Comonotonic latent variables are introduced into general factor models, in order to allow non-linear transformations of latent factors, so that various multivariate dependence structures can be captured. Through decomposing each univariate marginal into several components, and letting some components belong to different sets of comonotonic latent variables, a great variety of multivariate model...

The paper discusses the use of latent variables in psychology and social science research. Local independence, expected value true scores, and nondeterministic functions of observed variables are three types of definitions for latent variables. These definitions are reviewed and an alternative "sample realizations" definition is presented. Another section briefly describes identification, laten...

This paper addresses the problem of how to represent free variables and subexpressions involving-bindings. The aim is to apply what is known as higher-order abstract syntax to higher-order term rewriting systems. Directly applying-reduction for the purpose of subterm-replacement is incompatible with the requirements of term-rewriting. A new meta-level representation of subterms is developed tha...

In this paper, we introduce a new fragment of the first-order temporal language, called the monodic fragment, in which all formulas beginning with a temporal operator (Since or Until) have at most one free variable. We show that the satisfiability problem for monodic formulas in various linear time structures can be reduced to the satisfiability problem for a certain fragment of classical first...

Van Lambalgen (1990) proposed a translation from a language containing a generalized quantifier Q into a first-order language enriched with a family of predicates Rs, for every arity i (or an infinitary predicate R) which takes Qz~(z, yl, . . . , y,~) to Vz(R(z, yl,..., g,~) --" ~b(x, Yl,..., Y,~)) (gl . . . . . g~ are precisely the free variables of Qzq~). The logic of Q (without ordinary quan...

Term-generic logic (TGL) is a first-order logic parameterized with terms defined axiomatically (rather than constructively), by requiring them to only provide generic notions of free variable and substitution satisfying reasonable properties. TGL has a complete Gentzen system generalizing that of first-order logic. A certain fragment of TGL, called Horn, possesses a much simpler Gentzen system,...

Suppose we observe samples of a subset of a collection of random variables. No additional information is provided about the number of latent variables, nor of the relationship between the latent and observed variables. Is it possible to discover the number of latent components, and to learn a statistical model over the entire collection of variables? We address this question in the setting in w...

The standard first-order reading of modality does not bind individual variables, i.e., if x is free in F (x), then x remains free in 2F (x). Accordingly, if 2 stands for ‘provable in arithmetic,’ ∀x2F (x) states that F (n) is provable for any given value of n = 0, 1, 2, . . .; this corresponds to a de re reading of modality. The other, de dicto meaning of 2F (x), suggesting that F (x) is deriva...

This paper introduces a nested sequent system for predicate logic. The system features a structural universal quantifier and a universally closed existential rule. One nice consequence of this is that proofs of sentences cannot contain free variables. Another nice consequence is that the assumption of a non-empty domain is isolated in a single inference rule. This rule can be removed or added a...