Related papers: Foundations of Inference
We study lattices in free abelian groups of infinite rank that are invariant under the action of the infinite symmetric group, with emphasis on finiteness of their equivariant bases. Our framework provides a new method for proving…
We give a precise estimate for the number of lattice points in certain bounded subsets of $\mathbb{R}^{n}$ that involve `hyperbolic spikes' and occur naturally in multiplicative Diophantine approximation. We use Wilkie's o-minimal structure…
For a broad class of input-output maps, arguments based on the coding theorem from algorithmic information theory (AIT) predict that simple (low Kolmogorov complexity) outputs are exponentially more likely to occur upon uniform random…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
Measures of dependence among variables, and measures of information content and shared information have become valuable tools of multi-variable data analysis. Information measures, like marginal entropies, mutual and multi-information, have…
A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a…
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…
We study how to infer new choices from previous choices in a conservative manner. To make such inferences, we use the theory of choice functions: a unifying mathematical framework for conservative decision making that allows one to impose…
This short note presents a new relation between coherent spaces and finiteness spaces. This takes the form of a functor from COH to FIN commuting with the additive and multiplicative structure of linear logic. What makes this correspondence…
The relationship between Lexical-Functional Grammar (LFG) functional structures (f-structures) for sentences and their semantic interpretations can be expressed directly in a fragment of linear logic in a way that explains correctly the…
Valuation based systems verifying an idempotent property are studied. A partial order is defined between the valuations giving them a lattice structure. Then, two different strategies are introduced to represent valuations: as infimum of…
A central question for causal inference is to decide whether a set of correlations fit a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for…
Probabilistic models require the notion of event space for defining a probability measure. An event space has a probability measure which ensues the Kolmogorov axioms. However, the probabilities observed from distinct sources, such as that…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
This work presents a conceptual synthesis of causal discovery and inference frameworks, with a focus on how foundational assumptions -- causal sufficiency, causal faithfulness, and the causal Markov condition -- are formalized and…
Description Logics (DLs) are used in knowledge-based systems to represent and reason about terminological knowledge of the application domain in a semantically well-defined manner. In this thesis, we establish a number of novel complexity…
Using the ideas of abstract algebra, we introduce the basic concepts of abstract probability theory that generalize the Kolmogorov's probability theory, possibility theory and other theories that deal with uncertainty. Based on abstract…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
The purpose of this paper is to outline a simple set of axioms for basic set theory from which most fundamental facts can be derived. The key to the whole project is a new axiom of set theory which I dubbed "The Law of Extremes". It allows…
This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general…