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We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
Probability theory is far from being the most general mathematical theory of uncertainty. A number of arguments point at its inability to describe second-order ('Knightian') uncertainty. In response, a wide array of theories of uncertainty…
Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the same. In the case of reasoning about…
It is shown that the ability of the interval probability representation to capture epistemological independence is severely limited. Two events are epistemologically independent if knowledge of the first event does not alter belief (i.e.,…
One cannot justifiably presuppose the physical salience of structures derived via decoherence theory based upon an entirely uninterpreted use of the quantum formalism. Non-probabilistic accounts of the emergence of probability via…
Many models of economics assume that individuals distort objective probabilities. We propose a simple consistency condition on distortion functions, which we term distortion coherence, that ensures that the function commutes with…
There are two reasons why uncertainty may not be adequately described by Probability Theory. The first one is due to unique or nearly-unique events, that either never realized or occurred too seldom for frequencies to be reliably measured.…
The apparent failure of individual probabilistic expressions to distinguish uncertainty about truths from uncertainty about probabilistic assessments have prompted researchers to seek formalisms where the two types of uncertainties are…
Bayesian inference systems should be able to explain their reasoning to users, translating from numerical to natural language. Previous empirical work has investigated the correspondence between absolute probabilities and linguistic…
The classical propositional assumption-based model is extended to incorporate probabilities for the assumptions. Then it is placed into the framework of evidence theory. Several authors like Laskey, Lehner (1989) and Provan (1990) already…
The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said…
It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how "embarrassing" it…
With the rise of increasingly powerful and user-facing NLP systems, there is growing interest in assessing whether they have a good representation of uncertainty by evaluating the quality of their predictive distribution over outcomes. We…
This paper investigates the problem of finding a preference relation on a set of acts from the knowledge of an ordering on events (subsets of states of the world) describing the decision-maker (DM)s uncertainty and an ordering of…
We construct the belief function that quantifies the agent, beliefs about which event of Q will occurred when he knows that the event is selected by a chance set-up and that the probability function associated to the chance set up is only…
The general use of subjective probabilities to model belief has been justified using many axiomatic schemes. For example, ?consistent betting behavior' arguments are well-known. To those not already convinced of the unique fitness and…
This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…
The classical conception of falsification presents scientific theories as entities that are decisively refuted when their predictions fail. This picture has long been challenged by both philosophical analysis and scientific practice, yet…