相关论文: Typicality Defended
Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is…
We show that every general theory \`a la Keisler with the Schr\"oder-Bernstein property is stable. This generalizes the corresponding result from classical logic due to John Goodrick. Our proof uses the classical result (generalized to the…
The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…
This paper explains why internal and external validity cannot be simultaneously maximised. It introduces "evidential states" to represent the information available for causal inference and shows that routine study operations (restriction,…
In this note we give some variations on an extension of Caratheodory's normality criterion due to Grahl and Nevo.
The aim of this work is to point out a strong structural phenomenon hidden behind the existence of normalizers through the investigation of this property in the non-pointed context: given any category E, a certain property of the fibration…
We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting bottom is strongly normalising provided all its `stratified approximations'…
Jakob Bernoulli, working in the late 17th century, identified a gap in contemporary probability theory. He cautioned that it was inadequate to specify force of proof (probability of provability) for some kinds of uncertain arguments. After…
We strengthen the standard bifurcation theorems for saddle-node, transcritical, pitchfork, and period-doubling bifurcations of maps. Our new formulation involves adding one or two extra terms to the standard truncated normal forms with…
In this paper we prove Chaitin's ``heuristic principle'', {\it the theorems of a finitely-specified theory cannot be significantly more complex than the theory itself}, for an appropriate measure of complexity. We show that the measure is…
For obtaining causal inferences that are objective, and therefore have the best chance of revealing scientific truths, carefully designed and executed randomized experiments are generally considered to be the gold standard. Observational…
In our paper "Essential normality, essential norms and hyperrigidity" we claimed that the restriction of the identity representation of a certain operator system (constructed from a polynomial ideal) has the unique extension property,…
Cultural trends and popularity cycles can be observed all around us, yet our theories of social influence and identity expression do not explain what perpetuates these complex, often unpredictable social dynamics. We propose a theory of…
This expository paper advocates an approach to physics in which ``typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions…
Many authors noted that the principle of relativity, together with space-time symmetries, suffices to derive Lorentz-like coordinate transformations between inertial frames. These contain a free parameter, $k$, (equal to $c^{-2}$ in special…
Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common…
In this paper, we show that the likelihood-ratio measure (a) is invariant with respect to dominating sigma-finite measures, (b) satisfies logical consequences which are not satisfied by standard $p$-values, (c) respects frequentist…
This paper builds on no-go theorems to the effect that quantum theory is inconsistent with observations being absolute; that is, unique and non-relative. Unlike the existing no-go results, the one introduced here is based on a…
We defend a new theory of statistical evidence, which we call Robust Bayesianism (RB). We prove that, under widely accepted assumptions, RB entails the law of likelihood [Royall, 1997], the likelihood principle [Berger and Wolpert, 1988],…
In this discussion we demonstrate that fiducial distributions provide a natural example of an inference paradigm that does not obey Strong Likelihood Principle while still satisfying the Weak Conditionality Principle. [arXiv:1302.7021]