Erratum to: Database preference queries - a possibilistic logic approach with symbolic priorities

This paper proposes a first comparative study of the expressive power of two approaches to the representation of preferences: conditional preferences networks (CP-nets) and a logical preference representation framework, namely possibilistic logic. It is shown that possibilistic logic, using a method for handling symbolic priority weights, can always provide complete preorders compatible with the partial CP-net order. Although CP-nets provide an intuitive appealing setting for expressing preferences, possibilistic logic appears to be somewhat more flexible for that purpose.

This paper describes a logical machinery for computing decisions, where the available knowledge on the state of the world is described by a possibilistic propositional logic base (i.e., a collection of logical statements associated with qualitative certainty levels), and where the preferences of the user are also described by another possibilistic logic base whose formula weights are interpreted in terms of priorities. Two attitudes are allowed for the decision maker: a pessimistic risk-averse one and an optimistic one. The computed decisions are in agreement with a qualitative counterpart to the classical theory of expected utility, recently developed by three of the authors. A link is established between this logical view of qualitative decision making and an ATMS-based computation procedure. Efficient algorithms for computing pessimistic and optimistic optimal decisions are finally given in this logical setting (using some previous work of the fourth author).

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.

Explainability and formal verification of neural networks may be crucial when using these models to perform critical tasks.Pursuing explainability properties, we present a method for approximating neural networks by piecewise linear functions, which is a step to achieve a logical representation of the network.We also explain how such logical representations may be applied in the formal verification of some properties of neural networks.Furthermore, we present the results of an empirical experiment where the methods introduced are used in a case study.A path towards explainability of neural networks that compute piecewise linear functions is to represent them in a more amenable format, given by pairs comprehending a domain region and a linear function that realizes the network computation in such region.Further, from such a regional representation, a logical representation may be given, for instance, by a pair of formulas of ukasiewicz infinitely-valued logic ( ).A polynomial procedure that builds this logical representation is introduced in [Preto and Finger 2020, Preto and Finger 2022].However, neural networks do not necessarily compute piecewise linear functions.And neural networks that compute such functions may have an exponential regional format representation in the size of their traditional graph representations.The main goal of this work is to propose a method for approximating neural networks by piecewise linear functions in regional format, allowing their approximate logical representation in .Another path to reliability in critical tasks for neural networks is to formally verify properties of interest concerning them.In [Preto and Finger 2023a, Preto andFinger 2023b], some of these properties are codified in the language of departing from the network representation in such logical system.Then, the properties are verified through decisions about satisfiability and logical consequence of their codification.This work aims to present these concepts through examples and to perform an empirical experiment of formal verification using the logical approximation of a neural network.

Sugeno integrals are well-known qualitative aggregation functions in multiple criteria decision making. They return a global evaluation between the minimum and the maximum of the input criteria values. They can model sophisticated aggregation schemes through a system of priorities that applies to any subset of criteria and can take into account some kind of synergy inside subsets of criteria. Although a given Sugeno integral specifies a particular way of implicitly describing a set of entities reaching some global satisfaction level, it is hard to figure out what is the underlying explicit meaning of such an integral in practice (even if the priority level associated to each subset of criteria has a precise meaning). The paper proposes an answer to this problem. Any capacity on a finite set can be represented by a special possibilistic logic base containing positive prioritised clauses, and conversely any possibilistic logic base can represent a set-function. Moreover, Sugeno integral can be represented by a possibilistic logic base expressing how it behaves (thanks to a mapping between the scale and a set of logical atoms reflecting the different values for each criterion). Viewing a Sugeno integral as a set of prioritized logically expressed goals has not only the advantage to make the contents of a Sugeno integral more readable, but it also prompts Sugeno integrals into the realm of logic, and makes it possible to define entailment between them.

Corrigendum to “Navigation in large subway networks: An informational approach” [Physica A 390 (2011) 374–386

This paper deals with the evaluation of database preference queries in the framework of a preference model based on the notion of outranking. It describes an efficient technique that involves a pre-filtering step, whose aim is to limit the number of pairwise tuple comparisons necessary to determine the best answers to a query.

In the framework of quantitative possibility theory, two representation modes were developed: logical-based representation in terms of quantitative possibilistic bases and graphical-based representation in terms of product-based possibilistic networks. This paper deals with logical and graphical representations of uncertain information using a quantitative possibility theory framework. We first provide a deep analysis of the relationships between these two forms of representational frameworks. Then, in the logical setting, we develop syntactic relations between penalty logic and quantitative possibilistic logic. These translations are useful for different applications and are interesting for taking advantage of each format at the inferential level. We also provide an algorithm for reasoning with quantitative possibilistic logic. The algorithm takes inspiration from the syntactic relations between quantitative possibilistic logic bases and penalty logic. Finally, we provide experimental results that compare the uncertainty propagation algorithms developed for the possibilistic product-based networks and the inference algorithms based on WMAXSAT developed in this paper.

The paper discusses the use of product-based possibilistic networks for representing conditional preference statements on discrete variables. The approach uses non-instantiated possibility weights to define conditional preference tables. Moreover, additional information about the relative strengths of symbolic weights can be taken into account. It yields a partial preference order among possible choices corresponding to a symmetric form of Pareto ordering. In the case of Boolean variables, this partial ordering coincides with the inclusion between the sets of preference statements that are violated. Furthermore, this graphical model has two logical counterparts in terms of possibilistic logic and penalty logic. The flexibility and the representational power of the approach are stressed. Besides, algorithms for handling optimization and dominance queries are provided.

The themes for this conference are thus focused on "Innovating and Inspiring Soft Computing and Intelligent Pattern Recognition"

Recently, neural networks have been increasingly applied to remote sensing imagery classification. The conventional neural network classifier performs learning from the representative information within a problem domain on a one-pixel-one-class basis; therefore, class mixture and the degree of membership of a pixel are generally not taken into account, often resulting in a poor classification accuracy. Based on the framework of a dynamic learning neural network (DL), this communications proposes a fuzzy version (FDL) based on two steps: network representation of fuzzy logic and assignment of membership. Comparisons between the DL and FDL are made by applying both neural networks to SAR image classification. Experimental results show that the FDL has faster convergence rate than that of DL. In addition, the separability between similar classes is improved. Moreover, the classification results match better with ground truth.

Group decision-making, in which a collective decision needs to be derived from individual agents’ preferences has been an active area of research. In group decisionmaking, autonomous agents need some procedures or mechanisms that can collect preference information from them and make a decision; or some protocols that enable them to be involved in the decision process, to interact with each other and to jointly make a collective decision. Examples include preference aggregation mechanisms, negotiation protocols, voting procedures, and auctions. This thesis studies the problem of agent-based group decision-making in various problem settings, proposing several efficient approaches to support multiple agents in reaching efficient and fair collective decisions overmultiple issues. The research work in this thesis can be divided into two parts, addressing the agent-based group decision-making problem in circumstances in which there is, respectively, complete and incomplete information available. The first part of this thesis focuses on preference aggregation in combinatorial domains, provided all agents’ preferences. Structured preferences Conditional Preference Network (CP-nets) and its variant Trade-off enhanced CP-nets (TCP-nets) are used as formal models for representing the agents’ preferences in group decision-making. Before going into the problem of making a group decision from a collection of CP-nets or TCP-nets, the problem of individual preference reasoning is studied and a computationally efficient heuristic algorithm for dominance testing in CP-nets, which forms the basis for many group decision-making mechanisms, is introduced. Subsequently, we consider the group decision-making problem with multiple agents’ CP-nets and TCP-nets. As the space of possible outcomes in combinatorial domains has a size exponential in the number of variables, computational complexity in group decision-making will be one of the issues that need to be addressed. Two computationally efficient approaches are proposed in order to support agent-based group decisionmaking in combinatorial domains with different decision criteria: (i) an approach that converts the qualitative preferences derived from CP-nets or TCP-nets into numerical penalty scoring functions, and then searches for an optimal collective decision based on the individual penalty scores; and (ii) an approach that focuses on combinatorial vote and computes the winners (i.e., winning alternatives) from a collection of CP-nets according to Majority voting rule. The second part of this thesis is concerned with the disadvantage of disclosing preference information in group decision-making and considers the incomplete information setting. Two negotiation approaches are presented in order to support agent-based group decision-making in, respectively, combinatorial domains and in domains with multiple continuous issues. Firstly, a negotiation protocol in combinatorial domains is proposed, which enables agents to distributively make decisions and leads them to Pareto-optimal agreements under incomplete information setting. Then for the domains with multiple continuous issues, a cooperative mediated negotiation approach is proposed to support the agents searching for joint utility gains and reaching an efficient and fair agreement. For every approach introduced in this thesis, experiments are carried out and the results are presented and analysed in order to provide insights into the performance of these approaches.

The widespread of applications like e-commerce and recommendation systems requires the use of efficient customization techniques and user preferences handling. In database community a lot of research on this topic has been focused on extending standard SQL with preference facilities in order to provide personalized query answering. More specifically, user preferences are an essential ingredient of personalized database applications. In this paper, we consider the conditional preference queries (cp-queries) of CPrefSQL query language where user preferences are specified by a set of conditional rules. We propose new algorithms based on a technique we called preference partition that outperform the state-of-the-art algorithms for CPrefSQL preference operators significantly decreasing the number of scans over database.

Possibilistic preference networks