Introduction to computability logic

Introduction to Computability Theory

These are notes for a short introductory course on Computability Theory (or recursive function theory). The basic notion of computability is defined in terms of a simple imperative programming language.

An Introduction to Computability Theory

This paper will give an introduction to the fundamentals of computability theory. Based on Robert Soare’s textbook, The Art of Turing Computability: Theory and Applications, we examine concepts including the Halting problem, properties of Turing jumps and degrees, and Post’s Theorem. In the paper, we will assume the reader has a conceptual understanding of computer programs.

Computability and Logic

Intuitionistic computability logic I

Computability logic (CL) is a systematic formal theory of computational tasks and resources, which, in a sense, can be seen as a semantics-based alternative to (the syntactically introduced) linear logic. With its expressive and flexible language, where formulas represent computational problems and “truth” is understood as algorithmic solvability, CL potentially offers a comprehensive logical b...

From formulas to cirquents in computability logic

Computability logic (CoL) is a recently introduced semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Its expressions represent interactive computational tasks seen as games played by a machine against the environment, and “truth” is understood as existence of an a...