Related papers: Free Theorems Simply, via Dinaturality
This article revisits standard theorems from elementary number theory from a constructive, algorithmic, and proof-theoretic perspective, framed within the theory of computable functionals TCF. Key examples include B\'ezout's identity, the…
This is a joint introduction to classical and free probability, which are twin sisters. We first review the foundations of classical probability, notably with the main limiting theorems (CLT, CCLT, PLT, CPLT), and with a look into examples…
A class of algebras is constructed using free fermions and the invariant antisymmetric tensors associated with irreducible holonomy groups. (This version contains minor typographical corrections and some additional references. )
Extracting metaphors and analogies from free text requires high-level reasoning abilities such as abstraction and language understanding. Our study focuses on the extraction of the concepts that form metaphoric analogies in literary texts.…
Humans surpass the cognitive abilities of most other animals in our ability to "chunk" concepts into words, and then combine the words to combine the concepts. In this process, we make "infinite use of finite means", enabling us to learn…
Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities.…
Given an algebra A, presented by generators and relations, i.e. as a quotient of a tensor algebra by an ideal, we construct a free algebra resolution of A, i.e. a differential graded algebra which is quasi-isomorphic to A and which is…
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
Variable environment is the time-honored way of making sense of free variables, used in programming language theory as well when writing interpreters and some compilers. Algebraic effects give another way, as was pointed already at HOPE…
Contextuality has been identified as a potential resource responsible for the quantum advantage in several tasks. It is then necessary to develop a resource-theoretic framework for contextuality, both in its standard and generalized forms.…
We discuss free probability theory and free harmonic analysis from a categorical perspective. In order to do so, we extend first the set of analytic convolutions and operations and then show that the comonadic structure governing free…
A different general philosophy, to be called Full Randomness (FR), for the analysis of random effects models is presented, involving a notion of reducing or preferably eliminating fixed effects, at least formally. For example, under FR…
The algorithmic independence of conditionals, which postulates that the causal mechanism is algorithmically independent of the cause, has recently inspired many highly successful approaches to distinguish cause from effect given only…
We introduce a finite version of free probability and show the link between recent results using polynomial convolutions and the traditional theory of free probability. One tool for accomplishing this is a seemingly new transformation that…
Dependencies have played a significant role in database design for many years. They have also been shown to be useful in query optimization. In this paper, we discuss dependencies between lexicographically ordered sets of tuples. We…
Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine…
Manual ontology construction takes time, resources, and domain specialists. Supporting a component of this process for automation or semi-automation would be good. This project and dissertation provide a Formal Concept Analysis and WordNet…
Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…
The work relates to the automatic generation of logical specifications, considered as sets of temporal logic formulas, extracted directly from developed software models. The extraction process is based on the assumption that the whole…
Automatic extraction of cause-effect relationships from natural language texts is a challenging open problem in Artificial Intelligence. Most of the early attempts at its solution used manually constructed linguistic and syntactic rules on…