Critical Agents Supporting Interactive Theorem Proving

We introduce a resource adaptive agent mechanism which supports the user of an interactive theorem proving system. The mechanism, an extension of [5], uses a two layered architecture of agent societies to suggest applicable commands together with appropriate command argument instantiations. Experiments with this approach show that its effectiveness can be further improved by introducing a resource concept. In this paper we provide an abstract view on the overall mechanism, motivate the necessity of an appropriate resource concept and discuss its realization within the agent architecture.

[1]  Jörg Denzinger,et al.  Knowledge-based Cooperation between Theorem Provers by Techs , 1999 .

[2]  Alan Bundy,et al.  The Use of Explicit Plans to Guide Inductive Proofs , 1988, CADE.

[3]  Christoph G. Jung Experimenting with Layered, Resource-Adapting Agents in the RoboCup Simulation , 1999 .

[4]  Christoph Benzmüller,et al.  System Description: LEO - A Higher-Order Theorem Prover , 1998, CADE.

[5]  Christoph Lüth,et al.  International Workshop on User Interfaces for Theorem Provers , 2005 .

[6]  Michael J. C. Gordon,et al.  Edinburgh LCF: A mechanised logic of computation , 1979 .

[7]  H. Simon,et al.  Models of Bounded Rationality: Empirically Grounded Economic Reason , 1997 .

[8]  W. Bibel,et al.  Automated deduction : a basis for applications , 1998 .

[9]  J. Denzinger,et al.  Cooperating Theorem Provers , 1998 .

[10]  Volker Sorge,et al.  ΩMEGA : Towards a mathematical assistant , 1997 .

[11]  Volker Sorge,et al.  Omega: Towards a Mathematical Assistant , 1997, CADE.

[12]  Volker Sorge,et al.  A Distributed Graphical User Interface for the Interactive Proof System , 1998 .

[13]  G. Gentzen Untersuchungen über das logische Schließen. I , 1935 .

[14]  Michael Fisher An alternative approach to concurrent theorem-proving , 1997, Parallel Processing for Artificial Intelligence 3.

[15]  Christoph G. Jung Layered and Resource-Adapting Agents in the RoboCup Simulation , 1998, RoboCup.

[16]  Shlomo Zilberstein,et al.  Models of Bounded Rationality , 1995 .

[17]  Volker Sorge,et al.  A Blackboard Architecture for Guiding Interactive Proofs , 1998, AIMSA.

[18]  G. Gentzen Untersuchungen über das logische Schließen. II , 1935 .

[19]  M. Gordon,et al.  Introduction to HOL: a theorem proving environment for higher order logic , 1993 .

[20]  Michael Fisher,et al.  An Open Approach to Concurrent Theorem-Proving , 1995 .

[21]  Volker Sorge,et al.  Towards Fine-Grained Proof Planning with Critical Agents , 1999 .

[22]  Christian Gerber,et al.  Resource Management for Boundedly Optimal Agent Societies , 1998 .

[23]  Peter B. Andrews An introduction to mathematical logic and type theory - to truth through proof , 1986, Computer science and applied mathematics.

[24]  Robin Milner,et al.  Edinburgh lcf: a mechanized logic of computation , 1978 .