Skip to main content Skip to main navigation menu Skip to site footer
  • Register
  • Login
  • Language
    • English
    • Język Polski
  • Menu
  • Home
  • Current
  • Archives
  • Online First Articles
  • About
    • About the Journal
    • Submissions
    • Editorial Team
    • Advisory Board
    • Peer Review Process
    • Logic and Logical Philosophy Committee
    • Open Access Policy
    • Privacy Statement
    • Contact
  • Register
  • Login
  • Language:
  • English
  • Język Polski

Logic and Logical Philosophy

Simulation Logic
  • Home
  • /
  • Simulation Logic
  1. Home /
  2. Archives /
  3. Vol. 23 No. 3 (2014): September /
  4. Articles

Simulation Logic

Authors

  • Gerard Allwein Naval Research Laboratory, Washington
  • William L. Harrison University of Missouri, Columbia, Missouri
  • David Andrews University of Arkansas, Fayetteville, Arkansas

DOI:

https://doi.org/10.12775/LLP.2013.027

Keywords

modal logic, simulations, Hilbert systems, Kripke, modal algebras

Abstract

Simulation relations have been discovered in many areas: Computer Science, philosophical and modal logic, and set theory. However, the simulation condition is strictly a first-order logic statement. We extend modal logic with modalities and axioms, the latter’s modeling conditions are the simulation conditions. The modalities are normal, i.e., commute with either conjunctions or disjunctions and preserve either Truth or Falsity (respectively). The simulations are considered arrows in a category where the objects are descriptive, general frames. One can augment the simulation modalities by axioms for requiring the underlying modeling simulations to be bisimulations or to be p-morphisms. The modal systems presented are multi-sorted and both sound and complete with respect to their algebraic and Kripke semantics.

Author Biographies

William L. Harrison, University of Missouri, Columbia, Missouri

Dept. of Computer Science

David Andrews, University of Arkansas, Fayetteville, Arkansas

Dept. of Computer Science and Computer Engineering

References

Adamek, J., and J. Rosicky, Locally Presentable and Accessible Categories, London Mathematical Society, 1994. Lecture Note Series 189.

Gerard Allwein, G., and J.M. Dunn, “Kripke models for linear logic”, Journal of Symbolic Logic, 58 (1993): 514–545. DOI: 10.2307/2275217

Allwein, G., and W.L. Harrison, “Partially ordered modalities”, pages 1–20 in Proceedings of the Advances in Modal Logic Conference, 2010, Springer-Verlag, 2010.

Birkhoff, G., and J.D. Lipson, “Heterogeneous algebras”, Journal of Computational Theory, 8 (1968): 115–133. DOI: 10.1016/S0021-9800(70)80014-X

Blackburn, P., M. de Rijke, and Y. Venema, Modal Logic, Cambridge University Press, 2001. Cambridge Tracts in Theoretical Computer Science, No. 53.

Chellas, B.F., Modal Logic: An Introduction, Cambridge University Press, 1980.

Chou, Ching-Tsun, “A simple treatment of property preservation via simulation”, Technical Report, Department of Computer Science, University of California at Los Angeles, 1995.

Dummett, M.A.E., and E.J. Lemmon, “Modal logics between S4 and S5”, Zeitschrift für mathematische Logik and Grundlagen der Mathematik, 5 (1959): 250–264.

Dunn, J.M., “Gaggle theory: An abstraction of galois connections and residuation with applications to negation and various logical operations”, pages 31–51 in Logics in AI, Proceedings European Workshop JELIA, LNCS 478, Springer-Verlag, 1990.

Dunn, J.M., and G. Hardegree, Algebraic Methods in Philosophical Logic, Oxford Logic Guides 41. Oxford University Press, 2001.

Freyd, P.J., and A. Scedrov, Categories and Allegories, North-Holland, 1990.

Kupke, C., A. Kurz, and Y. Venema, “Stone coalgebras”, pages 170–190 in Coalgebraic Methods in Computer Science, Electronic Notes in Theoretical Computer Science, H.P. Gumm (ed.), volume 82 of 1, 2003.

Lemmon, E.J., “An Introduction to Modal Logic: The “Lemmon Notes””, American Philosophical Quarterly Monograph Series, 11, 1977.

Meyer, R.K., “New axiomatics for relevant logics. I”, Journal of Philosophical Logic, 3 (1974): 53–86. DOI: 10.1007/BF00652071

Sangiorgi, D., “On the origins of bisimulation and coinduction”, ACM Trans. Program. Lang. Syst., 31 (2009), 4:15:1–15:41. DOI: 10.1145/1516507.1516510

Sangiorgi, D.. Introduction to Bisimulation and Coinduction, Cambridge University Press, 2012.

Szor, P., The Art of Computer Virus Research and Defense, AddisonWesley Professional, 2005.

Wells, Ch., and M. Barr, “The formal description of data types using sketches”, pages 490–527 in LNCS 298, Mathematical Foundations of Programming Language Semantics, 1987.

Logic and Logical Philosophy

Downloads

  • PDF

Published

2013-09-15

How to Cite

1.
ALLWEIN, Gerard, HARRISON, William L. & ANDREWS, David. Simulation Logic. Logic and Logical Philosophy [online]. 15 September 2013, T. 23, nr 3, s. 277–299. [accessed 5.2.2023]. DOI 10.12775/LLP.2013.027.
  • PN-ISO 690 (Polish)
  • ACM
  • ACS
  • APA
  • ABNT
  • Chicago
  • Harvard
  • IEEE
  • MLA
  • Turabian
  • Vancouver
Download Citation
  • Endnote/Zotero/Mendeley (RIS)
  • BibTeX

Issue

Vol. 23 No. 3 (2014): September

Section

Articles

Stats

Number of views and downloads: 113
Number of citations: 2

Crossref
Scopus
Google Scholar
Europe PMC

Search

Search

Browse

  • Browse Author Index
  • Issue archive

User

User

Current Issue

  • Atom logo
  • RSS2 logo
  • RSS1 logo

Information

  • For Readers
  • For Authors
  • For Librarians

Newsletter

Newsletter
Unsubscribe

Language

  • English
  • Język Polski

Tags

Search using one of provided tags:

modal logic, simulations, Hilbert systems, Kripke, modal algebras
Up

Akademicka Platforma Czasopism

Najlepsze czasopisma naukowe i akademickie w jednym miejscu

apcz.umk.pl

Partners

  • Akademia Ignatianum w Krakowie
  • Akademickie Towarzystwo Andragogiczne
  • Fundacja Copernicus na rzecz Rozwoju Badań Naukowych
  • Instytut Historii im. Tadeusza Manteuffla Polskiej Akademii Nauk
  • Instytut Kultur Śródziemnomorskich i Orientalnych PAN
  • Karmelitański Instytut Duchowości w Krakowie
  • Państwowa Akademia Nauk Stosowanych w Krośnie
  • Państwowa Akademia Nauk Stosowanych we Włocławku
  • Państwowa Wyższa Szkoła Zawodowa im. Stanisława Pigonia w Krośnie
  • Polskie Towarzystwo Ekonomiczne
  • Polskie Towarzystwo Ludoznawcze
  • Towarzystwo Miłośników Torunia
  • Towarzystwo Naukowe w Toruniu
  • Uniwersytet im. Adama Mickiewicza w Poznaniu
  • Uniwersytet Mikołaja Kopernika
  • Uniwersytet w Białymstoku
  • Uniwersytet Warszawski
  • Wojewódzka Biblioteka Publiczna - Książnica Kopernikańska
  • Wyższe Seminarium Duchowne w Pelplinie / Wydawnictwo Diecezjalne „Bernardinum" w Pelplinie

© 2021- Nicolaus Copernicus University Accessibility statement Shop