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

Logical problems with nonmonotonicity
  • Home
  • /
  • Logical problems with nonmonotonicity
  1. Home /
  2. Archives /
  3. Vol. 23 No. 2 (2014): June /
  4. Articles

Logical problems with nonmonotonicity

Authors

  • Piotr Łukowski University of Łodź,

DOI:

https://doi.org/10.12775/LLP.2014.004

Keywords

monotonic inference, nonmonotonic inference, Makinsonès nonmonotonic constructions, enthymeme, background assumptions, admissible valuations, nonstructural superclassical logic

Abstract

A few years ago, believing that human thinking is nonmonotonic, I tried to reconstruct a nonmonotonic reasoning by application of two monotonic procedures. I called them “step forward” and “step backward” (see [4]). The first procedure is just a consequence operation responsible for an extension of the set of beliefs. The second one, defined on the base of the logic of falsehood reconstructed for the given logic of truthfulness, is responsible for a reduction of the set of beliefs. Both procedures taken together were successfully verified by using so-called AGM (see [5]), postulates for expansion, contraction and revision formulated by Alchourrón, Gärdenfors and Makinson (e.g. [1]). Reasoning composed of the mutual application of both procedures seemed to be quite natural for modeling our thinking. At that time, I supposed that it should be nonmonotonic but I was wrong. It turned out impossible to satisfy a definition of the nonmonotonic inference by reasoning composed both steps. To understand why this is impossible, I began to analyze how nonmonotonicity is obtainable in some well-known cases in the literature. I analyzed the problem from two points of view: (1) non-formal examples for nonmonotonicity and (2) formal constructions of nonmonotonic operations/relations. The result of those investigations was astonishing: none of the considered by me cases of nonmonotonicity belonging to point (1) and almost none belonging to (2) satisfies the definition of nonmonotonic inference. Arguments against the nonmonotonic character of well-known examples for nonmonotonicity of human thinking are more precisely presented in [6]. I present them below an abbreviated version of them.

Author Biography

Piotr Łukowski, University of Łodź,

Department of Cognitive Science, Institute of Psychology

References

Alchourron, C., P. Gärdenfors and D. Makinson, “On the logic of theory change: contraction functions and their associated revision functions”, Theoria, 48 (1985): 4–37. DOI: 10.1111/j.1755-2567.1982.tb00480.x

Gabbay, Dov M., C.J. Hogger and J.A. Robinson, Handbook of Logic in Artificial Intelligence and Logic Programming, Volume 3, Clarendon Press, Oxford, 1994.

Ginsberg, Matthew L., “AI and nonmonotonic reasoning”, pages 1–33 in [2].

Łukowski, Piotr, “A formalisation of the “step forward — step backward” reasoning”, Anales del Seminario de Historia de la Filosofia, 18 (2001): 109–124.

Łukowski, Piotr, “The procedures for belief revision”, pages 249–268 in Towards Mathematical Philosophy, Trends in Logic 28, Springer, 2009.

Łukowski, Piotr, “Is human reasoning really nonmonotonic?”, Logic and Logical Philosophy, 22 (2013): 63–73. DOI: 10.12775/LLP.2013.004

Poole, David, “Default logic”, pages 189–215 in [2].

Makinson, David, “General patterns in nonmonotonic reasoning”, pages 35–110 in [2].

Makinson, David, Bridgges from Classical to Nonmonotonic Logic, Text In Computing, Vol. 5, published by King’s College, 2005.

Shoham, Y., Reasoning About Change, MIT Press, Cambridge, USA 1988.

Logic and Logical Philosophy

Downloads

  • PDF

Published

2014-02-07

How to Cite

1.
ŁUKOWSKI, Piotr. Logical problems with nonmonotonicity. Logic and Logical Philosophy. Online. 7 February 2014. Vol. 23, no. 2, pp. 171-188. [Accessed 4 July 2025]. DOI 10.12775/LLP.2014.004.
  • ISO 690
  • ACM
  • ACS
  • APA
  • ABNT
  • Chicago
  • Harvard
  • IEEE
  • MLA
  • Turabian
  • Vancouver
Download Citation
  • Endnote/Zotero/Mendeley (RIS)
  • BibTeX

Issue

Vol. 23 No. 2 (2014): June

Section

Articles

Stats

Number of views and downloads: 483
Number of citations: 0

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

Subscribe Unsubscribe

Language

  • English
  • Język Polski

Tags

Search using one of provided tags:

monotonic inference, nonmonotonic inference, Makinsonès nonmonotonic constructions, enthymeme, background assumptions, admissible valuations, nonstructural superclassical logic
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
  • Instytut Tomistyczny
  • Karmelitański Instytut Duchowości w Krakowie
  • Ministerstwo Kultury i Dziedzictwa Narodowego
  • Państwowa Akademia Nauk Stosowanych w Krośnie
  • Państwowa Akademia Nauk Stosowanych we Włocławku
  • Państwowa Wyższa Szkoła Zawodowa im. Stanisława Pigonia w Krośnie
  • Polska Fundacja Przemysłu Kosmicznego
  • Polskie Towarzystwo Ekonomiczne
  • Polskie Towarzystwo Ludoznawcze
  • Towarzystwo Miłośników Torunia
  • Towarzystwo Naukowe w Toruniu
  • Uniwersytet im. Adama Mickiewicza w Poznaniu
  • Uniwersytet Komisji Edukacji Narodowej w Krakowie
  • 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