Mathematica--A System for Doing Mathematics by Computer.

Lecture Notes in Economics and Mathematical Systems

Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.

Remarks on the Foundations of Mathematics. By L. Wittgenstein. Edited by G. H. Von Wright, R. Rhees and G. E. M. Anscombe. Translated by G. E. M. Anscombe. Pp. 400. 37s. 6d. 1956. (Basil Blackwell, Oxford)

Multiagent Systems is the title of a collection of papers dedicated to surveying specific themes of Multiagent Systems (MAS) and Distributed Artificial Intelligence (DAI). All of them authored by leading researchers of this dynamic multidisciplinary field.

/pdf/multiagent-systems-a-modern-approach-to-distributed-5fon0donq1.pdf

Multiagent systems: a modern approach to distributed artificial intelligence

Dependent type theories have a long history of being used for theorem proving One aspect of type theory which makes it very powerful as a proof language is that it mixes deduction with computation This also makes type theory a good candidate for programming---the strength of the type system allows properties of programs to be stated and established, and the computational properties provide semantics for the programs

This thesis is concerned with bridging the gap between the theoretical presentations of type theory and the requirements on a practical programming language Although there are many challenging research problems left to solve before we have an industrial scale programming language based on type theory, this thesis takes us a good step along the way

/pdf/towards-a-practical-programming-language-based-on-dependent-3lmfc1es25.pdf

Towards a practical programming language based on dependent type theory

Syntax for Variable Binders: An Overview . . . . . . . . . . . . . . . . . . . . 239 Dale Miller Goal-Directed Proof Search in Multiple-Conclusioned Intuitionistic Logic . . 254 James Harland, Tatjana Lutovac, and Michael Winikoff Efficient EM Learning with Tabulation for Parameterized Logic Programs . 269 Yoshitaka Kameya and Taisuke Sato Model Generation Theorem Proving with Finite Interval Constraints . . . . . 285 Reiner Hähnle, Ryuzo Hasegawa, and Yasuyuki Shirai Combining Mobile Processes and Declarative Programming . . . . . . . . . . . . . 300 Rachid Echahed and Wendelin Serwe

Computational Logic — CL 2000

Ωmega is a mixed-initiative system with the ultimate purpose of supporting theorem proving in main-stream mathematics and mathematics education. The current system consists of a proof planner and an integrated collection of tools for formulating problems, proving subproblems, and proof presentation.

/pdf/omega-towards-a-mathematical-assistant-1euugzqchq.pdf

Omega: Towards a Mathematical Assistant

Despite two decades of work learning classifier systems researchers have had relatively little to say on the subject of what makes a problem difficult for a classifier system. Wilson's accuracy-based XCS, a promising and increasingly popular classifier system, is, we feel, the natural first choice of classifier system with which to address this issue. To make the task more tractable we limit our considerations to a restricted, but very important, class of problems. Most significantly, we consider only single step reinforcement learning problems and the use of the standard binary/ternary classifier systems language. In addition to distinguishing several dimensions of problem complexity for XCS, we consider their interactions, identify bounding cases of difficulty, and consider complexity metrics for XCS. Based on these results we suggest a simple template for ternary single step test suites to more comprehensively evaluate classifier systems.

What Makes a Problem Hard for XCS

Mechanized reasoning systems and computer algebra systems have different objectives. Their integration is highly desirable, since formal proofs often involve both of the two different tasks proving and calculating. Even more important, proof and computation are often interwoven and not easily separable.

In this article we advocate an integration of computer algebra into mechanized reasoning systems at the proof plan level. This approach allows us to view the computer algebra algorithms as methods, that is, declarative representations of the problem-solving knowledge specific to a certain mathematical domain. Automation can be achieved in many cases by searching for a hierarchic proof plan at the method level by using suitable domain-specific control knowledge about the mathematical algorithms. In other words, the uniform framework of proof planning allows us to solve a large class of problems that are not automatically solvable by separate systems.

Our approach also gives an answer to the correctness problems inherent in such an integration. We advocate an approach where the computer algebra system produces high-level protocol information that can be processed by an interface to derive proof plans. Such a proof plan in turn can be expanded to proofs at different levels of abstraction, so the approach is well suited for producing a high-level verbalized explication as well as for a low-level, machine-checkable, calculus-level proof.

We present an implementation of our ideas and exemplify them using an automatically solved example.

Changes in the criterion of ‘rigor of the proof’ engender major revolutions in mathematics. H. Poincare, 1905

Integrating Computer Algebra into Proof Planning

ΩMEGA is a mixed-initiative system with the ultimate purpose of supporting theorem proving in main-stream mathematics and mathematics education. The current system consists of a proof planner and an integrated collection of tools for formulating problems, proving subproblems, and proof presentation.

ΩMEGA : Towards a mathematical assistant

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