Scalable Uncertainty Management

This paper proposes a concise overview of the role of possibility theory in logical approaches to reasoning under uncertainty. It shows that three traditions of reasoning under or about uncertainty (set-functions, epistemic logic and three-valued logics) can be reconciled in the setting of possibility theory. We offer a brief presentation of basic possibilistic logic, and of its generalisation that comes close to a modal logic albeit with simpler more natural epistemic semantics. Past applications to various reasoning tasks are surveyed, and future lines of research are also outlined.

This paper is an overview of the discrete Sugeno integrals and their applications when the evaluation scale is a totally ordered set. The various expressions of the Sugeno integrals are presented. Some major characterisation results are recalled: results based on characteristic properties and act-based axiomatisation. We discuss the properties of a preference relation modelling by a Sugeno integral. We also present its power expression to represent a dataset and its interpretation with a set of if-then rules.

We propose an extension of Poole’s independent choice logic based on a relaxation of the underlying independence assumptions. A credal semantics involving multiple joint probability mass functions over the possible worlds is adopted. This represents a conservative approach to probabilistic logic programming achieved by considering all the mass functions consistent with the probabilistic facts. This allows to model tasks for which independence among some probabilistic choices cannot be assumed, and a specific dependence model cannot be assessed. Preliminary tests on an object ranking application show that, despite the loose underlying assumptions, informative inferences can be extracted.

The use of Bayesian networks has been shown to be powerful for supporting decision making, for example in a medical context. A particularly useful inference task is the most probable explanation (MPE), which provides the most likely assignment to all the random variables that is consistent with the given evidence. A downside of this MPE solution is that it is static and not very informative for (medical) domain experts. In our research to overcome this problem, we were inspired by recent research results on augmenting Bayesian networks with argumentation theory. We use arguments to generate explanations of the MPE solution in natural language to make it more understandable for the domain expert. Moreover, the approach allows decision makers to further explore explanations of different scenarios providing more insight why certain alternative explanations are considered less probable than the MPE solution.

Despite the vagueness and uncertainty that is intrinsic in any medical act, interpretation and decision (including acts of data reporting and representation of relevant medical conditions), still little research has focused on how to explicitly take this uncertainty into account. In this paper, we focus on a general and wide-spread HL7 terminology, which is grounded on a traditional and well-established convention, to represent severity of health conditions (e.g., pain, visible signs), ranging from absent to very severe (as a matter of fact, different versions of this standard present minor differences, like ‘minor’ instead of ‘mild’, or ‘fatal’ inst ead of ‘very severe’). Our aim is to provide a fuzzy version of this terminology. To this aim, we conducted a questionnaire-based qualitative research study involving a relatively large sample of clinicians to represent numerically the five different labels of the standard terminology: absent, mild, moderate, severe and very severe. Using the collected values we then present and discuss three different possible representations that address the vagueness of medical interpretation by taking into account the perceptions of domain experts. In perspective, our hope is to use the resulting fuzzifications to improve machine learning approaches to medicine.

While many systems exist for reasoning with Description Logics knowledge bases, very few of them are able to cope with uncertainty. BUNDLE is a reasoning system, exploiting an underlying non-probabilistic reasoner (Pellet), able to perform inference w.r.t. Probabilistic Description Logics. In this paper, we report on a new modular version of BUNDLE that can use other OWL (non-probabilistic) reasoners and various approaches to perform probabilistic inference. BUNDLE can now be used as a standalone desktop application or as a library in OWL API-based applications that need to reason over Probabilistic Description Logics. Due to the introduced modularity, BUNDLE performance now strongly depends on the method and OWL reasoner chosen to obtain the set of justifications. We provide an evaluation on several datasets as the inference settings vary.

The current availability of large volumes of health care data makes it a promising data source to new views on disease interaction. Most of the times, patients have multiple diseases instead of a single one (also known as multimorbidity), but the small size of most clinical research data makes it hard to impossible to investigate this issue. In this paper, we propose a latent-based approach to expand patient evolution in temporal electronic health records, which can be uninformative due to its very general events. We introduce the notion of clusters of hidden states allowing for an expanded understanding of the multiple dynamics that underlie events in such data. Clusters are defined as part of hidden Markov models learned from such data, where the number of hidden states is not known beforehand. We evaluate the proposed approach based on a large dataset from Dutch practices of patients that had events on comorbidities related to atherosclerosis. The discovered clusters are further correlated to medical-oriented outcomes in order to show the usefulness of the proposed method.

Complex decisions in human decision-making may arise when the Emotional Intelligence and Rational Reasoning produce different preference ordering between alternatives. From a mathematical point of view, complex decisions can be defined as decisions where a preference ordering between random variables cannot be represented by a linear functional. The Asymmetric and the Symmetric Choquet integrals with respect to non additive-measures have been defined as aggregation operators of data sets and as a tool to assess an ordering between random variables. They could be considered to represent preference orderings of the conscious and unconscious mind when a human being make decision. Sufficient conditions are given such that the two integral representations of a coherent upper conditional prevision by the Asymmetric Choquet integral and the Symmetric Choquet integral with respect to Hausdorff outer measures coincide and linearity holds.

The aim of this paper is to define the counterpart of separable belief functions for capacities valued on a finite totally ordered set. Evidence theory deals with the issue of merging unreliable elementary testimonies. Separable belief functions are the results of this merging process. However not all belief functions are separable. Here, we start with a possibility distribution on the power set of a frame of discernment that plays the role of a basic probability assignment. It turns out that any capacity can be induced by the qualitative counterpart of the definition of a belief function (replacing sum by $$\max $$ ). Then, we consider a qualitative counterpart of Dempster rule of combination applied to qualitative capacities, via their qualitative Möbius transforms. We study the class of capacities, called separable capacities, that can be generated by applying this combination rule to simple support capacities, each focusing on a subset of the frame of discernment. We compare this decomposition with the one of general capacities as a maximum over a finite set of necessity measures. The relevance of this framework to the problem of information fusion from unreliable sources is explained.

To satisfy a fluctuating demand and achieve a high level of quality and service, companies must take into account several features when designing new products in order to become or remain market leaders. When a single company is unable to meet this objective alone, it is appropriate for it to join its actions with other companies. The product design consists of the complex task to select from various potential actions that allowing the fulfilment of several requirements: functional, technical, environmental, economic, security, etc. Furthermore, the task is even more difficult when actions are related to distinct services or companies that do not necessarily know the capacities of each others which makes complex the coordination of joint actions. Interactions between services may be affected by antagonist personal interests.Based on a multiple criteria decision analysis (MCDA) framework and a fuzzy model that links actions to the satisfaction of objectives, this paper proposes to treat two extreme views related to the collective selection of the necessary actions to design a product: (1) The first point of view corresponds to an ideal situation where each service reveals its capacities and the unique objective is to succeed in the realization of the common goal; (2) the second point of view corresponds to a more realistic situation where only necessary information for the progress of collective action are shared and where collective and personal goals coexist and are to be taken into account. The first situation corresponds to a classical case where a single decision maker (DM) has to express his preferences then a classical optimization problem under constraints has to be solved in order to efficiently select actions. In the second situation the services do not share the same preferences and each service wants to maximize its gain, in this case we propose to build a negotiated solution between services.

This paper proposes to exploit heterogeneous data, i.e. data described by both numerical and categorical features, so as to gain knowledge about the categorical attributes from the numerical ones. More precisely, it aims at discovering whether, according to a given data set, based on information provided by the numerical attributes, some categorical attributes actually are ordinal ones and, additionally, at establishing ranking relations between the category values. To that aim, the paper proposes the 3-step methodology OSACA, standing for Order Seeking Algorithm for Categorical Attributes: it first consists in extracting gradual patterns from the numerical attributes, to identify rich ranking information about the data; it then applies mathematical morphology tools, more precisely alternated filters, to induce an associated order on the categorical attributes. The third step evaluates the quality of the candidate rankings through an original measure derived from the rank entropy discrimination.

Distribution-aware answer set sampling has a wide range of potential applications, for example in the area of probabilistic logic programming or for the computation of approximate solutions of combinatorial or search problems under uncertainty. This paper introduces algorithms for the sampling of answer sets under given probabilistic constraints. Our approaches allow for the specification of probability distributions over stable models using probabilistically weighted facts and rules as constraints for an approximate sampling task with specifiable accuracy. At this, we do not impose any independence requirements on random variables. An experimental evaluation investigates the performance characteristics of the presented algorithms.

Axiom pinpointing refers to the problem of finding the axioms in an ontology that are relevant for understanding a given entailment or consequence. One approach for axiom pinpointing, known as glass-box, is to modify a classical decision procedure for the entailments into a method that computes the solutions for the pinpointing problem. Recently, consequence-based decision procedures have been proposed as a promising alternative for tableaux-based reasoners for standard ontology languages. In this work, we present a general framework to extend consequence-based algorithms with axiom pinpointing.

A coherence-based probability semantics for categorical syllogisms of Figure I, which have transitive structures, has been proposed recently (Gilio, Pfeifer, & Sanfilippo [15]). We extend this work by studying Figure II under coherence. Camestres is an example of a Figure II syllogism: from Every P is M and No S is M infer No S is P. We interpret these sentences by suitable conditional probability assessments. Since the probabilistic inference of $$\bar{P}|S$$ from the premise set $$\{M|P,\bar{M}|S\}$$ is not informative, we add $$p(S|(S \vee P))>0$$ as a probabilistic constraint (i.e., an “existential import assumption”) to obtain probabilistic informativeness. We show how to propagate the assigned (precise or interval-valued) probabilities to the sequence of conditional events $$(M|P,\bar{M}|S, S|(S \vee P))$$ to the conclusion $$\bar{P}|S$$ . Thereby, we give a probabilistic meaning to the other syllogisms of Figure II. Moreover, our semantics also allows for generalizing the traditional syllogisms to new ones involving generalized quantifiers (like Most S are P) and syllogisms in terms of defaults and negated defaults.

When combining beliefs from different sources, often not only new knowledge but also conflicts arise. In this paper, we investigate how we can measure the disagreement among sources. We start our investigation with disagreement measures that can be induced from inconsistency measures in an automated way. After discussing some problems with this approach, we propose a new measure that is inspired by the $$\eta $$ -inconsistency measure. Roughly speaking, it measures how well we can satisfy all sources simultaneously. We show that the new measure satisfies desirable properties, scales well with respect to the number of sources and illustrate its applicability in inconsistency-tolerant reasoning.

We extend the classic propositional tableau method in order to compute the models given by the semantics of the Priest’s paraconsistent logic of paradox. Without loss of generality, we assume that the knowledge base is represented through propositional statements in NNF, which leads to use only two rules from the classical propositional tableau calculus for computing the paraconsistent models. We consider multisets to represent branches of the tableau tree and we extend the classical closed branches in order to compute the paradoxical models of formulas of the knowledge base. A sound and complete algorithm is provided.

Several gradual semantics for abstract and bipolar argumentation have been proposed in the literature, ascribing to each argument a value taken from a scale, i.e. an ordered set. These values somewhat match the arguments’ dialectical status and provide an indication of their dialectical strength, in the context of the given argumentation framework. These research efforts have been complemented by formulations of several properties that these gradual semantics may satisfy. More recently a synthesis of many literature properties into more general groupings based on parametric definitions has been proposed. In this paper we show how this generalised parametric formulation enables the identification of new properties not previously considered in the literature and discuss their usefulness to capture alternative requirements coming from different application contexts.

In this paper we consider, in the framework of coherence, four different definitions of conjunction among conditional events. In each of these definitions the conjunction is still a conditional event. We first recall the different definitions of conjunction; then, given a coherent probability assessment (x, y) on a family of two conditional events $$\{A|H,B|K\}$$ , for each conjunction $$(A|H) \wedge (B|K)$$ we determine the (best) lower and upper bounds for the extension $$z=P[(A|H) \wedge (B|K)]$$ . We show that, in general, these lower and upper bounds differ from the classical Fréchet-Hoeffding bounds. Moreover, we recall a notion of conjunction studied in recent papers, such that the result of conjunction of two conditional events A|H and B|K is (not a conditional event, but) a suitable conditional random quantity, with values in the interval [0, 1]. Then, we remark that for this conjunction, among other properties, the Fréchet-Hoeffding bounds are preserved.

Probabilistic relational models (PRMs) were introduced to extend the modelling and reasoning capacities of Bayesian networks from propositional to relational domains. PRMs are typically learned from relational data, by extracting from these data both a dependency structure and its numerical parameters. For this purpose, a large and rich data set is required, which proves prohibitive for many real-world applications. Since a PRM’s structure can often be readily elicited from domain experts, we propose manual construction by an approach that combines qualitative concepts adapted from qualitative probabilistic networks (QPNs) with stepwise quantification. To this end, we introduce qualitative probabilistic relational models (QPRMs) and tailor an existing algorithm for qualitative probabilistic inference to these new models.

Data interoperability is a major issue in data management for data science and big data analytics. Probabilistic data integration (PDI) is a specific kind of data integration where extraction and integration problems such as inconsistency and uncertainty are handled by means of a probabilistic data representation. This allows a data integration process with two phases: (1) a quick partial integration where data quality problems are represented as uncertainty in the resulting integrated data, and (2) using the uncertain data and continuously improving its quality as more evidence is gathered. The main contribution of this paper is an iterative approach for incorporating evidence of users in the probabilistically integrated data. Evidence can be specified as hard or soft rules (i.e., rules that are uncertain themselves).

Positional scoring rules are frequently used for aggregating rankings (for example in social choice and in sports). These rules are highly sensitive to the weights associated to positions: depending on the weights, a different winner may be selected. In this paper we explicitly consider the role of weight uncertainty in both the case of monotone decreasing weights and of convex decreasing weights. First we discuss the problem of finding possible winners (candidates that may win for a feasible instantiation of the weights) based on previous works that established a connection with the notion of stochastic dominance. Second, we adopt decision-theoretic methods (minimax regret, maximum advantage, expected value) to pick a winner based on the weight uncertainty and we provide a characterization of these methods. Finally, we show some applications of our methodology in real datasets.

The setting of this paper is the general information theory and the pseudo-analysis. We consider the general information measure J, defined without probability for crisp sets or without fuzzy measure for fuzzy sets and we propose a particular information measure for intersection of two sets. The pseudo-analysis is used to generalize the definition of independence and it leads to a functional equation. This equation belongs to a system of functional equations. We present some solutions of this system.

The BDI architecture, where agents are modelled based on their beliefs, desires, and intentions, provides a practical approach to developing intelligent agent systems. However, these systems either do not include any capability for first-principles planning (FPP), or they integrate FPP in a rigid and ad-hoc manner that does not define the semantical behaviour. In this paper, we propose a novel operational semantics for incorporating FPP as an intrinsic planning capability to achieve goals in BDI agent systems. To achieve this, we introduce a declarative goal intention to keep track of declarative goals used by FPP and develop a detailed specification of the appropriate operational behaviour when FPP is pursued, succeeded or failed, suspended, or resumed in the BDI agent systems. Furthermore, we prove that BDI agent systems and FPP are theoretically compatible for principled integration in both offline and online planning manner. The practical feasibility of this integration is demonstrated, and we show that the resulting agent framework combines the strengths of both BDI agent systems and FPP, thus substantially improving the performance of BDI agent systems when facing unforeseen situations.

In this research note, we sketch the idea to use (aspects of) imprecise probability models to handle unobserved heterogeneity in statistical (regression) models. Unobserved heterogeneity (frailty) is a frequent issue in many applications, arising whenever the underlying probability distributions depend on unobservable individual characteristics (like personal attitudes or hidden genetic dispositions). We consider imprecise sampling models where the likelihood contributions depend on individual parameters, varying in an interval (cuboid). Based on this, and a hyperparameter controlling the amount of ambiguity, we directly fit a credal set to the data. We introduce the basic concepts of this credal maximum likelihood approach, sketch first aspects of practical calculation of the resulting estimators by constrained optimization, derive some first general properties and finally discuss some ideas of a data-dependent choice of the hyperparameter.

Different types of graphical representation for local preferences have been proposed in the literature. Graphs may be directed or not. Modeling may be quantitative or qualitative. Principles for extending local preferences to complete configurations may be based on different independence assumptions. Some extensions of such graphical representation settings to multiple agent preferences have been proposed, with different ways of handling agents: they may be viewed just as a set of individual agents, or described in terms of attribute values inducing a partition of the set of agents in terms of subcategories, or they may be reduced to some anonymous statistical counting. The fact that preferences pertain to multiple agents raises the question of either working with a collective graphical representation or aggregating individual preferences, the preferences of each agent being then represented as a graph. Moreover the multiple agent nature of the representation enriches the types of preference queries that can be addressed. The purpose of this short note is to start with a brief survey of the main graphical preference models found in the literature, such as CP-nets, $$\pi $$ -pref nets, GAI networks, and to discuss their multiple agent extensions in an organized way, with a view to understand how the different representation options could be combined when possible.

We propose a generic numerical measure of inconsistency of a database with respect to a set of integrity constraints. It is based on an abstract repair semantics. A particular inconsistency measure associated to cardinality-repairs is investigated; and we show that it can be computed via answer-set programs.

We propose SLAC, a sparse approximation to a Lipschitz constant estimator that can be utilised to obtain uncertainty bounds around predictions of a regression method. As we demonstrate in a series of experiments on real-world and synthetic data, this approach can yield fast and robust predictive uncertainty bounds that are as reliable as those of Gaussian Processes or Bayesian Neural Networks, while reducing computational effort markedly.

Within the context of ontology learning, we consider the problem of selecting candidate axioms through a suitable score. Focusing on subsumption axioms, this score is learned coupling support vector regression with a special similarity measure inspired by the Jaccard index and justified by semantic considerations. We show preliminary results obtained when the proposed methodology is applied to pairs of candidate OWL axioms, and compare them with an analogous inference procedure based on fuzzy membership induction.

In this paper we consider a hybrid possibilistic-probabilistic alternative approach to Probabilistic Preference Logic Networks (PPLNs). Namely, we first adopt a possibilistic model to represent the beliefs about uncertain strict preference statements, and then, by means of a pignistic probability transformation, we switch to a probabilistic-based credulous inference of new preferences for which no explicit (or transitive) information is provided. Finally, we provide a tractable approximate method to compute these probabilities.

Mainstream approaches to uncertainty modeling in relational databases are probabilistic. Still some researchers persist in proposing representations based on possibility theory. They are motivated by the ability of this latter setting for modeling epistemic uncertainty and by its qualitative nature. Interestingly enough, several possibilistic models have been proposed over time, and have been motivated by different application needs ranging from database querying, to database design and to data cleaning. Thus, one may distinguish between four different frameworks ordered here according to an increasing representation power: databases with (i) layered tuples; (ii) certainty-qualified attribute values; (iii) attribute values restricted by general possibility distributions; (iv) possibilistic c-tables. In each case, we discuss the role of the possibility-necessity duality, the limitations and the benefit of the representation settings, and their suitability with respect to different tasks.

Argumentation-based recommender systems constitute an interesting tool to provide reasoned recommendations in complex domains with unresolved contradictory information situations and incomplete information. In these systems, the use of contextual information becomes a central issue in order to come up with personalized recommendations. An argumentative recommender system that offers mechanisms to handle contextual aspects of the recommendation domain provides an important ability that can be exploited by the user. However, in most of existing works, this issue has not been extensively studied. In this work, we propose an argumentation-based formalization for dealing with this issue. We present a general framework that allows the design of recommender systems capable of handling queries that can include (possibly inconsistent) contextual information under which recommendations should be computed. To answer a query, in the proposed argumentation-based approach, the system first selects alternative instances according to the user’s supplied contextual information, and then makes recommendations, in both cases through a defeasible argumentative analysis.