On a fundamental theorem of mathematical logic

On a Fundamental Problem of Deontic Logic

The usual presentations of deontic logic, whether axiomatic or semantic, treat norms as if they could bear truth-values. A fundamental problem of deontic logic, we believe, is to reconstruct it in accord with the philosophical position that norms direct rather than describe, and are neither true nor false. (Alchourrón and Bulygin 1981) have indeed made such a construction, refining an earlier o...

A Fundamental Theorem of Stereo?

The complete set of measurements that could ever be used by a passive 3D vision algorithm is the plenoptic function or light-field. We give a concise characterization of when the light-field of a Lambertian scene uniquely determines its shape and, conversely, when the shape is inherently ambiguous. In particular, we show that stereo computed from the light-field is ambiguous if and only if the ...

On Conley's fundamental theorem of dynamical systems

To the memory of Charles C. Conley We generalize Conley's fundamental theorem of dynamical systems in Conley index theory. We also conclude the existence of a regular index filtration for every Morse decomposition. 1. Introduction. Conley is mostly known for his fundamental theorem of dynami-cal systems and his homotopy index theory [1]. In the former, he proved that every continuous flow on a ...

On the Fundamental Theorem of Algebra

Fundamental Theorem of Calculus

A simple but rigorous proof of the Fundamental Theorem of Calculus is given in geometric calculus, after the basis for this theory in geometric algebra has been explained. Various classical examples of this theorem, such as the Green’s and Stokes’ theorem are discussed, as well as the new theory of monogenic functions, which generalizes the concept of an analytic function of a complex variable ...