Generalized basic probability assignments

Dempster-Shafer theory allows to construct belief functions from (precise) basic probability assignments. The present paper extends this idea substantially. By considering SETS of basic probability assignments, an appealing constructive approach to general interval probability (general imprecise probabilities) is achieved, which allows for a very flexible modelling of uncertain knowledge

Special Cases

International audienceThis chapter reviews special cases of lower previsions, that are instrumental in practical applications. We emphasize their various advantages and drawbacks, as well as the kind of problems in which they can be the most useful

Quantifying Degrees of E-admissibility in Decision Making with Imprecise Probabilities

This paper is concerned with decision making using imprecise probabilities. In the first part, we introduce a new decision criterion that allows for explicitly modeling how far decisions that are optimal in terms of Walley’s maximality are accepted to deviate from being optimal in the sense of Levi’s E-admissibility. For this criterion, we also provide an efficient and simple algorithm based on linear programming theory. In the second part of the paper, we propose two new measures for quantifying the extent of E-admissibility of an E-admissible act, i.e. the size of the set of measures for which the corresponding act maximizes expected utility. The first measure is the maximal diameter of this set, while the second one relates to the maximal barycentric cube that can be inscribed into it. Also here, for both measures, we give linear programming algorithms capable to deal with them. Finally, we discuss some ideas in the context of ordinal decision theory. The paper concludes with a stylized application examples illustrating all introduced concepts

Quantifying Degrees of E-admissibility in Decicion Making with Imprecise Probabilities

This paper is concerned with decision making using imprecise probabilities. In the first part, we introduce a new decision criterion that allows for explicitly modeling how far decisions that are optimal in terms of Walley’s maximality are accepted to deviate from being optimal in the sense of Levi’s E-admissibility. For this criterion, we also provide an efficient and simple algorithm based on linear programming theory. In the second part of the paper, we propose two new measures for quantifying the extent of E-admissibility of an E-admissible act, i.e. the size of the set of measures for which the corresponding act maximizes expected utility. The first measure is the maximal diameter of this set, while the second one relates to the maximal barycentric cube that can be inscribed into it. Also here, for both measures, we give linear programming algorithms capable to deal with them. Finally, we discuss some ideas in the context of ordinal decision theory. The paper concludes with a stylized application examples illustrating all introduced concepts

Concepts for Decision Making under Severe Uncertainty with Partial Ordinal and Partial Cardinal Preferences

We introduce three different approaches for decision making under uncertainty if (I) there is only partial (both cardinally and ordinally scaled) information on an agent’s preferences and (II) the uncertainty about the states of nature is described by a credal set (or some other imprecise probabilistic model). Particularly, situation (I) is modeled by a pair of binary relations, one specifying the partial rank order of the alternatives and the other modeling partial information on the strength of preference. Our first approach relies on decision criteria constructing complete rankings of the available acts that are based on generalized expectation intervals. Subsequently, we introduce different concepts of global admissibility that construct partial orders between the available acts by comparing them all simultaneously. Finally, we define criteria induced by suitable binary relations on the set of acts and, therefore, can be understood as concepts of local admissibility. For certain criteria, we provide linear programming based algorithms for checking optimality/admissibility of acts. Additionally, the paper includes a discussion of a prototypical situation by means of a toy example

A Probabilistic Modelling Approach for Rational Belief in Meta-Epistemic Contexts

This work is part of the larger project INTEGRITY. Integrity develops a conceptual frame integrating beliefs with individual (and consensual group) decision making and action based on belief awareness. Comments and criticisms are most welcome via email. The text introduces the conceptual (internalism, externalism), quantitative (probabilism) and logical perspectives (logics for reasoning about probabilities by Fagin, Halpern, Megiddo and MEL by Banerjee, Dubois) for the framework

A Probabilistic Modelling Approach for Rational Belief in Meta-Epistemic Contexts

This work is part of the larger project INTEGRITY. Integrity develops a conceptual frame integrating beliefs with individual (and consensual group) decision making and action based on belief awareness. Comments and criticisms are most welcome via email. Starting with a thorough discussion of the conceptual embedding in existing schools of thought and liter- ature we develop a framework that aims to be empirically adequate yet scalable to epistemic states where an agent might testify to uncertainly believe a propositional formula based on the acceptance that a propositional formula is possible, called accepted truth. The familiarity of human agents with probability assignments make probabilism particularly appealing as quantitative modelling framework for defeasible reasoning that aspires empirical adequacy for gradual belief expressed as credence functions. We employ the inner measure induced by the probability measure, going back to Halmos, interpreted as estimate for uncertainty. Doing so omits generally requiring direct probability assignments testi�ed as strength of belief and uncertainty by a human agent. We provide a logical setting of the two concepts uncertain belief and accepted truth, completely relying on the the formal frameworks of 'Reasoning about Probabilities' developed by Fagin, Halpern and Megiddo and the 'Metaepistemic logic MEL' developed by Banerjee and Dubois. The purport of Probabilistic Uncertainty is a framework allowing with a single quantitative concept (an inner measure induced by a probability measure) expressing two epistemological concepts: possibilities as belief simpliciter called accepted truth, and the agents' credence called uncertain belief for a criterion of evaluation, called rationality. The propositions accepted to be possible form the meta-epistemic context(s) in which the agent can reason and testify uncertain belief or suspend judgement

A Probabilistic Modelling Approach for Rational Belief in Meta-Epistemic Contexts

This work is part of the larger project INTEGRITY. Integrity develops a conceptual frame integrating beliefs with individual (and consensual group) decision making and action based on belief awareness. Comments and criticisms are most welcome via email. Starting with a thorough discussion of the conceptual embedding in existing schools of thought and liter- ature we develop a framework that aims to be empirically adequate yet scalable to epistemic states where an agent might testify to uncertainly believe a propositional formula based on the acceptance that a propositional formula is possible, called accepted truth. The familiarity of human agents with probability assignments make probabilism particularly appealing as quantitative modelling framework for defeasible reasoning that aspires empirical adequacy for gradual belief expressed as credence functions. We employ the inner measure induced by the probability measure, going back to Halmos, interpreted as estimate for uncertainty. Doing so omits generally requiring direct probability assignments testi�ed as strength of belief and uncertainty by a human agent. We provide a logical setting of the two concepts uncertain belief and accepted truth, completely relying on the the formal frameworks of 'Reasoning about Probabilities' developed by Fagin, Halpern and Megiddo and the 'Metaepistemic logic MEL' developed by Banerjee and Dubois. The purport of Probabilistic Uncertainty is a framework allowing with a single quantitative concept (an inner measure induced by a probability measure) expressing two epistemological concepts: possibilities as belief simpliciter called accepted truth, and the agents' credence called uncertain belief for a criterion of evaluation, called rationality. The propositions accepted to be possible form the meta-epistemic context(s) in which the agent can reason and testify uncertain belief or suspend judgement

A Probabilistic Modelling Approach for Rational Belief in Meta-Epistemic Contexts

This work is part of the larger project INTEGRITY. Integrity develops a conceptual frame integrating beliefs with individual (and consensual group) decision making and action based on belief awareness. Comments and criticisms are most welcome via email. The text introduces the conceptual (internalism, externalism), quantitative (probabilism) and logical perspectives (logics for reasoning about probabilities by Fagin, Halpern, Megiddo and MEL by Banerjee, Dubois) for the framework

A methodology for the selection of a paradigm of reasoning under uncertainty in expert system development

The aim of this thesis is to develop a methodology for the selection of a paradigm of reasoning under uncertainty for the expert system developer. This is important since practical information on how to select a paradigm of reasoning under uncertainty is not generally available. The thesis explores the role of uncertainty in an expert system and considers the process of reasoning under uncertainty. The possible sources of uncertainty are investigated and prove to be crucial to some aspects of the methodology. A variety of Uncertainty Management Techniques (UMTs) are considered, including numeric, symbolic and hybrid methods. Considerably more information is found in the literature on numeric methods, than the latter two. Methods that have been proposed for comparing UMTs are studied and comparisons reported in the literature are summarised. Again this concentrates on numeric methods, since there is more literature available. The requirements of a methodology for the selection of a UMT are considered. A manual approach to the selection process is developed. The possibility of extending the boundaries of knowledge stored in the expert system by including meta-data to describe the handling of uncertainty in an expert system is then considered. This is followed by suggestions taken from the literature for automating the process of selection. Finally consideration is given to whether the objectives of the research have been met and recommendations are made for the next stage in researching a methodology for the selection of a paradigm of reasoning under uncertainty in expert system development