Probabilistic constraint reasoning

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia Informática, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Probabilistic constraint reasoning with Monte Carlo integration to robot localization

This work studies the combination of safe and probabilistic reasoning through the hybridization of Monte Carlo integration techniques with continuous constraint programming. In continuous constraint programming there are variables ranging over continuous domains (represented as intervals) together with constraints over them (relations between variables) and the goal is to find values for those variables that satisfy all the constraints (consistent scenarios). Constraint programming “branch-and-prune” algorithms produce safe enclosures of all consistent scenarios. Special proposed algorithms for probabilistic constraint reasoning compute the probability of sets of consistent scenarios which imply the calculation of an integral over these sets (quadrature). In this work we propose to extend the “branch-and-prune” algorithms with Monte Carlo integration techniques to compute such probabilities. This approach can be useful in robotics for localization problems. Traditional approaches are based on probabilistic techniques that search the most likely scenario, which may not satisfy the model constraints. We show how to apply our approach in order to cope with this problem and provide functionality in real time.

Efficient paraconsistent reasoning with rules and ontologies for the semantic web

Ontologies formalized by means of Description Logics (DLs) and rules in the form of Logic Programs (LPs) are two prominent formalisms in the field of Knowledge Representation and Reasoning. While DLs adhere to the OpenWorld Assumption and are suited for taxonomic reasoning, LPs implement reasoning under the Closed World Assumption, so that default knowledge can be expressed. However, for many applications it is useful to have a means that allows reasoning over an open domain and expressing rules with exceptions at the same time. Hybrid MKNF knowledge bases make such a means available by formalizing DLs and LPs in a common logic, the Logic of Minimal Knowledge and Negation as Failure (MKNF). Since rules and ontologies are used in open environments such as the Semantic Web, inconsistencies cannot always be avoided. This poses a problem due to the Principle of Explosion, which holds in classical logics. Paraconsistent Logics offer a solution to this issue by assigning meaningful models even to contradictory sets of formulas. Consequently, paraconsistent semantics for DLs and LPs have been investigated intensively. Our goal is to apply the paraconsistent approach to the combination of DLs and LPs in hybrid MKNF knowledge bases. In this thesis, a new six-valued semantics for hybrid MKNF knowledge bases is introduced, extending the three-valued approach by Knorr et al., which is based on the wellfounded semantics for logic programs. Additionally, a procedural way of computing paraconsistent well-founded models for hybrid MKNF knowledge bases by means of an alternating fixpoint construction is presented and it is proven that the algorithm is sound and complete w.r.t. the model-theoretic characterization of the semantics. Moreover, it is shown that the new semantics is faithful w.r.t. well-studied paraconsistent semantics for DLs and LPs, respectively, and maintains the efficiency of the approach it extends.

Improving practical reasoning and argumentation

This thesis justifies the need for and develops a new integrated model of practical reasoning and argumentation. After framing the work in terms of what is reasonable rather than what is rational (chapter 1), I apply the model for practical argumentation analysis and evaluation provided by Fairclough and Fairclough (2012) to a paradigm case of unreasonable individual practical argumentation provided by mass murderer Anders Behring Breivik (chapter 2). The application shows that by following the model, Breivik is relatively easily able to conclude that his reasoning to mass murder is reasonable – which is understood to be an unacceptable result. Causes for the model to allow such a conclusion are identified as conceptual confusions ingrained in the model, a tension in how values function within the model, and a lack of creativity from Breivik. Distinguishing between dialectical and dialogical, reasoning and argumentation, for individual and multiple participants, chapter 3 addresses these conceptual confusions and helps lay the foundation for the design of a new integrated model for practical reasoning and argumentation (chapter 4). After laying out the theoretical aspects of the new model, it is then used to re-test Breivik’s reasoning in light of a developed discussion regarding the motivation for the new place and role of moral considerations (chapter 5). The application of the new model shows ways that Breivik could have been able to conclude that his practical argumentation was unreasonable and is thus argued to have improved upon the Fairclough and Fairclough model. It is acknowledged, however, that since the model cannot guarantee a reasonable conclusion, improving the critical creative capacity of the individual using it is also of paramount importance (chapter 6). The thesis concludes by discussing the contemporary importance of improving practical reasoning and by pointing to areas for further research (chapter 7).

Associations, causation and model in psychiatry

This paper discusses models, associations and causation in psychiatry. The different types of association (linear, positive, negative, exponential, partial, U shaped relationship, hidden and spurious) between variables involved in mental disorders are presented as well as the use of multiple regression analysis to disentangle interrelatedness amongst multiple variables. A useful model should have internal consistency, external validity and predictive power; be dynamic in order to accommodate new sound knowledge; and should fit facts rather than they other way around. It is argued that whilst models are theoretical constructs they also convey a style of reasoning and can change clinical practice. Cause and effect are complex phenomena in that the same cause can yield different effects. Conversely, the same effect can have a different range of causes. In mental disorders and human behaviour there is always a chain of events initiated by the indirect and remote cause; followed by intermediate causes; and finally the direct and more immediate cause. Causes of mental disorders are grouped as those: (i) which are necessary and sufficient; (ii) which are necessary but not sufficient; and (iii) which are neither necessary nor sufficient, but when present increase the risk for mental disorders.

A foundation model for marxian breakdown theories based on a new falling rate of profit mechanism (Long version)

The paper presents a foundation model for Marxian theories of the breakdown of capitalism based on a new falling rate of profit mechanism. All of these theories are based on one or more of "the historical tendencies": a rising capital-wage bill ratio, a rising capitalist share and a falling rate of profit. The model is a foundation in the sense that it generates these tendencies in the context of a model with a constant subsistence wage. The newly discovered generating mechanism is based on neo-classical reasoning for a model with land. It is non-Ricardian in that land augmenting technical progress can be unboundedly rapid. Finally, since the model has no steady state, it is necessary to use a new technique, Chaplygin's method, to prove the result.

A foundation model for marxian breakdown theories based on a new falling rate of profit mechanism.

The paper presents a foundation model for Marxian theories of the breakdown of capitalism based on a new falling rate of profit mechanism. All of these theories are based on one or more of ?the historical tendencies?: a rising capital-wage bill ratio, a rising capitalist share and a falling rate of profit. The model is a foundation in the sense that it generates these tendencies in the context of a model with a constant subsistence wage. The newly discovered generating mechanism is based on neo-classical reasoning for a model with land. It is non-Ricardian in that land augmenting technical progress can be unboundedly rapid. Finally, since the model has no steady state, it is necessary to use a new technique, Chaplygin?s method, to prove the result.

Model-based diagnosis system: application to constructed wetlands

Report for the scientific sojourn carried out at the Model-based Systems and Qualitative Reasoning Group (Technical University of Munich), from September until December 2005. Constructed wetlands (CWs), or modified natural wetlands, are used all over the world as wastewater treatment systems for small communities because they can provide high treatment efficiency with low energy consumption and low construction, operation and maintenance costs. Their treatment process is very complex because it includes physical, chemical and biological mechanisms like microorganism oxidation, microorganism reduction, filtration, sedimentation and chemical precipitation. Besides, these processes can be influenced by different factors. In order to guarantee the performance of CWs, an operation and maintenance program must be defined for each Wastewater Treatment Plant (WWTP). The main objective of this project is to provide a computer support to the definition of the most appropriate operation and maintenance protocols to guarantee the correct performance of CWs. To reach them, the definition of models which represent the knowledge about CW has been proposed: components involved in the sanitation process, relation among these units and processes to remove pollutants. Horizontal Subsurface Flow CWs are chosen as a case study and the filtration process is selected as first modelling-process application. However, the goal is to represent the process knowledge in such a way that it can be reused for other types of WWTP.

Interactive Epistemology and Reasoning: On the Foundations of Game Theory

Game theory describes and analyzes strategic interaction. It is usually distinguished between static games, which are strategic situations in which the players choose only once as well as simultaneously, and dynamic games, which are strategic situations involving sequential choices. In addition, dynamic games can be further classified according to perfect and imperfect information. Indeed, a dynamic game is said to exhibit perfect information, whenever at any point of the game every player has full informational access to all choices that have been conducted so far. However, in the case of imperfect information some players are not fully informed about some choices. Game-theoretic analysis proceeds in two steps. Firstly, games are modelled by so-called form structures which extract and formalize the significant parts of the underlying strategic interaction. The basic and most commonly used models of games are the normal form, which rather sparsely describes a game merely in terms of the players' strategy sets and utilities, and the extensive form, which models a game in a more detailed way as a tree. In fact, it is standard to formalize static games with the normal form and dynamic games with the extensive form. Secondly, solution concepts are developed to solve models of games in the sense of identifying the choices that should be taken by rational players. Indeed, the ultimate objective of the classical approach to game theory, which is of normative character, is the development of a solution concept that is capable of identifying a unique choice for every player in an arbitrary game. However, given the large variety of games, it is not at all certain whether it is possible to device a solution concept with such universal capability. Alternatively, interactive epistemology provides an epistemic approach to game theory of descriptive character. This rather recent discipline analyzes the relation between knowledge, belief and choice of game-playing agents in an epistemic framework. The description of the players' choices in a given game relative to various epistemic assumptions constitutes the fundamental problem addressed by an epistemic approach to game theory. In a general sense, the objective of interactive epistemology consists in characterizing existing game-theoretic solution concepts in terms of epistemic assumptions as well as in proposing novel solution concepts by studying the game-theoretic implications of refined or new epistemic hypotheses. Intuitively, an epistemic model of a game can be interpreted as representing the reasoning of the players. Indeed, before making a decision in a game, the players reason about the game and their respective opponents, given their knowledge and beliefs. Precisely these epistemic mental states on which players base their decisions are explicitly expressible in an epistemic framework. In this PhD thesis, we consider an epistemic approach to game theory from a foundational point of view. In Chapter 1, basic game-theoretic notions as well as Aumann's epistemic framework for games are expounded and illustrated. Also, Aumann's sufficient conditions for backward induction are presented and his conceptual views discussed. In Chapter 2, Aumann's interactive epistemology is conceptually analyzed. In Chapter 3, which is based on joint work with Conrad Heilmann, a three-stage account for dynamic games is introduced and a type-based epistemic model is extended with a notion of agent connectedness. Then, sufficient conditions for backward induction are derived. In Chapter 4, which is based on joint work with Jérémie Cabessa, a topological approach to interactive epistemology is initiated. In particular, the epistemic-topological operator limit knowledge is defined and some implications for games considered. In Chapter 5, which is based on joint work with Jérémie Cabessa and Andrés Perea, Aumann's impossibility theorem on agreeing to disagree is revisited and weakened in the sense that possible contexts are provided in which agents can indeed agree to disagree.

Allostatic working memory processing in schizophrenia: Human and animal model coherence

The most evident symptoms of schizophrenia are severe impairment of cognitive functions like attention, abstract reasoning and working memory. The latter has been defined as the ability to maintain and manipulate on-line a limited amount of information. Whereas several studies show that working memory processes are impaired in schizophrenia, the specificity of this deficit is still unclear. Results obtained with a new paradigm, involving visuospatial, dynamic and static working memory processing, suggest that schizophrenic patients rely on a specific compensatory strategy. An animal model of schizophrenia with a transient deficit in glutathione during the development reveals similar substitutive processing, masking the impairment in working memory functions in specific test conditions only. Taken together, these results show coherence between working memory deficits in schizophrenic patients and in animal models. More generally, it is possible to consider that the pathological state may be interpreted as a reduced homeostatic reserve. However, this may be balanced in specific situations by efficient allostatic strategies. Thus, the pathological condition would remain latent in several situations, due to such allostatic regulations. However, to maintain a performance based on highly specific strategies requires in turn specific conditions, limitating adaptative resources in humans and in animals. In summary, we suggest that the psychological and physical load to maintain this rigid allostatic state is very high in patients and animal subjects.

Endogenous depth of reasoning

We introduce a model of strategic thinking in games of initial response. Unlike standard level-k models, in this framework the player's `depth of reasoning' is endogenously determined, andit can be disentangled from his beliefs over his opponent's cognitive bound. In our approach,individuals act as if they follow a cost-benefit analysis. The depth of reasoning is a function ofthe player's cognitive abilities and his payoffs. The costs are exogenous and represent the gametheoretical sophistication of the player; the benefit instead is related to the game payoffs. Behavioris in turn determined by the individual's depth of reasoning and his beliefs about the reasoningprocess of the opponent. Thus, in our framework, payoffs not only affect individual choices inthe traditional sense, but they also shape the cognitive process itself. Our model delivers testableimplications on players' chosen actions as incentives and opponents change. We then test themodel's predictions with an experiment. We administer different treatments that vary beliefs overpayoffs and opponents, as well as beliefs over opponents' beliefs. The results of this experiment,which are not accounted for by current models of reasoning in games, strongly support our theory.Our approach therefore serves as a novel, unifying framework of strategic thinking that allows forpredictions across games.

Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model.

Interior crises are understood as discontinuous changes of the size of a chaotic attractor that occur when an unstable periodic orbit collides with the chaotic attractor. We present here numerical evidence and theoretical reasoning which prove the existence of a chaos-chaos transition in which the change of the attractor size is sudden but continuous. This occurs in the Hindmarsh¿Rose model of a neuron, at the transition point between the bursting and spiking dynamics, which are two different dynamic behaviors that this system is able to present. Moreover, besides the change in attractor size, other significant properties of the system undergoing the transitions do change in a relevant qualitative way. The mechanism for such transition is understood in terms of a simple one-dimensional map whose dynamics undergoes a crossover between two different universal behaviors

A cognitive hierarchy model of behavior in the action commitment game

We apply the cognitive hierarchy model of Camerer et al. (Q J Econ 119(3):861-898, 2004)-where players have different levels of reasoning-to Huck et al. (Games Econ Behav 38:240-264, 2002) discrete version of Hamilton and Slutsky (Games Econ Behav 2:29-46, 1990) action commitment game-a duopoly with endogenous timing of entry. We show that, for an empirically reasonable average number of thinking steps, the model rules out Stackelberg equilibria, generates Cournot outcomes including delay, and outcomes where the first mover commits to a quantity higher than Cournot but lower than Stackelberg leader. We show that a cognitive hierarchy model with quantal responses can explain the most important features of the experimental data on the action commitment game in (2002). In order to gauge the success of the model in fitting the data, we compare it to a noisy Nash model. We find that the cognitive hierarchy model with quantal responses fits the data better than the noisy Nash model.

Model-based objects recognition in industrial environments for autonomous vehicles control

Behavior-based navigation of autonomous vehicles requires the recognition of the navigable areas and the potential obstacles. In this paper we describe a model-based objects recognition system which is part of an image interpretation system intended to assist the navigation of autonomous vehicles that operate in industrial environments. The recognition system integrates color, shape and texture information together with the location of the vanishing point. The recognition process starts from some prior scene knowledge, that is, a generic model of the expected scene and the potential objects. The recognition system constitutes an approach where different low-level vision techniques extract a multitude of image descriptors which are then analyzed using a rule-based reasoning system to interpret the image content. This system has been implemented using a rule-based cooperative expert system

Model-based objects recognition in man-made environments

We describe a model-based objects recognition system which is part of an image interpretation system intended to assist autonomous vehicles navigation. The system is intended to operate in man-made environments. Behavior-based navigation of autonomous vehicles involves the recognition of navigable areas and the potential obstacles. The recognition system integrates color, shape and texture information together with the location of the vanishing point. The recognition process starts from some prior scene knowledge, that is, a generic model of the expected scene and the potential objects. The recognition system constitutes an approach where different low-level vision techniques extract a multitude of image descriptors which are then analyzed using a rule-based reasoning system to interpret the image content. This system has been implemented using CEES, the C++ embedded expert system shell developed in the Systems Engineering and Automatic Control Laboratory (University of Girona) as a specific rule-based problem solving tool. It has been especially conceived for supporting cooperative expert systems, and uses the object oriented programming paradigm