Ptarithmetic

The present article introduces ptarithmetic (short for “polynomial time arithmetic”) — a formal number theory similar to the well known Peano arithmetic, but based on the recently born computability logic instead of classical logic. The formulas of ptarithmetic represent interactive computational problems rather than just true/false statements, and their “truth” is understood as existence of a polynomial time solution. The system of ptarithmetic elaborated in this article is shown to be sound and complete. Sound in the sense that every theorem T of the system represents an interactive number-theoretic computational problem with a polynomial time solution and, furthermore, such a solution can be effectively extracted from a proof of T . And complete in the sense that every interactive number-theoretic problem with a polynomial time solution is represented by some theorem T of the system. The paper is self-contained, and can be read without any prior familiarity with computability logic

Ptarithmetic

The present article introduces ptarithmetic (short for "polynomial time arithmetic") -- a formal number theory similar to the well known Peano arithmetic, but based on the recently born computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html) instead of classical logic. The formulas of ptarithmetic represent interactive computational problems rather than just true/false statements, and their "truth" is understood as existence of a polynomial time solution. The system of ptarithmetic elaborated in this article is shown to be sound and complete. Sound in the sense that every theorem T of the system represents an interactive number-theoretic computational problem with a polynomial time solution and, furthermore, such a solution can be effectively extracted from a proof of T. And complete in the sense that every interactive number-theoretic problem with a polynomial time solution is represented by some theorem T of the system. The paper is self-contained, and can be read without any previous familiarity with computability logic.Comment: Substantially better versions are on their way. Hence the present article probably will not be publishe

Extracting expertise from experts: Methods for knowledge acquisition

Knowledge acquisition is the biggest bottleneck in the development of expert systems. Fortunately, the process of translating expert knowledge to a form suitable for expert system development can benefit from methods developed by cognitive science to reveal human knowledge structures. There are two classes of these investigative methods, direct and indirect. We provide reviews, criteria for use, and literature sources for all principal methods. Direct methods discussed are: interviews, questionnaires, observation of task performance, protocol analysis, interruption analysis, closed curves, and inferential flow analysis. Indirect methods include: multidimensional scaling, hierarchical clustering, general weighted networks, ordered trees, and repertory grid analysis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73498/1/j.1468-0394.1987.tb00139.x.pd