Related papers: Multi-sorted logic and logical geometry: some prob…
Possibility theory offers either a qualitive, or a numerical framework for representing uncertainty, in terms of dual measures of possibility and necessity. This leads to the existence of two kinds of possibilistic causal graphs where the…
The purpose of this paper is to discuss how topology and geometry provide, in many instances, the connective tissue that enables logical comprehension. We illustrate this theme with many examples including Venn diagrams, knot diagrams,…
We present an introductory survey to first order logic for metric structures and its applications to C*-algebras.
This is a set of 288 questions written for a Moore-style course in Mathematical Logic. I have used these (or some variation) four times in a beginning graduate course. Topics covered are: propositional logic axioms of ZFC wellorderings and…
One of the most powerful ideas in the study and classification of algebraic varieties is the notion of a model: that is, to single out an object, in the appropriate isomorphism class, with nice properties. This survey aims to define and…
This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and…
We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…
In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.
Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of…
Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This…
In this paper we present a novel approach to graph (and structural) limits based on model theory and analysis. The role of Stone and Gelfand dualities is displayed prominently and leads to a general theory, which we believe is naturally…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we…
This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…
A multi-relational graph maintains two or more relations over a vertex set. This article defines an algebra for traversing such graphs that is based on an $n$-ary relational algebra, a concatenative single-relational path algebra, and a…
The main purpose of this paper is to present a new approach to logic or what we will call superlogic. This approach constitutes a new way of looking at the connection between quantum mechanics and logic. It is a {\it geometrisation} of the…
Our goal is to provide a survey of some topics in quasiconformal analysis of current interest. We try to emphasize ideas and leave proofs and technicalities aside. Several easily stated open problems are given. Most of the results are joint…
Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…