Every normal logic program has a 2-valued semantics: theory, extensions, applications, implementations

Trabalho apresentado no âmbito do Doutoramento em Informática, como requisito parcial para obtenção do grau de Doutor em InformáticaAfter a very brief introduction to the general subject of Knowledge Representation and Reasoning with Logic Programs we analyse the syntactic structure of a logic program and how it can influence the semantics. We outline the important properties of a 2-valued semantics for Normal Logic Programs, proceed to define the new Minimal Hypotheses semantics with those properties and explore how it can be used to benefit some knowledge representation and reasoning mechanisms. The main original contributions of this work, whose connections will be detailed in the sequel, are: • The Layering for generic graphs which we then apply to NLPs yielding the Rule Layering and Atom Layering — a generalization of the stratification notion; • The Full shifting transformation of Disjunctive Logic Programs into (highly nonstratified)NLPs; • The Layer Support — a generalization of the classical notion of support; • The Brave Relevance and Brave Cautious Monotony properties of a 2-valued semantics; • The notions of Relevant Partial Knowledge Answer to a Query and Locally Consistent Relevant Partial Knowledge Answer to a Query; • The Layer-Decomposable Semantics family — the family of semantics that reflect the above mentioned Layerings; • The Approved Models argumentation approach to semantics; • The Minimal Hypotheses 2-valued semantics for NLP — a member of the Layer-Decomposable Semantics family rooted on a minimization of positive hypotheses assumption approach; • The definition and implementation of the Answer Completion mechanism in XSB Prolog — an essential component to ensure XSB’s WAM full compliance with the Well-Founded Semantics; • The definition of the Inspection Points mechanism for Abductive Logic Programs;• An implementation of the Inspection Points workings within the Abdual system [21] We recommend reading the chapters in this thesis in the sequence they appear. However, if the reader is not interested in all the subjects, or is more keen on some topics rather than others, we provide alternative reading paths as shown below. 1-2-3-4-5-6-7-8-9-12 Definition of the Layer-Decomposable Semantics family and the Minimal Hypotheses semantics (1 and 2 are optional) 3-6-7-8-10-11-12 All main contributions – assumes the reader is familiarized with logic programming topics 3-4-5-10-11-12 Focus on abductive reasoning and applications.FCT-MCTES (Fundação para a Ciência e Tecnologia do Ministério da Ciência,Tecnologia e Ensino Superior)- (no. SFRH/BD/28761/2006

A New Class of Explanations for Classifiers with Non-Binary Features

Two types of explanations have received significant attention in the literature recently when analyzing the decisions made by classifiers. The first type explains why a decision was made and is known as a sufficient reason for the decision, also an abductive or PI-explanation. The second type explains why some other decision was not made and is known as a necessary reason for the decision, also a contrastive or counterfactual explanation. These explanations were defined for classifiers with binary, discrete and, in some cases, continuous features. We show that these explanations can be significantly improved in the presence of non-binary features, leading to a new class of explanations that relay more information about decisions and the underlying classifiers. Necessary and sufficient reasons were also shown to be the prime implicates and implicants of the complete reason for a decision, which can be obtained using a quantification operator. We show that our improved notions of necessary and sufficient reasons are also prime implicates and implicants but for an improved notion of complete reason obtained by a new quantification operator that we define and study in this paper

Compositional synthesis of reactive systems

Synthesis is the task of automatically deriving correct-by-construction implementations from formal specifications. While it is a promising path toward developing verified programs, it is infamous for being hard to solve. Compositionality is recognized as a key technique for reducing the complexity of synthesis. So far, compositional approaches require extensive manual effort. In this thesis, we introduce algorithms that automate these steps. In the first part, we develop compositional synthesis techniques for distributed systems. Providing assumptions on other processes' behavior is fundamental in this setting due to inter-process dependencies. We establish delay-dominance, a new requirement for implementations that allows for implicitly assuming that other processes will not maliciously violate the shared goal. Furthermore, we present an algorithm that computes explicit assumptions on process behavior to address more complex dependencies. In the second part, we transfer the concept of compositionality from distributed to single-process systems. We present a preprocessing technique for synthesis that identifies independently synthesizable system components. We extend this approach to an incremental synthesis algorithm, resulting in more fine-grained decompositions. Our experimental evaluation shows that our techniques automate the required manual efforts, resulting in fully automated compositional synthesis algorithms for both distributed and single-process systems.Synthese ist die Aufgabe korrekte Implementierungen aus formalen Spezifikation abzuleiten. Sie ist zwar ein vielversprechender Weg für die Entwicklung verifizierter Programme, aber auch dafür bekannt schwer zu lösen zu sein. Kompositionalität gilt als eine Schlüsseltechnik zur Verringerung der Komplexität der Synthese. Bislang erfordern kompositionale Ansätze einen hohen manuellen Aufwand. In dieser Dissertation stellen wir Algorithmen vor, die diese Schritte automatisieren. Im ersten Teil entwickeln wir kompositionale Synthesetechniken für verteilte Systeme. Aufgrund der Abhängigkeiten zwischen den Prozessen ist es in diesem Kontext von grundlegender Bedeutung, Annahmen über das Verhalten der anderen Prozesse zu treffen. Wir etablieren Delay-Dominance, eine neue Anforderung für Implementierungen, die es ermöglicht, implizit anzunehmen, dass andere Prozesse das gemeinsame Ziel nicht böswillig verletzen. Darüber hinaus stellen wir einen Algorithmus vor, der explizite Annahmen über das Verhalten anderer Prozesse ableitet, um komplexere Abhängigkeiten zu berücksichtigen. Im zweiten Teil übertragen wir das Konzept der Kompositionalität von verteilten auf Einzelprozesssysteme. Wir präsentieren eine Vorverarbeitungmethode für die Synthese, die unabhängig synthetisierbare Systemkomponenten identifiziert. Wir erweitern diesen Ansatz zu einem inkrementellen Synthesealgorithmus, der zu feineren Dekompositionen führt. Unsere experimentelle Auswertung zeigt, dass unsere Techniken den erforderlichen manuellen Aufwand automatisieren und so zu vollautomatischen Algorithmen für die kompositionale Synthese sowohl für verteilte als auch für Einzelprozesssysteme führen

Sequence-Oriented Diagnosis of Discrete-Event Systems

Model-based diagnosis has always been conceived as set-oriented, meaning that a candidate is a set of faults, or faulty components, that explains a collection of observations. This perspective applies equally to both static and dynamical systems. Diagnosis of discrete-event systems (DESs) is no exception: a candidate is traditionally a set of faults, or faulty events, occurring in a trajectory of the DES that conforms with a given sequence of observations. As such, a candidate does not embed any temporal relationship among faults, nor does it account for multiple occurrences of the same fault. To improve diagnostic explanation and support decision making, a sequence-oriented perspective to diagnosis of DESs is presented, where a candidate is a sequence of faults occurring in a trajectory of the DES, called a fault sequence. Since a fault sequence is possibly unbounded, as the same fault may occur an unlimited number of times in the trajectory, the set of (output) candidates may be unbounded also, which contrasts with set-oriented diagnosis, where the set of candidates is bounded by the powerset of the domain of faults. Still, a possibly unbounded set of fault sequences is shown to be a regular language, which can be defined by a regular expression over the domain of faults, a property that makes sequence-oriented diagnosis feasible in practice. The task of monitoring-based diagnosis is considered, where a new candidate set is generated at the occurrence of each observation. The approach is based on three different techniques: (1) blind diagnosis, with no compiled knowledge, (2) greedy diagnosis, with total knowledge compilation, and (3) lazy diagnosis, with partial knowledge compilation. By knowledge we mean a data structure slightly similar to a classical DES diagnoser, which can be generated (compiled) either entirely offline (greedy diagnosis) or incrementally online (lazy diagnosis). Experimental evidence suggests that, among these techniques, only lazy diagnosis may be viable in non-trivial application domains