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18
Probabilistic logic and probabilistic networks
, 2008
"... While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches ..."
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Cited by 17 (13 self)
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While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches to probabilistic logic fit into a simple unifying framework: logically complex evidence can be used to associate probability intervals or probabilities with sentences. Specifically, we show in Part I that there is a natural way to present a question posed in probabilistic logic, and that various inferential procedures provide semantics for that question: the standard probabilistic semantics (which takes probability functions as models), probabilistic argumentation (which considers the probability of a hypothesis being a logical consequence of the available evidence), evidential probability (which handles reference classes and frequency data), classical statistical inference
Objective Bayesian nets
 We Will Show Them! Essays in Honour of Dov Gabbay
, 2005
"... I present a formalism that combines two methodologies: objective Bayesianism and Bayesian nets. According to objective Bayesianism, an agent’s degrees of belief (i) ought to satisfy the axioms of probability, (ii) ought to satisfy constraints imposed by background knowledge, and (iii) should otherwi ..."
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Cited by 12 (10 self)
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I present a formalism that combines two methodologies: objective Bayesianism and Bayesian nets. According to objective Bayesianism, an agent’s degrees of belief (i) ought to satisfy the axioms of probability, (ii) ought to satisfy constraints imposed by background knowledge, and (iii) should otherwise be as noncommittal as possible (i.e. have maximum entropy). Bayesian nets offer an efficient way of representing and updating probability functions. An objective Bayesian net is a Bayesian net representation of the maximum entropy probability function. I show how objective Bayesian nets can be constructed, updated and combined, and how they can deal with cases in which the agent’s background knowledge includes knowledge of qualitative influence relationships, e.g. causal influences. I then sketch a number of applications of the resulting formalism, showing how it can shed light on probability logic, causal modelling, logical reasoning, semantic reasoning, argumentation
Causal pluralism versus epistemic causality
, 2007
"... It is tempting to analyse causality in terms of just one of the indicators of causal relationships, e.g., mechanisms, probabilistic dependencies or independencies, counterfactual conditionals or agency considerations. While such an analysis will surely shed light on some aspect of our concept of cau ..."
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Cited by 7 (5 self)
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It is tempting to analyse causality in terms of just one of the indicators of causal relationships, e.g., mechanisms, probabilistic dependencies or independencies, counterfactual conditionals or agency considerations. While such an analysis will surely shed light on some aspect of our concept of cause, it will fail to capture the whole, rather multifarious, notion. So one might instead plump for pluralism: a different analysis for a different occasion. But we do not seem to have lots of different kinds of cause—just one eclectic notion. The resolution of this conundrum, I think, requires us to accept that our causal beliefs are generated by a wide variety of indicators, but to deny that this variety of indicators yields a variety of concepts of cause. This focus on the relation between evidence and causal beliefs leads to what I call epistemic causality. Under this view, certain causal beliefs are appropriate or rational on the basis of observed evidence; our notion of cause can be understood purely in terms of these rational
Inductive influence
 British Journal for the Philosophy of Science
"... Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief 1 to the next raven being black, however many other black ravens have 2 been observed. I argue that this objection can be overcome by appealing to objective Bay ..."
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Cited by 7 (6 self)
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Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief 1 to the next raven being black, however many other black ravens have 2 been observed. I argue that this objection can be overcome by appealing to objective Bayesian nets, a formalism for representing objective Bayesian degrees of belief. Under this account, previous observations exert an inductive influence on the next observation. I show how this approach can be used to capture the JohnsonCarnap continuum of inductive methods, as well as the NixParis continuum, and show how inductive influence can
Objective Bayesianism, Bayesian Conditionalisation
, 2008
"... Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between ..."
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Cited by 7 (6 self)
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Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between the two forms of updating reflects negatively on Bayesian conditionalisation rather than on objective Bayesian updating. The paper also reviews some existing criticisms and justifications of conditionalisation, arguing in particular that the diachronic Dutch book justification fails because diachronic Dutch book arguments are subject to a reductio: in certain circumstances one can Dutch book an agent however she changes her degrees of belief. One may also criticise objective Bayesianism on the grounds that its norms are not compulsory but voluntary, the result of a stance. It is argued that this second objection also misses the mark, since objective
Objective bayesian probabilistic logic
 Journal of Algorithms
"... This paper develops connections between objective Bayesian epistemology—which holds that the strengths of an agent’s beliefs should be representable by probabilities, should be calibrated with evidence of empirical probability, and should otherwise be equivocal—and probabilistic logic. After introdu ..."
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Cited by 6 (4 self)
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This paper develops connections between objective Bayesian epistemology—which holds that the strengths of an agent’s beliefs should be representable by probabilities, should be calibrated with evidence of empirical probability, and should otherwise be equivocal—and probabilistic logic. After introducing objective Bayesian epistemology over propositional languages, the formalism is extended to handle predicate languages. A rather general probabilistic logic is formulated and then given a natural semantics in terms of objective Bayesian epistemology. The machinery of objective Bayesian nets and objective credal nets is introduced and this machinery is applied to provide a calculus for probabilistic logic that meshes with the objective Bayesian semantics.
Objective Bayesianism with predicate languages. Synthese
, 2008
"... Objective Bayesian probability is often defined over rather simple domains, e.g., finite event spaces or propositional languages. This paper investigates the extension of objective Bayesianism to firstorder logical languages. It is argued that the objective Bayesian should choose a probability func ..."
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Cited by 5 (5 self)
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Objective Bayesian probability is often defined over rather simple domains, e.g., finite event spaces or propositional languages. This paper investigates the extension of objective Bayesianism to firstorder logical languages. It is argued that the objective Bayesian should choose a probability function, from all those that satisfy constraints imposed by background knowledge, that is closest to a particular frequencyinduced probability function which generalises the λ = 0 function of Carnap’s continuum of inductive methods.
Interpreting probability in causal models for cancer
 Causality and probability in the sciences, Texts in Philosophy
, 2007
"... How should probabilities be interpreted in causal models in the social and health sciences? In this paper we take a step towards answering this question by investigating the case of cancer in epidemiology and arguing that the objective Bayesian interpretation is most appropriate in this domain. ..."
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Cited by 3 (3 self)
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How should probabilities be interpreted in causal models in the social and health sciences? In this paper we take a step towards answering this question by investigating the case of cancer in epidemiology and arguing that the objective Bayesian interpretation is most appropriate in this domain.
Epistemic Complexity from an Objective Bayesian Perspective
"... Causality, meaningful complexity and knowledge construction ..."
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Cited by 3 (3 self)
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Causality, meaningful complexity and knowledge construction
Philosophies of probability
 Handbook of the Philosophy of Mathematics, Volume 4 of the Handbook of the Philosophy of Science
"... This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of ..."
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Cited by 3 (2 self)
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This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of mathematics in general.