Algebraic Structures of Mathematical Foundations

On the Mathematical Foundations of Syntactic Structures

Chomsky’s highly influential Syntactic Structures (SS) has been much praised its originality, explicitness, and relevance for subsequent cognitive science. Such claims are greatly overstated. SS contains no proof that English is beyond the power of finite state description (it is not clear that Chomsky ever gave a sound mathematical argument for that claim). The approach advocated by SS springs...

The Mathematical Foundations of Bond Graphs-I. Algebraic Theory

Elementary mathematical concepts from linear algebra are used to develop an independent theory for non-directed bond graphs. The dejinition of a bond graph is given and its structure as a combinatorial object is studied. This is accomplished by constructing a vector space, called the bond space of the bond graph. Topological information is encoded in the bond graph by dejining a subspace of the...

Foundations of Algebraic Logic

Newly formulated foundations of algebraic logic will be presented. Although it aims at applications to mathematical psychology, results within this paper is universal and so is expected to be applied to other branches as well.

Mathematical Foundations of Photogrammetry

Photogrammetry uses photographic cameras to obtain information about the 3D world. The basic principle of photogrammetric measurement is straightforward: recording a light ray in a photographic image corresponds to observing a direction from the camera to the 3D scene point where the light was reflected or emitted. From this relation, procedures have been derived to orient cameras relative to e...

Mathematical Foundations of Supersymmetry