We study the necessary and sufficient conditions on Abelianizable first class constraints. The necessary condition is derived from topological considerations on the structure of gauge group. The sufficient condition is obtained by applying the theorem of implicit function in calculus. Since the sufficient conditions are related to the geometrical structure of the constraint surface and the exis...

We introduce a proper display calculus for (non-distributive) Lattice Logic which is sound, complete, conservative, and enjoys cut-elimination and subformula property. Properness (i.e. closure under uniform substitution of all parametric parts in rules) is the main interest and added value of the present proposal, and allows for the smoothest Belnap-style proof of cut-elimination. Our proposal ...

The result of forgetting some predicates in a first-order sentence may not exist in the sense that it might not be captured by any first-order sentences. This, indeed, severely restricts the usage of forgetting in applications. To address this issue, we propose a notion called k-forgetting, also called bounded forgetting in general, for any fixed number k. We present several equivalent characte...

These notes discuss formalizing contexts as first class objects. The basic relation is ist(c, p). It asserts that the proposition p is true in the context c. The most important formulas relate the propositions true in different contexts. Introducing contexts as formal objects will permit axiomatizations in limited contexts to be expanded to transcend the original limitations. This seems necessa...

We introduce generalized quantifiers, as defined in Tarskian semantics by Mostowski and Lindström, in logics using the Hodges semantics, e.g., IF-logic and dependence logic. For this we introduce the multivalued dependence atom and observe the similarities with the, by Väänänen and Grädel, newly introduced independence atom.

In this paper, we introduce EVE, a generic framework for event detection where events can also include outliers, model changes and drifts. Various methods for event detection have been proposed for different types of events. However, many of them make the same or very similar prior assumptions but use different notations and formalizations. EVE provides a general framework for event detection, ...

Let Ln be the first-order language for Nn. Thus, Ln contains the symbols =, 1, 2, . . . , n interpreted in Nn as the identity and the natural numbers 1, 2, . . . , n. By Fn we denote the set of all formulas of Ln. Hence, Fn is the smallest set such that: a. ti = tj ∈ Fn, b. if A,B ∈ Fn, then: ¬A, A → B, A∧B, A∨B, A ≡ B, ∨

We consider a method for extending instrumental variables methods in order to estimate the overall effect of a treatment or exposure. The approach is designed for settings in which the instrument influences both the treatment of interest and a secondary treatment also influenced by the primary treatment. We demonstrate that, while instrumental variables methods may be used to estimate the joint...