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Model Finding for Exploration

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Protocols, Strands, and Logic

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13066))

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Abstract

We survey recent results in model finding, focusing on the notion of a model finding assistant to help users, even users not trained in logic, understand their software artifacts. The technical results discussed have all been previously published; the presentation here highlights two themes: (i) geometric logic and homomorphism orders as natural foundations for model finding, and (ii) an implemetation dichotomy between direct model finding and model finding with the aid of SAT- and SMT-solvers. We give generic high-level algorithms for the central problems of programming against such solvers; lower-level details are determined based on the category of homomorphisms being used.

This work was partially supported by the U.S. National Science Foundation

Dedicated to Joshua Guttman, with appreciation for his insights and with gratitude for his friendship.

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Notes

  1. 1.

    A technical philosophical term Joshua has been known to employ ....

  2. 2.

    Confusingly, some authors use “geometric” to refer to what is more broadly called “positive existential”. For them a “geometric theory” is a collection of quantified implications between “geometric formulas” (thus the axioms themselves are not “geometric formulas”).

  3. 3.

    Completeness of this algorithm does not require that the models \(\mathbb {{M}}\) we work with are minimal. But if we do work with minimal models there will be fewer iterations.

  4. 4.

    somewhat confusingly, names are called “bounds” in the Alloy community.

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Note and Acknowledgements

This paper surveys some recent work—foundational and applied—by a variety of authors in model finding. All of it has been previously published. My purpose in gathering this material into one place is to point out the shared foundations for a number of different model finders and to identify some differences in their aspirations and in their functionalities.

As the technical content of this paper draws so heavily on previous work with coauthors, my feeling of gratitude to my colleagues is stronger than usual. I want to particularly thank Natasha Danas, Joshua Guttman, Kathi Fisler, Shriram Krishnamurthi, Timothy Nelson, John Ramsdell, and Salman Saghafi for their insights and contributions.

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  1. Worcester Polytechnic Institute, Worcester, USA

    Daniel J. Dougherty

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Editors and Affiliations

  1. Department of Computer Science, Worcester Polytechnic Institute, Worcester, MA, USA

    Daniel Dougherty

  2. Th.M. Siebel Center for Computer Science, University of Illinois Urbana-Champaign, Urbana, IL, USA

    José Meseguer

  3. Institute of Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark

    Sebastian Alexander Mödersheim

  4. J83K, The MITRE Corporation, Bedford, MA, USA

    Paul Rowe

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Dougherty, D.J. (2021). Model Finding for Exploration. In: Dougherty, D., Meseguer, J., Mödersheim, S.A., Rowe, P. (eds) Protocols, Strands, and Logic. Lecture Notes in Computer Science(), vol 13066. Springer, Cham. https://doi.org/10.1007/978-3-030-91631-2_9

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