A qualitative logic of decision

An important aspect of intelligent behavior is the ability to reason, make decisions, and act in spite of uncertainty. This paper presents a qualitative logic of decision that supports decision-making under uncertainty. To be specific, the paper presents a knowledge representation language based upon subjective Bayesian decision theory that aims to capture some aspects of common-sense reasoning associated with making decisions about actions. The language addresses the problem of describing justifications of rational choices in situations where the alternatives involve trading off potential losses and gains. The logic and an associated qualitative arithmetic are implemented in an efficient PROLOG program. Examples illustrate their use in several concrete decision-making situations

Fusion of imprecise qualitative information

In this paper, we present a new 2-tuple linguistic representation model, i.e. Distribution Function Model (DFM), for combining imprecise qualitative information using fusion rules drawn from Dezert-Smarandache Theory (DSmT) framework. Such new approach allows to preserve the precision and efficiency of the combination of linguistic information in the case of either equidistant or unbalanced label model. Some basic operators on imprecise 2-tuple labels are presented together with their extensions for imprecise 2-tuple labels. We also give simple examples to show how precise and imprecise qualitative information can be combined for reasoning under uncertainty. It is concluded that DSmT can deal efficiently with both precise and imprecise quantitative and qualitative beliefs, which extends the scope of this theory

Deductive Reasoning Under Uncertainty Using a Water Tank Analogy

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds would commit themselves to executing physically impossible tasks

Argumentation for Knowledge Representation, Conflict Resolution, Defeasible Inference and Its Integration with Machine Learning

Modern machine Learning is devoted to the construction of algorithms and computational procedures that can automatically improve with experience and learn from data. Defeasible argumentation has emerged as sub-topic of artificial intelligence aimed at formalising common-sense qualitative reasoning. The former is an inductive approach for inference while the latter is deductive, each one having advantages and limitations. A great challenge for theoretical and applied research in AI is their integration. The first aim of this chapter is to provide readers informally with the basic notions of defeasible and non-monotonic reasoning. It then describes argumentation theory, a paradigm for implementing defeasible reasoning in practice as well as the common multi-layer schema upon which argument-based systems are usually built. The second aim is to describe a selection of argument-based applications in the medical and health-care sectors, informed by the multi-layer schema. A summary of the features that emerge from the applications under review is aimed at showing why defeasible argumentation is attractive for knowledge-representation, conflict resolution and inference under uncertainty. Open problems and challenges in the field of argumentation are subsequently described followed by a future outlook in which three points of integration with machine learning are proposed

Generalized belief change with imprecise probabilities and graphical models

We provide a theoretical investigation of probabilistic belief revision in complex frameworks, under extended conditions of uncertainty, inconsistency and imprecision. We motivate our kinematical approach by specializing our discussion to probabilistic reasoning with graphical models, whose modular representation allows for efficient inference. Most results in this direction are derived from the relevant work of Chan and Darwiche (2005), that first proved the inter-reducibility of virtual and probabilistic evidence. Such forms of information, deeply distinct in their meaning, are extended to the conditional and imprecise frameworks, allowing further generalizations, e.g. to experts' qualitative assessments. Belief aggregation and iterated revision of a rational agent's belief are also explored