This piece argues that neither character nor the lure/allure of the tempting object/subject may matter nearly so much as the structure--the mathematical structure--of the tempting situation. The implicature of this finding is that, perhaps, neither rehabilitation (which oftentimes just doesn't work even when--and after--it appears to work) nor retribution is the proper purpose of incarceration--rather simple incapacitation is. The effect of the finding is to dramatically limit the scope within which free will is actually operative in a range of situations. (...) A further implicature of this finding is that so-called "sting operations" are completely immoral. (shrink)

In this paper, we defend and extend a (simple) mathematical model of /akrasia/. The probability is due to Professor Peter Milne.

The starting point of this work is the gap between two distinct traditions in information engineering: knowledge representation and data-driven modelling. The first tradition emphasizes logic as a tool for representing beliefs held by an agent. The second tradition claims that the main source of knowledge is made of observed data, and generally does not use logic as a modelling tool. However, the emergence of fuzzy logic has blurred the boundaries between these two traditions by putting forward fuzzy rules as (...) a Janus-faced tool that may represent knowledge, as well as approximate non-linear functions representing data. This paper lays bare logical foundations of data-driven reasoning whereby a set of formulas is understood as a set of observed facts rather than a set of beliefs. Several representation frameworks are considered from this point of view: classical logic, possibility theory, belief functions, epistemic logic, fuzzy rule-based systems. Mamdani's fuzzy rules are recovered as belonging to the data-driven view. In possibility theory a third set-function, different from possibility and necessity plays a key role in the data-driven view, and corresponds to a particular modality in epistemic logic. A bi-modal logic system is presented which handles both beliefs and observations, and for which a completeness theorem is given. Lastly, our results may shed new light in deontic logic and allow for a distinction between explicit and implicit permission that standard deontic modal logics do not often emphasize. (shrink)

Combining testimonial reports from independent and partially reliable information sources is an important problem of uncertain reasoning. Within the framework of Dempster-Shafer theory, we propose a general model of partially reliable sources which includes several previously known results as special cases. The paper reproduces these results, gives a number of new insights, and thereby contributes to a better understanding of this important application of reasoning with uncertain and incomplete information.

There are a number of reasons for being interested in uncertainty, and there are also a number of uncertainty formalisms. These formalisms are not unrelated. It is argued that they can all be reflected as special cases of the approach of taking probabilities to be determined by sets of probability functions defined on an algebra of statements. Thus, interval probabilities should be construed as maximum and minimum probabilities within a set of distributions, Glenn Shafer's belief functions should be construed as (...) lower probabilities, etc. Updating probabilities introduces new considerations, and it is shown that the representation of belief as a set of probabilities conflicts in this regard with the updating procedures advocated by Shafer. The attempt to make subjectivistic probability plausible as a doctrine of rational belief by making it more flowery — i.e., by adding new dimensions — does not succeed. But, if one is going to represent beliefs by sets of distributions, those sets of distributions might as well be based in statistical knowledge, as they are in epistemological or evidential probability. (shrink)

The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

An introduction to Dempster-Shafter Theory, from a lecture at the Northern Institute of Philosophy in 2010.

The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

Some decisions result in cognitive consequences such as information gained and information lost. The focus of this study, however, is decisions with consequences that are partly or completely noncognitive. These decisions are typically referred to as ‘real-life decisions’. According to a common complaint, the challenges of real-life decision making cannot be met by decision theory. This complaint has at least two principal motives. One is the maximizing objection that to require agents to determine the optimal act under real-world constraints is (...) unrealistic. The other is the precision objection that the numeric requirements for applying decision theory are overly demanding for real-life decisions. Responses to both objections are aired in the History section of this chapter. The maximizing objection is addressed with reference to work by Weirich and Pollock, while the precision objection is countered via a proposal by Kyburg and another by Gärdenfors and Sahlin. However, the Current Research section urges a different response to the precision objection by introducing a comparative version of decision theory. Drawing on Chu and Halpern’s notion of generalized expected utility, this version of decision theory permits many choices to be based on merely comparative plausibilities and utilities. Finally, the Further Research section undertakes an open-ended exploration of three of the assumptions upon which this form of decision theory (and many others) is based: transitivity, independence, and plausibilistic decision rules. (shrink)

The focus of this study is cognitive choice: the selection of one cognitive option (a hypothesis, a theory, or an axiom, for instance) rather than another. The study proposes that cognitive choice should be based on the plausibilities of states posited by rival cognitive options and the utilities of these options' information outcomes. The proposal introduces a form of decision theory that is novel because comparative; it permits many choices among cognitive options to be based on merely comparative plausibilities and (...) utilities. This form of decision theory intersects with recommendations by advocates of decision theory for cognitive choice, on the one hand, and defenders of comparative evaluation of scientific hypotheses and theories, on the other. But it differs from prior decision-theoretic proposals because it requires no more than minimal precision in specifying plausibilities and utilities. And it differs from comparative proposals because none has shown how comparative evaluations can be carried out within a decision-theoretic framework. (shrink)

We present new probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment, called Zλ- and lexλ-entailment, which are parameterized through a value λ ∈ [0,1] that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of λ = 0 and λ = 1, the notions of Zλ- and lexλ-entailment coincide with probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment that have been recently introduced by the author. We show (...) that the notions of Zλ- and lexλ-entailment have similar properties as their classical counterparts. In particular, they both satisfy the rationality postulates of System P and the property of Rational Monotonicity. Moreover, Zλ-entailment is weaker than lexλ-entailment, and both Zλ- and lexλ-entailment are proper generalizations of their classical counterparts. (shrink)