Reflection using the derivability conditions

Numerical Investigation of Birefringene Effect on the Light Reflection

In the present paper, the problem of light reflection from a birefringent medium and thin film is considered. First, the analytical equations governing the propagation of a plane and harmonic electromagnetic wave in an infinite, birefringent, linear, non-dispersive, non-absorbing, and non-magnetic medium is derived from Maxwell equations. Then, using phase matching condition and boundary condit...

Encoding Atomic Categories: Rendering It Strictly Directed

This paper solves the directed counterpart of a problem addressed in Language in Action (Van Benthem 1991: 108–9). There it is observed that LP derivability in an atomic goal category can be mimicked by LP derivability using one atomic category only. The abbreviation LP refers to the non-directed Lambek calculus with Permutation, a system which has also become known as the Lambek-Van Benthem ca...

Statistical theory of logical derivability

A generalization of notions like "theory" in the sense of mathematical logic, "Markov (normal) algorithm" etc., is described; the new notion is called "formal system". The generalization of notions "validity", and also of notion "provability" of formulas is the notion "derivability". Derivability is studied using statistical methods, analogous to the methods used in the statistical theory of de...

Redundancies in the Hilbert-Bernays Derivability Conditions for Gödel's Second Incompleteness Theorem

A Graph-Theoretic Approach to Sequent Derivability in the Lambek Calculus

A graph-theoretic construction for representing the derivational side-conditions in the construction of axiomatic linkages for Lambek proof nets is presented, along with a naive algorithm that applies it to the sequent derivability problem for the Lambek Calculus. Some basic properties of this construction are also presented, and some complexity issues related to parsing with Lambek Categorial ...