Possibilistic functional dependencies and their relationship to possibility theory

This paper introduces possibilistic functional dependencies. These dependencies are associated with a particular possibility distribution over possible worlds of a classical database. The possibility distribution reflects a layered view of the database. The highest layer of the (classical) database consists of those tuples that certainly belong to it, while the other layers add tuples that only possibly belong to the database, with different levels of possibility. The relation between the confidence levels associated with the tuples and the possibility distribution over possible database worlds is discussed in detail in the setting of possibility theory. A possibilistic functional dependency is a classical functional dependency associated with a certainty level that reflects the highest confidence level where the functional dependency no longer holds in the layered database. Moreover, the relationship between possibilistic functional dependencies and possibilistic logic formulas is established. Related work is reviewed, and the intended use of possibilistic functional dependencies is discussed in the conclusion

The Role of preferences in logic programming: nonmonotonic reasoning, user preferences, decision under uncertainty

Intelligent systems that assist users in fulfilling complex tasks need a concise and processable representation of incomplete and uncertain information. In order to be able to choose among different options, these systems also need a compact and processable representation of the concept of preference. Preferences can provide an effective way to choose the best solutions to a given problem. These solutions can represent the most plausible states of the world when we model incomplete information, the most satisfactory states of the world when we express user preferences, or optimal decisions when we make decisions under uncertainty. Several domains, such as, reasoning under incomplete and uncertain information, user preference modeling, and qualitative decision making under uncertainty, have benefited from advances on preference representation. In the literature, several symbolic approaches of nonclassical reasoning have been proposed. Among them, logic programming under answer set semantics offers a good compromise between symbolic representation and computation of knowledge and several extensions for handling preferences. Nevertheless, there are still some open issues to be considered in logic programming. In nonmonotonic reasoning, first, most approaches assume that exceptions to logic program rules are already specified. However, sometimes, it is possible to consider implicit preferences based on the specificity of the rules to handle incomplete information. Secondly, the joint handling of exceptions and uncertainty has received little attention: when information is uncertain, the selection of default rules can be a matter of explicit preferences and uncertainty. In user preference modeling, although existing logic programming specifications allow to express user preferences which depend both on incomplete and contextual information, in some applications, some preferences in some context may be more important than others. Furthermore, more complex preference expressions need to be supported. In qualitative decision making under uncertainty, existing logic programming-based methodologies for making decisions seem to lack a satisfactory handling of preferences and uncertainty. The aim of this dissertation is twofold: 1) to tackle the role played by preferences in logic programming from different perspectives, and 2) to contribute to this novel field by proposing several frameworks and methods able to address the above issues. To this end, we will first show how preferences can be used to select default rules in logic programs in an implicit and explicit way. In particular, we propose (i) a method for selecting logic program rules based on specificity, and (ii) a framework for selecting uncertain default rules based on explicit preferences and the certainty of the rules. Then, we will see how user preferences can be modeled and processed in terms of a logic program (iii) in order to manage user profiles in a context-aware system and (iv) in order to propose a framework for the specification of nested (non-flat) preference expressions. Finally, in the attempt to bridge the gap between logic programming and qualitative decision under uncertainty, (v) we propose a classical- and a possibilistic-based logic programming methodology to compute an optimal decision when uncertainty and preferences are matters of degrees.Els sistemes intel.ligents que assisteixen a usuaris en la realització de tasques complexes necessiten una representació concisa i formal de la informació que permeti un raonament nomonòton en condicions d’incertesa. Per a poder escollir entre les diferents opcions, aquests sistemes solen necessitar una representació del concepte de preferència. Les preferències poden proporcionar una manera efectiva de triar entre les millors solucions a un problema. Aquestes solucions poden representar els estats del món més plausibles quan es tracta de modelar informació incompleta, els estats del món més satisfactori quan expressem preferències de l’usuari, o decisions òptimes quan estem parlant de presa de decisió incorporant incertesa. L’ús de les preferències ha beneficiat diferents dominis, com, el raonament en presència d’informació incompleta i incerta, el modelat de preferències d’usuari, i la presa de decisió sota incertesa. En la literatura, s’hi troben diferents aproximacions al raonament no clàssic basades en una representació simbòlica de la informació. Entre elles, l’enfocament de programació lògica, utilitzant la semàntica de answer set, ofereix una bona aproximació entre representació i processament simbòlic del coneixement, i diferents extensions per gestionar les preferències. No obstant això, en programació lògica es poden identificar diferents problemes pel que fa a la gestió de les preferències. Per exemple, en la majoria d’enfocaments de raonament no-monòton s’assumeix que les excepcions a default rules d’un programa lògic ja estan expressades. Però de vegades es poden considerar preferències implícites basades en l’especificitat de les regles per gestionar la informació incompleta. A més, quan la informació és també incerta, la selecció de default rules pot dependre de preferències explícites i de la incertesa. En el modelatge de preferències del usuari, encara que els formalismes existents basats en programació lògica permetin expressar preferències que depenen d’informació contextual i incompleta, en algunes aplicacions, donat un context, algunes preferències poden ser més importants que unes altres. Per tant, resulta d’interès un llenguatge que permeti capturar preferències més complexes. En la presa de decisions sota incertesa, les metodologies basades en programació lògica creades fins ara no ofereixen una solució del tot satisfactòria pel que fa a la gestió de les preferències i la incertesa. L’objectiu d’aquesta tesi és doble: 1) estudiar el paper de les preferències en la programació lògica des de diferents perspectives, i 2) contribuir a aquesta jove àrea d’investigació proposant diferents marcs teòrics i mètodes per abordar els problemes anteriorment citats. Per a aquest propòsit veurem com les preferències es poden utilitzar de manera implícita i explícita per a la selecció de default rules proposant: (i) un mètode basat en l’especificitat de les regles, que permeti seleccionar regles en un programa lògic; (ii) un marc teòric per a la selecció de default rules incertes basat en preferències explícites i la incertesa de les regles. També veurem com les preferències de l’usuari poden ser modelades i processades usant un enfocament de programació lògica (iii) que suporti la creació d’un mecanisme de gestió dels perfils dels usuaris en un sistema amb reconeixement del context; (iv) que permeti proposar un marc teòric capaç d’expressar preferències amb fòrmules imbricades. Per últim, amb l’objectiu de disminuir la distància entre programació lògica i la presa de decisió amb incertesa proposem (v) una metodologia basada en programació lògica clàssica i en una extensió de la programació lògica que incorpora lògica possibilística per modelar un problema de presa de decisions i per inferir una decisió òptima.Los sistemas inteligentes que asisten a usuarios en tareas complejas necesitan una representación concisa y procesable de la información que permita un razonamiento nomonótono e incierto. Para poder escoger entre las diferentes opciones, estos sistemas suelen necesitar una representación del concepto de preferencia. Las preferencias pueden proporcionar una manera efectiva para elegir entre las mejores soluciones a un problema. Dichas soluciones pueden representar los estados del mundo más plausibles cuando hablamos de representación de información incompleta, los estados del mundo más satisfactorios cuando hablamos de preferencias del usuario, o decisiones óptimas cuando estamos hablando de toma de decisión con incertidumbre. El uso de las preferencias ha beneficiado diferentes dominios, como, razonamiento en presencia de información incompleta e incierta, modelado de preferencias de usuario, y toma de decisión con incertidumbre. En la literatura, distintos enfoques simbólicos de razonamiento no clásico han sido creados. Entre ellos, la programación lógica con la semántica de answer set ofrece un buen acercamiento entre representación y procesamiento simbólico del conocimiento, y diferentes extensiones para manejar las preferencias. Sin embargo, en programación lógica se pueden identificar diferentes problemas con respecto al manejo de las preferencias. Por ejemplo, en la mayoría de enfoques de razonamiento no-monótono se asume que las excepciones a default rules de un programa lógico ya están expresadas. Pero, a veces se pueden considerar preferencias implícitas basadas en la especificidad de las reglas para manejar la información incompleta. Además, cuando la información es también incierta, la selección de default rules pueden depender de preferencias explícitas y de la incertidumbre. En el modelado de preferencias, aunque los formalismos existentes basados en programación lógica permitan expresar preferencias que dependen de información contextual e incompleta, in algunas aplicaciones, algunas preferencias en un contexto puede ser más importantes que otras. Por lo tanto, un lenguaje que permita capturar preferencias más complejas es deseable. En la toma de decisiones con incertidumbre, las metodologías basadas en programación lógica creadas hasta ahora no ofrecen una solución del todo satisfactoria al manejo de las preferencias y la incertidumbre. El objectivo de esta tesis es doble: 1) estudiar el rol de las preferencias en programación lógica desde diferentes perspectivas, y 2) contribuir a esta joven área de investigación proponiendo diferentes marcos teóricos y métodos para abordar los problemas anteriormente citados. Para este propósito veremos como las preferencias pueden ser usadas de manera implícita y explícita para la selección de default rules proponiendo: (i) un método para seleccionar reglas en un programa basado en la especificad de las reglas; (ii) un marco teórico para la selección de default rules basado en preferencias explícitas y incertidumbre. También veremos como las preferencias del usuario pueden ser modeladas y procesadas usando un enfoque de programación lógica (iii) para crear un mecanismo de manejo de los perfiles de los usuarios en un sistema con reconocimiento del contexto; (iv) para crear un marco teórico capaz de expresar preferencias con formulas anidadas. Por último, con el objetivo de disminuir la distancia entre programación lógica y la toma de decisión con incertidumbre proponemos (v) una metodología para modelar un problema de toma de decisiones y para inferir una decisión óptima usando un enfoque de programación lógica clásica y uno de programación lógica extendida con lógica posibilística.Sistemi intelligenti, destinati a fornire supporto agli utenti in processi decisionali complessi, richiedono una rappresentazione dell’informazione concisa, formale e che permetta di ragionare in maniera non monotona e incerta. Per poter scegliere tra le diverse opzioni, tali sistemi hanno bisogno di disporre di una rappresentazione del concetto di preferenza altrettanto concisa e formale. Le preferenze offrono una maniera efficace per scegliere le miglior soluzioni di un problema. Tali soluzioni possono rappresentare gli stati del mondo più credibili quando si tratta di ragionamento non monotono, gli stati del mondo più soddisfacenti quando si tratta delle preferenze degli utenti, o le decisioni migliori quando prendiamo una decisione in condizioni di incertezza. Diversi domini come ad esempio il ragionamento non monotono e incerto, la strutturazione del profilo utente, e i modelli di decisione in condizioni d’incertezza hanno tratto beneficio dalla rappresentazione delle preferenze. Nella bibliografia disponibile si possono incontrare diversi approcci simbolici al ragionamento non classico. Tra questi, la programmazione logica con answer set semantics offre un buon compromesso tra rappresentazione simbolica e processamento dell’informazione, e diversi estensioni per la gestione delle preferenze sono state proposti in tal senso. Nonostante ció, nella programmazione logica esistono ancora delle problematiche aperte. Prima di tutto, nella maggior parte degli approcci al ragionamento non monotono, si suppone che nel programma le eccezioni alle regole siano già specificate. Tuttavia, a volte per trattare l’informazione incompleta è possibile prendere in considerazione preferenze implicite basate sulla specificità delle regole. In secondo luogo, la gestione congiunta di eccezioni e incertezza ha avuto scarsa attenzione: quando l’informazione è incerta, la scelta di default rule può essere una questione di preferenze esplicite e d’incertezza allo stesso tempo. Nella creazione di preferenze dell’utente, anche se le specifiche di programmazione logica esistenti permettono di esprimere preferenze che dipendono sia da un’informazione incompleta che da una contestuale, in alcune applicazioni talune preferenze possono essere più importanti di altre, o espressioni più complesse devono essere supportate. In un processo decisionale con incertezza, le metodologie basate sulla programmazione logica viste sinora, non offrono una gestione soddisfacente delle preferenze e dell’incertezza. Lo scopo di questa dissertazione è doppio: 1) chiarire il ruolo che le preferenze giocano nella programmazione logica da diverse prospettive e 2) contribuire proponendo in questo nuovo settore di ricerca, diversi framework e metodi in grado di affrontare le citate problematiche. Per prima cosa, dimostreremo come le preferenze possono essere usate per selezionare default rule in un programma in maniera implicita ed esplicita. In particolare proporremo: (i) un metodo per la selezione delle regole di un programma logico basato sulla specificità dell’informazione; (ii) un framework per la selezione di default rule basato sulle preferenze esplicite e sull’incertezza associata alle regole del programma. Poi, vedremo come le preferenze degli utenti possono essere modellate attraverso un programma logico, (iii) per creare il profilo dell’utente in un sistema context-aware, e (iv) per proporre un framework che supporti la definizione di preferenze complesse. Infine, per colmare le lacune in programmazione logica applicata a un processo di decisione con incertezza (v) proporremo una metodologia basata sulla programmazione logica classica e una metodologia basata su un’estensione della programmazione logica con logica possibilistica

Evaluating aggregate functions on possibilistic data

The need for extending information management systems to handle the imprecision of information found in the real world has been recognized. Fuzzy set theory together with possibility theory represent a uniform framework for extending the relational database model with these features. However, none of the existing proposals for handling imprecision in the literature has dealt with queries involving a functional evaluation of a set of items, traditionally referred to as aggregation. Two kinds of aggregate operators, namely, scalar aggregates and aggregate functions, exist. Both are important for most real-world applications, and are thus being supported by traditional languages like SQL or QUEL. This paper presents a framework for handling these two types of aggregates in the context of imprecise information. We consider three cases, specifically, aggregates within vague queries on precise data, aggregates within precisely specified queries on possibilistic data, and aggregates within vague queries on imprecise data. These extensions are based on fuzzy set-theoretical concepts such as the extension principle, the sigma-count operation, and the possibilistic expected value. The consistency and completeness of the proposed operations is shown

Semantics for possibilistic answer set programs: uncertain rules versus rules with uncertain conclusions

Although Answer Set Programming (ASP) is a powerful framework for declarative problem solving, it cannot in an intuitive way handle situations in which some rules are uncertain, or in which it is more important to satisfy some constraints than others. Possibilistic ASP (PASP) is a natural extension of ASP in which certainty weights are associated with each rule. In this paper we contrast two different views on interpreting the weights attached to rules. Under the first view, weights reflect the certainty with which we can conclude the head of a rule when its body is satisfied. Under the second view, weights reflect the certainty that a given rule restricts the considered epistemic states of an agent in a valid way, i.e. it is the certainty that the rule itself is correct. The first view gives rise to a set of weighted answer sets, whereas the second view gives rise to a weighted set of classical answer sets

Uncertainty in life cycle costing for long-range infrastructure. Part I: leveling the playing field to address uncertainties

Purpose Life cycle costing (LCC) is a state-of-the-art method to analyze investment decisions in infrastructure projects. However, uncertainties inherent in long-term planning question the credibility of LCC results. Previous research has not systematically linked sources and methods to address this uncertainty. Part I of this series develops a framework to collect and categorize different sources of uncertainty and addressing methods. This systematization is a prerequisite to further analyze the suitability of methods and levels the playing field for part II. Methods Past reviews have dealt with selected issues of uncertainty in LCC. However, none has systematically collected uncertainties and linked methods to address them. No comprehensive categorization has been published to date. Part I addresses these two research gaps by conducting a systematic literature review. In a rigorous four-step approach, we first scrutinized major databases. Second, we performed a practical and methodological screening to identify in total 115 relevant publications, mostly case studies. Third, we applied content analysis using MAXQDA. Fourth, we illustrated results and concluded upon the research gaps. Results and discussion We identified 33 sources of uncertainty and 24 addressing methods. Sources of uncertainties were categorized according to (i) its origin, i.e., parameter, model, and scenario uncertainty and (ii) the nature of uncertainty, i.e., aleatoric or epistemic uncertainty. The methods to address uncertainties were classified into deterministic, probabilistic, possibilistic, and other methods. With regard to sources of uncertainties, lack of data and data quality was analyzed most often. Most uncertainties having been discussed were located in the use stage. With regard to methods, sensitivity analyses were applied most widely, while more complex methods such as Bayesian models were used less frequently. Data availability and the individual expertise of LCC practitioner foremost influence the selection of methods. Conclusions This article complements existing research by providing a thorough systematization of uncertainties in LCC. However, an unambiguous categorization of uncertainties is difficult and overlapping occurs. Such a systemizing approach is nevertheless necessary for further analyses and levels the playing field for readers not yet familiar with the topic. Part I concludes the following: First, an investigation about which methods are best suited to address a certain type of uncertainty is still outstanding. Second, an analysis of types of uncertainty that have been insufficiently addressed in previous LCC cases is still missing. Part II will focus on these research gaps

Imperfect Data In Database Context. How Are They Stored In Extended Relational Databases

Building a more accurate reality model requires taking into account imperfect information present in our knowledge and language. This paper presents several aspects of data imperfection in the database context and the appropriate frameworks for their treatment. It’s concluding that null value, possibility distribution and probability theory are the best solutions to represent incomplete, imprecise and uncertain data. For each of these problems there are some relational model extension proposals, including data representation and relational algebra

Naive possibilistic classifiers for imprecise or uncertain numerical data

International audienceIn real-world problems, input data may be pervaded with uncertainty. In this paper, we investigate the behavior of naive possibilistic classifiers, as a counterpart to naive Bayesian ones, for dealing with classification tasks in the presence of uncertainty. For this purpose, we extend possibilistic classifiers, which have been recently adapted to numerical data, in order to cope with uncertainty in data representation. Here the possibility distributions that are used are supposed to encode the family of Gaussian probabilistic distributions that are compatible with the considered dataset. We consider two types of uncertainty: (i) the uncertainty associated with the class in the training set, which is modeled by a possibility distribution over class labels, and (ii) the imprecision pervading attribute values in the testing set represented under the form of intervals for continuous data. Moreover, the approach takes into account the uncertainty about the estimation of the Gaussian distribution parameters due to the limited amount of data available. We first adapt the possibilistic classification model, previously proposed for the certain case, in order to accommodate the uncertainty about class labels. Then, we propose an algorithm based on the extension principle to deal with imprecise attribute values. The experiments reported show the interest of possibilistic classifiers for handling uncertainty in data. In particular, the probability-to-possibility transform-based classifier shows a robust behavior when dealing with imperfect data