相关论文: 0-1 laws

We consider the evaluation of first-order queries over classes of databases with bounded expansion. The notion of bounded expansion is fairly broad and generalizes bounded degree, bounded treewidth and exclusion of at least one minor. It…

We show that a first order problem can approximate solutions of a robust optimization problem when the uncertainty set is scaled, and explore further properties of this first order problem.

The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…

The Univalent Foundations requires a logic that allows us to define structures on homotopy types, similar to how first-order logic with equality ($\text{FOL}_=$) allows us to define structures on sets. We develop the syntax, semantics and…

A regular language has the zero-one law if its asymptotic density converges to either zero or one. We prove that the class of all zero-one languages is closed under Boolean operations and quotients. Moreover, we prove that a regular…

The Riccati equation method is used for study the behavior of solutions of the systems of two linear first order ordinary differential equations. All types of oscillation and regularity of these system are revealed. A generalization of…

We introduce the concept of a class of graphs, or more generally, relational structures, being locally tree-decomposable. There are numerous examples of locally tree-decomposable classes, among them the class of planar graphs and all…

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…

We extend the convergence law for sparse random graphs proven by Lynch to arbitrary relational languages. We consider a finite relational vocabulary $\sigma$ and a first order theory $T$ for $\sigma$ composed of symmetry and…

This paper introduces a new type of covering process that covers the set of natural numbers using renewal processes as objects. Inspired by the behavior of prime numbers, the model in each step finds the smallest vacant point, $k$, and…

In previous work we defined and studied a notion of typicality, originated with B. Russell, for properties and objects in the context of general infinite first-order structures. In this paper we consider this notion in the context of finite…

Prime numbers appeared in contexts spanning statistical mechanics, quantum mechanics and dynamical systems. However, the mechanisms governing the irregularities observed in their sequence and linking them to physical systems remained…

First-order Goedel logics are a family of infinite-valued logics where the sets of truth values V are closed subsets of [0, 1] containing both 0 and 1. Different such sets V in general determine different Goedel logics G_V (sets of those…

If F(x) = e^G(x), where F(x) = \sum f(n)x^n and $G(x) = \sum g(n)x^n, with 0 \le g(n) = O(n^{theta n}/n!),theta in (0,1), and gcd(n : g(n) > 0)=1, then f(n) = o(f(n-1)). This gives an answer to Compton's request in Question 8.3 for an…

We present a first-order probabilistic epistemic logic, which allows combining operators of knowledge and probability within a group of possibly infinitely many agents. The proposed framework is the first order extension of the logic of…

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…

This work develops a framework to discover relations between the components of the solution to a given initial-value problem for a first-order system of ordinary differential equations. This is done by using sparse identification techniques…

The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions…

We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…

A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…