Using Extended Logic Programs to Formalize Commonsense Reasoning

In this dissertation, we investigate how commonsense reasoning can be formalized by using extended logic programs. In this investigation, we first use extended logic programs to formalize inheritance hierarchies with exceptions by adopting McCarthy's simple abnormality formalism to express uncertain knowledge. In our representation, not only credulous reasoning can be performed but also the ambiguity-blocking inheritance and the ambiguity-propagating inheritance in skeptical reasoning are simulated. In response to the anomalous extension problem, we explore and discover that the intuition underlying commonsense reasoning is a kind of forward reasoning. The unidirectional nature of this reasoning is applied by many reformulations of the Yale shooting problem to exclude the undesired conclusion. We then identify defeasible conclusions in our representation based on the syntax of extended logic programs. A similar idea is also applied to other formalizations of commonsense reasoning to achieve such a purpose

Reasoning in Non-probabilistic Uncertainty: Logic Programming and Neural Symbolic Computing as Examples

This article aims to achieve two goals: to show that probability is not the only way of dealing with uncertainty (and even more, that there are kinds of uncertainty which are for principled reasons not addressable with probabilistic means); and to provide evidence that logic-based methods can well support reasoning with uncertainty. For the latter claim, two paradigmatic examples are presented: logic programming with Kleene semantics for modelling reasoning from information in a discourse, to an interpretation of the state of affairs of the intended model, and a neural-symbolic implementation of input/output logic for dealing with uncertainty in dynamic normative contexts

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

Extensions of equilibrium logic by modal concepts

La logique Here-and-there (HT) est une logique monotone à trois valeurs, intermédiaire entre les logiques intuitionniste et classique. La logique de l'équilibre est un formalisme non-monotone dont la sémantique est donnée par un critère de minimalisation sur les modèles de la logique HT. Ce formalisme est fortement lié à la programmation orientée ensemble réponse (ASP), un paradigme relativement nouveau de programmation déclarative. La logique de l'équilibre constitue la base logique de l'ASP: elle reproduit la sémantique par ensemble réponse des programmes logiques et étend la syntaxe de l'ASP à des théories propositionnelles plus générales, i.e., des ensembles finis de formules propositionnelles. Cette thèse traite aussi bien des logiques modales sous-jacentes à la logique de l'équilibre que de ses extensions modales. Ceci nous permet de produire un cadre complet pour l'ASP et d'examiner de nouveau la base logique de l'ASP. A cet égard, nous présentons d'abord une logique modale monotone appelée MEM et capable de caractériser aussi bien l'existence d'un modèle de la logique de l'équilibre que la relation de conséquence dans ces modèles. La logique MEM reproduit donc la propriété de minimalisation qui est essentielle dans la définition des modèles de la logique de l'équilibre. Nous définissons ensuite une extension dynamique de la logique de l'équilibre. Pour ce faire, nous étendons le langage de la logique HT par deux ensembles de programmes atomiques qui permettent de mettre à jour, si possible, les valeurs de vérité des variables propositionnelles. Ces programmes atomiques sont ensuite combinés au moyen des connecteurs habituels de la logique dynamique. Le formalisme résultant est appelé logique Here-and-there dynamique (D-HT) et permet la mise-à-jour des modèles de la logique de l'équilibre. Par ailleurs, nous établissons un lien entre la logique D-HT et la logique dynamique des affectations propositionnelles (DL-PA): les affectations propositionnelles mettent à vrai ou à faux les valeurs de vérité des variables propositionnelles et transforment le modèle courant comme en logique dynamique propositionnelle. En conséquence, DL-PA constitue également une logique modale sous-jacente à la logique de l'équilibre. Au début des années 1990, Gelfond avait défini les spécifications épistémiques (E-S) comme une extension de la programmation logique disjonctive par des notions épistémiques. L'idée de base des E-S est de raisonner correctement à propos d'une information incomplète au moyen de la notion de vue-monde dans des situations où la notion précédente d'ensemble réponse n'est pas assez précise pour traiter le raisonnement de sens commun et où il y a une multitude d'ensembles réponses. Nous ajoutons ici des opérateurs épistémiques au langage original de la logique HT et nous définissons une version épistémique de la logique de l'équilibre. Cette version épistémique constitue une nouvelle sémantique non seulement pour les spécifications épistémiques de Gelfond, mais aussi plus généralement pour les programmes logiques épistémiques étendus. Enfin, nous comparons notre approche avec les sémantiques existantes et nous proposons une équivalence forte pour les théories de l'E-HT. Ceci nous conduit naturellement des E-S aux ASP épistémiques et peut être considéré comme point de départ pour les nouvelles extensions du cadre ASP.Here-and-there (HT) logic is a three-valued monotonic logic which is intermediate between classical logic and intuitionistic logic. Equilibrium logic is a nonmonotonic formalism whose semantics is given through a minimisation criterion over HT models. It is closely aligned with answer set programming (ASP), which is a relatively new paradigm for declarative programming. To spell it out, equilibrium logic provides a logical foundation for ASP: it captures the answer set semantics of logic programs and extends the syntax of answer set programs to more general propositional theories, i.e., finite sets of propositional formulas. This dissertation addresses modal logics underlying equilibrium logic as well as its modal extensions. It allows us to provide a comprehensive framework for ASP and to reexamine its logical foundations. In this respect, we first introduce a monotonic modal logic called MEM that is powerful enough to characterise the existence of an equilibrium model as well as the consequence relation in equilibrium models. The logic MEM thus captures the minimisation attitude that is central in the definition of equilibrium models. Then we introduce a dynamic extension of equilibrium logic. We first extend the language of HT logic by two kinds of atomic programs, allowing to update the truth value of a propositional variable here or there, if possible. These atomic programs are then combined by the usual dynamic logic connectives. The resulting formalism is called dynamic here-and-there logic (D-HT), and it allows for atomic change of equilibrium models. Moreover, we relate D-HT to dynamic logic of propositional assignments (DL-PA): propositional assignments set the truth values of propositional variables to either true or false and update the current model in the style of dynamic epistemic logics. Eventually, DL-PA constitutes an alternative monotonic modal logic underlying equilibrium logic. In the beginning of the 90s, Gelfond has introduced epistemic specifications (E-S) as an extension of disjunctive logic programming by epistemic notions. The underlying idea of E-S is to correctly reason about incomplete information, especially in situations when there are multiple answer sets. Related to this aim, he has proposed the world view semantics because the previous answer set semantics was not powerful enough to deal with commonsense reasoning. We here add epistemic operators to the original language of HT logic and define an epistemic version of equilibrium logic. This provides a new semantics not only for Gelfond's epistemic specifications, but also for more general nested epistemic logic programs. Finally, we compare our approach with the already existing semantics, and also provide a strong equivalence result for EHT theories. This paves the way from E-S to epistemic ASP, and can be regarded as a nice starting point for further frameworks of extensions of ASP

Formal Linguistic Models and Knowledge Processing. A Structuralist Approach to Rule-Based Ontology Learning and Population

2013 - 2014The main aim of this research is to propose a structuralist approach for knowledge processing by means of ontology learning and population, achieved starting from unstructured and structured texts. The method suggested includes distributional semantic approaches and NL formalization theories, in order to develop a framework, which relies upon deep linguistic analysis... [edited by author]XIII n.s

Machine ethics via logic programming

Machine ethics is an interdisciplinary field of inquiry that emerges from the need of imbuing autonomous agents with the capacity of moral decision-making. While some approaches provide implementations in Logic Programming (LP) systems, they have not exploited LP-based reasoning features that appear essential for moral reasoning. This PhD thesis aims at investigating further the appropriateness of LP, notably a combination of LP-based reasoning features, including techniques available in LP systems, to machine ethics. Moral facets, as studied in moral philosophy and psychology, that are amenable to computational modeling are identified, and mapped to appropriate LP concepts for representing and reasoning about them. The main contributions of the thesis are twofold. First, novel approaches are proposed for employing tabling in contextual abduction and updating – individually and combined – plus a LP approach of counterfactual reasoning; the latter being implemented on top of the aforementioned combined abduction and updating technique with tabling. They are all important to model various issues of the aforementioned moral facets. Second, a variety of LP-based reasoning features are applied to model the identified moral facets, through moral examples taken off-the-shelf from the morality literature. These applications include: (1) Modeling moral permissibility according to the Doctrines of Double Effect (DDE) and Triple Effect (DTE), demonstrating deontological and utilitarian judgments via integrity constraints (in abduction) and preferences over abductive scenarios; (2) Modeling moral reasoning under uncertainty of actions, via abduction and probabilistic LP; (3) Modeling moral updating (that allows other – possibly overriding – moral rules to be adopted by an agent, on top of those it currently follows) via the integration of tabling in contextual abduction and updating; and (4) Modeling moral permissibility and its justification via counterfactuals, where counterfactuals are used for formulating DDE.Fundação para a Ciência e a Tecnologia (FCT)-grant SFRH/BD/72795/2010 ; CENTRIA and DI/FCT/UNL for the supplementary fundin

Human reasoning and cognitive science

In the late summer of 1998, the authors, a cognitive scientist and a logician, started talking about the relevance of modern mathematical logic to the study of human reasoning, and we have been talking ever since. This book is an interim report of that conversation. It argues that results such as those on the Wason selection task, purportedly showing the irrelevance of formal logic to actual human reasoning, have been widely misinterpreted, mainly because the picture of logic current in psychology and cognitive science is completely mistaken. We aim to give the reader a more accurate picture of mathematical logic and, in doing so, hope to show that logic, properly conceived, is still a very helpful tool in cognitive science. The main thrust of the book is therefore constructive. We give a number of examples in which logical theorizing helps in understanding and modeling observed behavior in reasoning tasks, deviations of that behavior in a psychiatric disorder (autism), and even the roots of that behavior in the evolution of the brain

REBA: A Refinement-Based Architecture for Knowledge Representation and Reasoning in Robotics

This paper describes an architecture for robots that combines the complementary strengths of probabilistic graphical models and declarative programming to represent and reason with logic-based and probabilistic descriptions of uncertainty and domain knowledge. An action language is extended to support non-boolean fluents and non-deterministic causal laws. This action language is used to describe tightly-coupled transition diagrams at two levels of granularity, with a fine-resolution transition diagram defined as a refinement of a coarse-resolution transition diagram of the domain. The coarse-resolution system description, and a history that includes (prioritized) defaults, are translated into an Answer Set Prolog (ASP) program. For any given goal, inference in the ASP program provides a plan of abstract actions. To implement each such abstract action, the robot automatically zooms to the part of the fine-resolution transition diagram relevant to this action. A probabilistic representation of the uncertainty in sensing and actuation is then included in this zoomed fine-resolution system description, and used to construct a partially observable Markov decision process (POMDP). The policy obtained by solving the POMDP is invoked repeatedly to implement the abstract action as a sequence of concrete actions, with the corresponding observations being recorded in the coarse-resolution history and used for subsequent reasoning. The architecture is evaluated in simulation and on a mobile robot moving objects in an indoor domain, to show that it supports reasoning with violation of defaults, noisy observations and unreliable actions, in complex domains.Comment: 72 pages, 14 figure