Constraint-wish and satisfied-dissatisfied: an overview of two approaches for dealing with bipolar querying

In recent years, there has been an increasing interest in dealing with user preferences in flexible database querying, expressing both positive and negative information in a heterogeneous way. This is what is usually referred to as bipolar database querying. Different frameworks have been introduced to deal with such bipolarity. In this chapter, an overview of two approaches is given. The first approach is based on mandatory and desired requirements. Hereby the complement of a mandatory requirement can be considered as a specification of what is not desired at all. So, mandatory requirements indirectly contribute to negative information (expressing what the user does not want to retrieve), whereas desired requirements can be seen as positive information (expressing what the user prefers to retrieve). The second approach is directly based on positive requirements (expressing what the user wants to retrieve), and negative requirements (expressing what the user does not want to retrieve). Both approaches use pairs of satisfaction degrees as the underlying framework but have different semantics, and thus also different operators for criteria evaluation, ranking, aggregation, etc

Bipolar SQLf: a Flexible Querying Language for Relational Databases

International audienceFlexible querying of information systems allows expressing complex preferences in user queries. Such preferences can be modeled by fuzzy bipolar conditions which are made of constraints c and wishes w and interpreted as "to satisfy c and if possible to satisfy w".We de ne in this article the main elements of the Bipolar SQLf language, which is an SQL-like querying language based on a bipolar relational algebra. This language is an extension of the SQLf language. Basic statements (projection, selection, etc.) are firstly defined in terms of syntax, evaluation and calibration. Then, complex statements, such as bipolar queries based on nesting operators are studied in terms of expression, evaluation, query equivalence and backward compatibility with the SQLf language

Bipolarity and multipolarity in aggregation structures

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Fuzzy Bipolar Conditions of Type "or else"

International audiencePreviously studied fuzzy bipolar conditions of type "and if possible" are made of a mandatory condition c and an optional condition w. They allow expressing complex preferences of a conjunctive nature. We define in this paper, a new kind of fuzzy bipolar conditions of the form "or else" which express complex preferences of a disjunctive nature. We show that the "or else" form can be used as a negation operator of the "and if possible" form and vice versa. We also show that these both forms are compatible and, therefore, fuzzy bipolar conditions of both types can be used together in the same bipolar query

Causality Is Logically Definable-Toward an Equilibrium-Based Computing Paradigm of Quantum Agents and Quantum Intelligence (QAQI)

A survey on agents, causality and intelligence is presented and an equilibrium-based computing paradigm of quantum agents and quantum intelligence (QAQI) is proposed. In the survey, Aristotle’s causality principle and its historical extensions by David Hume, Bertrand Russell, Lotfi Zadeh, Donald Rubin, Judea Pearl, Niels Bohr, Albert Einstein, David Bohm, and the causal set initiative are reviewed; bipolar dynamic logic (BDL) is introduced as a causal logic for bipolar inductive and deductive reasoning; bipolar quantum linear algebra (BQLA) is introduced as a causal algebra for quantum agent interaction and formation. Despite the widely held view that causality is undefinable with regularity, it is shown that equilibrium-based bipolar causality is logically definable using BDL and BQLA for causal inference in physical, social, biological, mental, and philosophical terms. This finding leads to the paradigm of QAQI where agents are modeled as quantum ensembles; intelligence is revealed as quantum intelligence. It is shown that the ensembles formation, mutation and interaction of agents can be described as direct or indirect results of quantum causality. Some fundamental laws of causation are presented for quantum agent entanglement and quantum intelligence. Applicability is illustrated; major challenges are identified in equilibrium based causal inference and quantum data mining

Formal Concept Analysis from the Standpoint of Possibility Theory (ICFCA 2015)

International audienceFormal concept analysis (FCA) and possibility theory (PoTh) have been developed independently. They address different concerns in information processing: while FCA exploits relations linking objects and properties, and has applications in data mining and clustering, PoTh deals with the modeling of (graded) epistemic uncertainty. However, making a formal parallel between FCA and PoTh is fruitful. The four set-functions at work in PoTh have meaningful counterparts in FCA; this leads to consider operators neglected in FCA, and thus new fixed point equations. One of these pairs of equations, paralleling the one defining formal concepts in FCA, defines independent sub-contexts of objects and properties that have nothing in common. The similarity of the structures underlying FCA and PoTh is still more striking, using a cube of opposition (a device extending the traditional square of opposition in logic). Beyond the parallel between FCA and PoTh, this invited contribution, which largely relies on several past publications by the authors, also addresses issues pertaining to the possible meanings, degree of satisfaction vs. degree of certainty, of graded object-property links, which calls for distinct manners of handling the degrees. Other lines of interest for further research are briefly mentioned

The Point-Descriptor-Precedence representation for point configurations and movements

In this paper, we represent (moving) point configurations along a curved directed line qualitatively by means of a system of relational symbols based on two distance descriptors: one representing distance along the curved directed line and the other representing signed orthogonal distance to the curved directed line. The curved directed line represents the direction of the movement of interest. For instance, it could be straight as in the case of driving along a highway or could be curved as in the case of an intersection or a roundabout. Inspired by the Point Calculus, the order between the points on the curved directed line is described by means of a small set of binary relations () acting upon the distance descriptors. We call this representation the Point-Descriptor-Precedence-Static (PDPS) representation at a time point and Point-Descriptor-Precedence-Dynamic (PDPD) representation during a time interval. To illustrate how the proposed approach can be used to represent and analyse curved movements, some basic micro-analysis traffic examples are studied. Finally, we discuss some extensions of our work to highlight the practical benefits of PDP in identifying motion patterns that could be useful in GIS, autonomous vehicles, sports analytics, and gait analysis

Three-valued logics, uncertainty management and rough sets

This paper is a survey of the connections between three-valued logics and rough sets from the point of view of incomplete information management. Based on the fact that many three-valued logics can be put under a unique algebraic umbrella, we show how to translate three-valued conjunctions and implications into operations on ill-known sets such as rough sets. We then show that while such translations may provide mathematically elegant algebraic settings for rough sets, the interpretability of these connectives in terms of an original set approximated via an equivalence relation is very limited, thus casting doubts on the practical relevance of truth-functional logical renderings of rough sets

A critique of Tractarian semantics

This is a critique of the principal claims made within Ludwig Wittgenstein\u27s Tractatus Logico-Philosophicus. It traces the development of his thought from the time he dictated the pre-Tractarian Notes on Logic to Russell up until about 1932 when he began work on the Philosophical Grammar. The influence exercised upon him by Frege, Russell and Moore are considered at length. Chapter one examines Moore\u27s relational theory of judgment which Wittgenstein apparently accepted upon his arrival at Cambridge in 1911. From Moore Wittgenstein would inherit one of the fundamental metaphysical theses of the Tractatus, namely, that the world consists of facts rather than things. Wittgenstein\u27s attempt to overcome the relational theory\u27s inability to account for falsehood, negation, and the possibility of truly ascribing false beliefs to others would herald some of the principal theses of Tractarian semantics: that propositional signs must exhibit bipolarity, that a distinction must be drawn between Sinn and Bedeutung, and that a distinction holds between what can be said and what can only be shown. Chapter Two examines how these theses are sharpened by considering the influence of Frege and the manner in which Wittgenstein disposes of Russell\u27s Paradox. considerable attention is given to the issue of whether Frege is to be interpreted as a semantic Platonist. It is argued that he is not, and that Tractarian semantics shores up the problematic features of Frege\u27s philosophy which make it susceptible to the paradox. From Frege Wittgenstein derives the idea that all representation requires a structured medium. The chapter concludes by considering how this entails the falsehood of semantic Platonism. Chapter Three studies Wittgenstein\u27s argument for logical atomism and gives it a favorable assessment. The influence of Russell\u27s conception of logical analysis is considered. The chapter concludes by showing the way Wittgenstein\u27s thesis that there must be simple subsistent objects depends upon the truth of his Grundgedanke, i.e., the claim that the logical constants are not referring terms. Chapter Four examines the argument for the Grundgedanke, and defends it against criticism based upon phenomenological considerations for objectifying negativity. It is demonstrated that Wittgenstein\u27s view entails that a distinction must be drawn between propositions possessing sense and those that are senseless but no less a part of our language. Chapter Five examines Wittgenstein\u27s claim that the essence of a proposition consists in a propositional sign\u27s projective relation to the world, and it considers the Tractarian analysis of propositional attitude ascriptions. It is argued that the analysis of these sorts of sentences forms the principal problem with the Tractatus. The chapter includes a discussion of why the Color Exclusion Problem need not be considered problematic for the author of the Tractatus, and it defends the realistic interpretation given of the Tractatus throughout the dissertation against criticisms arising from a consideration of Wittgenstein\u27s remarks on solipsism