Related papers: On variable non-dependence of first-order formulas

Dependence is an important concept for many tasks in artificial intelligence. A task can be executed more efficiently by discarding something independent from the task. In this paper, we propose two novel notions of dependence in…

The concept of "stochastic precedence" between two real-valued random variables has often emerged in different applied frameworks. In this paper we consider a slightly more general, and completely natural, concept of stochastic precedence…

If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which…

For ordinary differential equations in the complex domain, a central problem is to understand, in a given equation or class of equations, those whose solutions do not present multivaluedness. We consider autonomous, first-order, quadratic…

We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the…

Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a…

We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…

In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…

A theory is NIP (resp. stable) if and only if every formula with parameters in two single variables is NIP (resp. does not have the order property).

In this note, we give a linear-size translation from formulas of first-order logic into equations of the calculus of relations preserving validity and finite validity. Our translation also gives a linear-size conservative reduction from…

Non-deductive reasoning systems are often {\em representation dependent}: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed this as a significant problem. For…

In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on…

The Contextuality-by-Default approach to determining and measuring the (non)contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables.…

We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.

Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with…

First Order Team Semantics is a generalization of Tarskian Semantics in which formulas are satisfied with respect to sets of assignments. In Team Semantics, it is possible to extend First Order Logic via new types of atoms that describe…

We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…

A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…

A policy describes the conditions under which an action is permitted or forbidden. We show that a fragment of (multi-sorted) first-order logic can be used to represent and reason about policies. Because we use first-order logic, policies…

Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper,…