相关论文: Logic Blog 2016

The recent success of Bayesian methods in neuroscience and artificial intelligence gives rise to the hypothesis that the brain is a Bayesian machine. Since logic and learning are both practices of the human brain, it leads to another…

We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found…

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…

Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the semantics given the real unit interval [0,1]. In a recent…

This two-parts paper offers a survey of linear logic and ludics, which were introduced by Girard in 1986 and 2001, respectively. Both theories revisit mathematical logic from first principles, with inspiration from and applications to…

The study of pinnacle sets has been a recent area of interest in combinatorics. Given a permutation, its pinnacle set is the set of all values larger than the values on either side of it. Largely inspired by conjectures posed by Davis,…

We verify a formula on the solution rank of the tautological system arising from ample complete intersections in a projective homogeneous space of a semisimple group conjectured by Huang--Lian--Yau--Yu arXiv:1801.01194. As an application,…

The concept of metastable convergence was identified by Tao;it allows converting theorems about convergence into stronger theorems about uniform convergence. The Uniform Metastability Principle (UMP) states that if $T$ is a theorem about…

Large language models (LLMs) have a substantial capacity for high-level analogical reasoning: reproducing patterns in linear text that occur in their training data (zero-shot evaluation) or in the provided context (few-shot in-context…

A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…

These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…

The aim of this paper is to generalize and improve two of the main model-theoretic results of "Stable group theory and approximate subgroups" by E. Hrushovski to the context of piecewise hyperdefinable sets. The first one is the existence…

We show that for every non-elementary hyperbolic group, an associated topological flow space admits a coding based on a transitive subshift of finite type. Applications include regularity results for Manhattan curves, the uniqueness of…

We prove a representation stability result for the second homology groups of Torelli subgroups of mapping class groups and automorphism groups of free groups. This strengthens the results of Boldsen-Hauge Dollerup and Day-Putman. We also…

To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…

The program Reverse Mathematics in the foundations of mathematics seeks to identify the minimal axioms required to prove theorems of ordinary mathematics. One always assumes the base theory, a logical system embodying computable…

In 1878, Jordan proved that if a finite group $G$ has a faithful representation of dimension $n$ over $\mathbb{C}$, then $G$ has a normal abelian subgroup with index bounded above by a function of $n$. The same result fails if one replaces…

The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing…

This paper is a study of first-order coherent logic from the point of view of duality and categorical logic. We prove a duality theorem between coherent hyperdoctrines and open polyadic Priestley spaces, which we subsequently apply to prove…

We construct a universal phantom subcategory on the blow-up of the complex projective plane in 11 general points. This phantom subcategory is the orthogonal complement of a non-full exceptional collection of line bundles of maximal length.…