Computability Theory
نویسندگان
چکیده
0. INTRODUCTION. Computability is perhaps the most significant and distinctive notion modern logic has introduced; in the guise of decidability and effective calculability it has a venerable history within philosophy and mathematics. Now it is also the basic theoretical concept for computer science, artificial intelligence and cognitive science. This essay discusses, at its heart, methodological issues that are central to any mathematical theory that is to reflect parts of our physical or intellectual experience. The discussion is grounded in historical developments that are deeply intertwined with meta-mathematical work in the foundations of mathematics. How is that possible, the reader might ask, when the essay is concerned solely with computability? This introduction begins to give an answer by first describing the context of foundational investigations in logic and mathematics and then sketching the main lines of the systematic presentation.
منابع مشابه
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.
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