The problems considered are easily expressible in P-log, a probabilistic language based on Answer Set Programming. Therefore, the Plog system was also applied to the programs. PICL was able to handle larger problems than Ailog2 and Plog. Moreover, it was the fastest of the three algorithms except for one case of one of dice games.

Strategies in Combined Learning via Logic Programs

We discuss the adoption of a three-valued setting for inductive concept learning. Distinguishing between what is true, what is false and what is unknown can be useful in situations where decisions have to be taken on the basis of scarce, ambiguous, or downright contradictory information. In a three-valued setting, we learn a definition for both the target concept and its opposite, considering positive and negative examples as instances of two disjoint classes. To this purpose, we adopt Extended Logic Programs (ELP) under a Well-Founded Semantics with explicit negation (WFSX) as the representation formalism for learning, and show how ELPs can be used to specify combinations of strategies in a declarative way also coping with contradiction and exceptions.Explicit negation is used to represent the opposite concept, while default negation is used to ensure consistency and to handle exceptions to general rules. Exceptions are represented by examples covered by the definition for a concept that belong to the training set for the opposite concept.Standard Inductive Logic Programming techniques are employed to learn the concept and its opposite. Depending on the adopted technique, we can learn the most general or the least general definition. Thus, four epistemological varieties occur, resulting from the combination of most general and least general solutions for the positive and negative concept. We discuss the factors that should be taken into account when choosing and strategically combining the generality levels for positive and negative concepts.In the paper, we also handle the issue of strategic combination of possibly contradictory learnt definitions of a predicate and its explicit negation.All in all, we show that extended logic programs under well-founded semantics with explicit negation add expressivity to learning tasks, and allow the tackling of a number of representation and strategic issues in a principled way.Our techniques have been implemented and examples run on a state-of-the-art logic programming system with tabling which implements WFSX.

Learning with Abduction

We investigate how abduction and induction can be integrated into a common learning framework through the notion of Abductive Concept Learning (ACL). ACL is an extension of Inductive Logic Programming (ILP) to the case in which both the background and the target theory are abductive logic programs and where an abductive notion of entailment is used as the coverage relation. In this framework, it is then possible to learn with incomplete information about the examples by exploiting the hypothetical reasoning of abduction. The paper presents the basic framework of ACL with its main characteristics. An algorithm for an intermediate version of ACL is developed by suitably extending the top-down ILP method and integrating this with an abductive proof procedure for Abductive Logic Programming (ALP). A prototype system has been developed and applied to learning problems with incomplete information.

Probabilistic Description Logics under the Distribution Semantics

Representing uncertain information is crucial for modeling real world domains. In this paper we present a technique for the integration of probabilistic information in Description Logics (DLs) that is based on the distribution semantics for probabilistic logic programs. In the resulting approach, that we called DISPONTE, the axioms of a probabilistic knowledge base (KB) can be annotated with a real number between 0 and 1. A probabilistic knowledge base then denes a probability distribution over regular KBs called worlds and the probability of a given query can be obtained from the joint distribution of the worlds and the query by marginalization. We present the algorithm BUNDLE for computing the probability of queries from DISPONTE knowledge bases. The algorithm exploits an underlying DL reasoner, such as Pellet, that is able to return explanations for queries. The explanations are encoded in a Binary Decision Diagram from which the probability of the query is computed. The experimentation of BUNDLE on probabilistic knowledge bases shows that it can handle knowledge bases of realistic size.