Computability and physical theories

Computability and Physical Theories

The familiar theories o f physics have the feature that the application o f the theory to make predictions in specific circumstances can be done by means o f an algorithm. We propose a more precise formulation of this feature--one based on the issue of whether or not the physically measurable numbers predicted by the theory are computable in the mathematical sense. Applying this formulation to ...

Computability As A Test On Linguistics Theories

Scientific theories are more than purely formal constructs, but linguistic artefacts that often rely on the rhetorical qualities of language to give their claims additional resonance and argumentative force. This reliance of theory upon language is even greater in those theoretical domains whose main concern is language itself, leading to a sometimes convenient blurring of content and form. Tho...

Towards applied theories based on computability logic

Computability logic (CL) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in it represent computational problems, “truth” means existence of an algorithmic solution, and proofs encode such solutions. Within the line of research devoted to finding axiomatizations fo...

Developing Theories of Types and Computability Thesis Proposal

Developing Theories of Types and Computability via Realizability

We investigate the development of theories of types and computability via realizability. In the rst part of the thesis, we suggest a general notion of realizability, based on weakly closed partial cartesian categories, which generalizes the usual notion of realizability over a partial combinatory algebra. We show how to construct categories of so-called assemblies and modest sets over any weakl...