Related papers: Exploring Steinitz-Rademacher polyhedra: A challen…
This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…
Reconciling the tension between inductive learning and deductive reasoning in first-order relational domains is a longstanding challenge in AI. We study the problem of answering queries in a first-order relational probabilistic logic…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
The purpose of this paper is to provide a both comprehensive and summarizing account on recent results about analysis and geometry on configuration spaces $\Gamma_X$ over Riemannian manifolds $X$. Particular emphasis is given to a complete…
We examine different generalizations of checking stack automata by allowing multiple input heads and multiple stacks, and characterize their computing power in terms of two-way multi-head finite automata and space-bounded Turing machines.…
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…
This dissertation presents new results on three different themes all related to matroid polytopes. First we investigate properties of Ehrhart polynomials of matroid polytopes, independence matroid polytopes, and polymatroids. We prove that…
The purpose of this paper is to report on the most recent developments in our ongoing investigation of the representation and manipulation of uncertainty in automated reasoning systems. In our earlier studies (Tong and Shapiro, 1985) we…
Machine reading comprehension has aroused wide concerns, since it explores the potential of model for text understanding. To further equip the machine with the reasoning capability, the challenging task of logical reasoning is proposed.…
Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…
This paper studies structure detection problems in high temperature ferromagnetic (positive interaction only) Ising models. The goal is to distinguish whether the underlying graph is empty, i.e., the model consists of independent Rademacher…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
Polygons are compound geometric objects, but when trying to understand the expected behavior of a large collection of random polygons -- or even to formalize what a random polygon is -- it is convenient to interpret each polygon as a point…
We study configurations of $n$ points and $n$ lines that form $\Theta(n^{4/3})$ incidences, when the point set is a Cartesian product. We prove structural properties of such configurations, such that there exist many families of parallel…
Learning in Riemannian orbifolds is motivated by existing machine learning algorithms that directly operate on finite combinatorial structures such as point patterns, trees, and graphs. These methods, however, lack statistical…
Coalgebras for analytic functors uniformly model graph-like systems where the successors of a state may admit certain symmetries. Examples of successor structure include ordered tuples, cyclic lists and multisets. Motivated by goals in…
This talk is a sneak preview of the project, 'proof theory for theories of ordinals'. Background, aims, survey and furture works on the project are given. Subsystems of second order arithmetic are embedded in recursively large ordinals and…
Convex polyhedra are the basis for several abstractions used in static analysis and computer-aided verification of complex and sometimes mission critical systems. For such applications, the identification of an appropriate…
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…