Related papers: A systematic way of analysing proofs in probabilit…
A number of writers(Joseph Halpern and Fahiem Bacchus among them) have offered semantics for formal languages in which inferences concerning probabilities can be made. Our concern is different. This paper provides a formalization of…
Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of…
Some quantitative results obtained by proof mining take the form of Herbrand disjunctions that may depend on additional parameters. We attempt to elucidate this fact through an extension to first-order arithmetic of the proof of Herbrand's…
Game comonads have brought forth a new approach to studying finite model theory categorically. By representing model comparison games semantically as comonads, they allow important logical and combinatorial properties to be exressed in…
Probabilistic Logic Programs (PLPs) generalize traditional logic programs and allow the encoding of models combining logical structure and uncertainty. In PLP, inference is performed by summarizing the possible worlds which entail the query…
We present SGDPLL(T), an algorithm that solves (among many other problems) probabilistic inference modulo theories, that is, inference problems over probabilistic models defined via a logic theory provided as a parameter (currently,…
In the interpretation of experimental data, one is actually looking for plausible explanations. We look for a measure of plausibility, with which we can compare different possible explanations, and which can be combined when there are…
Probabilistic and set-based methods are two approaches for model invalidation, parameter and state estimation. Both classes of methods use different types of data, i.e. deterministic or probabilistic data, which allow different statements…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
The Glivenko--Cantelli theorem is a uniform version of the strong law of large numbers. It states that for every IID sequence of random variables, the empirical measure converges to the underlying distribution (in the sense of uniform…
A method of calculating probability values from a system of marginal constraints is presented. Previous systems for finding the probability of a single attribute have either made an independence assumption concerning the evidence or have…
Many formal languages include binders as well as operators that satisfy equational axioms, such as commutativity. Here we consider the nominal language, a general formal framework which provides support for the representation of binders,…
Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as…
Many probabilistic programming languages allow programs to be run under constraints in order to carry out Bayesian inference. Running programs under constraints could enable other uses such as rare event simulation and probabilistic…
Coinduction occurs in two guises in Horn clause logic: in proofs of circular properties and relations, and in proofs involving construction of infinite data. Both instances of coinductive reasoning appeared in the literature before, but a…
Unitary quantum theory, having no Born Rule, is non-probabilistic. Hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements. Generalising and improving upon the…
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but…
The primary aim of Hilbert's proof theory was to establish the consistency of classical mathematics using finitary means only. Hilbert's strategy for doing this was to eliminate the infinite (in the form of unbounded quantifiers) from…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…