Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...) independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic independence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models. (shrink)

What are scientific theories and how should they be represented? In this article, I propose a causal–structural account, according to which scientific theories are to be represented as sets of interrelated causal and credal nets. In contrast with other accounts of scientific theories (such as Sneedian structuralism, Kitcher’s unificationist view, and Darden’s theory of theoretical components), this leaves room for causality to play a substantial role. As a result, an interesting account of explanation is provided, which sheds light on explanatory (...) unification within a causalist framework. The theory of classical genetics is used as a case study. 1 Introduction2 The Theory of Classical Genetics3 Three Philosophical Accounts of the Theory of Classical Genetics3.1 The structuralist account3.2 Kitcher’s unificationism3.3 Darden and theory change in science4 A Common Lacuna: Where is Causality?5 Woodward’s Interventionist Account of Causation6 Causal Bayes Nets and Their Interrelations6.1 Causal Bayes nets6.2 Relations among causal nets6.3 Credal nets and their interrelations7 The Theory of the Gene and its Causal Graph8 A First Exemplar: Stem Length in Pea Plants8.1 Three crosses on stem length in pea plants8.2 The causal graph for stem length in pea plants8.3 Morgan’s explanatory principles and the credal net for stem length in pea plants9 Explaining Mendel’s Crosses: A Causal–Structural Account10 Monohybrid Crosses with Complete Dominance11 Exemplars,Explanatory Patterns, Generic Credal Nets, and Mechanism Schemas12 Incomplete Dominance13 Anomalies14 Multi-hybrid Crosses with Independent Assortment15 Multi-hybrid Crosses with Linkage and Crossing-Over16 Double Crossing-Over and the Linear Order of the Gene17 Causal–Structural Explanation18 Explanatory Unification19 Concluding Remarks. (shrink)

Causal reasoning and game-theoretic reasoning are fundamental topics in artificial intelligence, among many other disciplines: this paper is concerned with their intersection. Despite their importance, a formal framework that supports both these forms of reasoning has, until now, been lacking. We offer a solution in the form of (structural) causal games, which can be seen as extending Pearl's causal hierarchy to the game-theoretic domain, or as extending Koller and Milch's multi-agent influence diagrams to the causal domain. We then consider three (...) key questions: i) How can the (causal) dependencies in games - either between variables, or between strategies - be modelled in a uniform, principled manner? ii) How may causal queries be computed in causal games, and what assumptions does this require? iii) How do causal games compare to existing formalisms? To address question i), we introduce mechanised games, which encode dependencies between agents' decision rules and the distributions governing the game. In response to question ii), we present definitions of predictions, interventions, and counterfactuals, and discuss the assumptions required for each. Regarding question iii), we describe correspondences between causal games and other formalisms, and explain how causal games can be used to answer queries that other causal or game-theoretic models do not support. Finally, we highlight possible applications of causal games, aided by an extensive open-source Python library. (shrink)

The field of of imprecise probability has matured, in no small part because of Teddy Seidenfeld’s decades of original scholarship and essential contributions to building and sustaining the ISIPTA community. Although the basic idea behind imprecise probability is (at least) 150 years old, a mature mathematical theory has only taken full form in the last 30 years. Interest in imprecise probability during this period has also grown, but many of the ideas that the mature theory serves can be difficult to (...) apprehend to those new to the subject. Although these fundamental ideas are common knowledge in the ISIPTA community, they are expressed, when they are expressed at all, obliquely, over the course of years with students and colleagues. -/- A single essay cannot convey the store of common knowledge from any research community, let alone the ISIPTA community. But, this essay nevertheless is an attempt to guide those familiar with the basic Bayesian framework to appreciate some of the elegant and powerful ideas that underpin the contemporary theory of lower previsions, which is the theory that most people associate with the term ‘imprecise probabilities’. (shrink)

In this paper we, an epistemologist and a machine learning scientist, argue that we need to pursue a novel area of philosophical research in AI – the ethics of belief for AI. Here we take the ethics of belief to refer to a field at the intersection of epistemology and ethics concerned with possible moral, practical, and other non-truth-related dimensions of belief. In this paper we will primarily be concerned with the normative question within the ethics of belief regarding what (...) agents – both human and artificial – ought to believe, rather than with questions concerning whether beliefs meet certain evaluative standards such as being true, being justified, constituting knowledge, etc. We suggest four topics in extant work in the ethics of (human) belief that can be applied to an ethics of AI belief: doxastic wronging by AI (morally wronging someone in virtue of beliefs held about them); morally owed beliefs (beliefs that agents are morally obligated to hold); pragmatic and moral encroachment (cases where the practical or moral features of a belief is relevant to its epistemic status, and in our case specifically to whether an agent ought to hold the belief); and moral responsibility for AI beliefs. We also indicate two relatively nascent areas of philosophical research that haven’t yet been generally recognized as ethics of AI belief research, but that do fall within this field of research in virtue of investigating various moral and practical dimensions of belief: the epistemic and ethical decolonization of AI; and epistemic injustice in AI. (shrink)

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli’s discussion of “convex Bayesianism” (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of “strong independence” (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli’s results and recent developments (...) on the axiomatization of non-binary preferences, and its impact on “complete” independence, are described. (shrink)

Additionally, the text shows how to develop computationally feasible methods to mesh with this framework.

When the likelihood ratio approach is employed for evidential reasoning in law, it is often necessary to employ subjective probabilities, which are probabilities derived from the opinions and judgement of a human. At least three concerns arise from the use of subjective probabilities in legal applications. Firstly, human beliefs concerning probabilities can be vague, ambiguous and inaccurate. Secondly, the impact of this vagueness, ambiguity and inaccuracy on the outcome of a probabilistic analysis is not necessarily fully understood. Thirdly, the provenance (...) of subjective probabilities and the associated potential sources of vagueness, ambiguity and inaccuracy tend to be poorly understood, making it difficult for the outcome of probabilistic reasoning to be explained and validated, which is crucial in legal applications. The former two concerns have been addressed by a wide body of research in AI. The latter, however, has received little attention. This paper presents a novel approach to employ argumentation to reason about probability distributions in probabilistic models. It introduces a range of argumentation schemes and corresponding sets of critical questions for the construction and validation of argument models that define sets of probability distributions. By means of an extended example, the paper demonstrates how the approach, argumentation schemes and critical questions can be employed for the development of models and their validation in legal applications of the likelihood ratio approach to evidential reasoning. (shrink)

This volume arose out of an international, interdisciplinary academic network on Probabilistic Logic and Probabilistic Networks involving four of us (Haenni, Romeijn, Wheeler and Williamson), called Progicnet and funded by the Leverhulme Trust from 2006–8. Many of the papers in this volume were presented at an associated conference, the Third Workshop on Combining Probability and Logic (Progic 2007), held at the University of Kent on 5–7 September 2007. The papers in this volume concern either the special focus on the connection (...) between probabilistic logic and probabilistic networks or the more general question of the links between probability and logic. Here we introduce probabilistic logic, probabilistic networks, current and future directions of research and also the themes of the papers that follow. (shrink)

This paper has two main parts. In the first part, we motivate a kind of indeterminate, suppositional credences by discussing the prospect for a subjective interpretation of a causal Bayesian network, an important tool for causal reasoning in artificial intelligence. A CBN consists of a causal graph and a collection of interventional probabilities. The subjective interpretation in question would take the causal graph in a CBN to represent the causal structure that is believed by an agent, and interventional probabilities in (...) a CBN to represent suppositional credences. We review a difficulty noted in the literature with such an interpretation, and suggest that a natural way to address the challenge is to go for a generalization of CBN that allows indeterminate credences. In the second part, we develop a decision-theoretic foundation for such indeterminate suppositional credences, by generalizing a theory of coherent choice functions to accommodate some form of act-state dependence. The upshot is a decision-theoretic framework that is not only rich enough to, so to speak, ground the probabilities in a subjectively interpreted causal network, but also interesting in its own right, in that it accommodates both act-state dependence and imprecise probabilities. (shrink)

Satisficing is a central concept in both individual and social multiagent decision making. In this paper we first extend the notion of satisficing by formally modeling the tradeoff between costs and decision failure. Second, we extend this notion of “neo”-satisficing into the context of social or multiagent decision making and interaction, and model the social conditioning of preferences in a satisficing framework.

Probabilistic Relational Models (PRMs) are a framework for compactly representing uncertainties (actually probabilities). They result from the combination of Bayesian Networks (BNs), Object-Oriented languages, and relational models. They are specifically designed for their efficient construction, maintenance and exploitation for very large scale problems, where BNs are known to perform poorly. Actually, in large-scale problems, it is often the case that BNs result from the combination of patterns (small BN fragments) repeated many times. PRMs exploit this feature by defining these patterns (...) only once (the so-called PRM’s classes) and using them through multiple instances, as prescribed by the Object-Oriented paradigm. This design induces low construction and maintenance costs. In addition, by exploiting the classes’ structures, PRM’s state-of-the-art inference algorithm “Structured Variable Elimination” (SVE) significantly outperforms BN’s classical inference algorithms (e.g., Variable Elimination, VE; Local Conditioning, LC). SVE is actually an extension of VE that simply exploits classes to avoid redundant computations. In this article, we show that SVE can be enhanced using LC. Although LC is often thought as being outperformed by VE-like algorithms in BNs, we do think that it should play an important role for PRMs because its features are very well suited for best exploiting PRM classes. In this article, relying on Faÿ and Jaffray’s works, we show how LC can be used in conjunction with VE and deduce an extension of SVE that outperforms it for large-scale problems. Numerical experiments highlight the practical efficiency of our algorithm. (shrink)