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

Beyond Mixed Logics
  • Home
  • /
  • Beyond Mixed Logics
  1. Home /
  2. Archives /
  3. Vol. 31 No. 4 (2022): December /
  4. Articles

Beyond Mixed Logics

Authors

  • Joaquín Toranzo Calderón IIF-SADAF--Consejo Nacional de Investigaciones Científicas y Técnicas, Department of Philosophy, Universidad de Buenos Aires https://orcid.org/0000-0003-1297-0912
  • Federico Pailos IIF-SADAF--Consejo Nacional de Investigaciones Científicas y Técnicas, Department of Philosophy, Universidad de Buenos Aires https://orcid.org/0000-0001-9991-2760

DOI:

https://doi.org/10.12775/LLP.2022.014

Keywords

many-valued logics, mixed consequence relations, mapping matrix, multiple conclusions interpretations

Abstract

In order to define some interesting consequence relations, certain generalizations have been proposed in a many-valued semantic setting that have been useful for defining what have been called pure, mixed and ordertheoretic consequence relations. But these generalizations are insufficient to capture some other interesting relations, like other intersective mixed relations (a relation that cannot be defined as a mixed relation, but only as the intersection of two mixed relations) or relations with a conjunctive (or, better, “universal”) interpretation for multiple conclusions. We propose a broader framework to define these cases, and many others, and to set a common background that allows for a direct compared analysis. At the end of the work, we illustrate some of these comparisons

References

Barrio, E., and F. Pailos, “Validities, antivalidities and contingencies: a multi-standard approach”, Journal of Philosophical Logic 51 (2022): 75–98. DOI: http://dx.doi.org/10.1007/s10992-021-09610-y

Bochvar, D. A., “On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus”, History and Philosophy of Logic 2, 1–2 (1981): 87–112. English translation of Bochvar’s paper of 1938. DOI: http://dx.doi.org/10.1080/01445348108837023

Chemla, E., P. Egré, and B. Spector, “Characterizing logical consequence in many-valued logics”, Journal of Logic and Computation 27, 7 (2017): 2193–2226. DOI: http://dx.doi.org/10.1093/logcom/exx001

Chemla, E., and P. Egré, “From many-valued consequence to many-valued connectives”, Synthese 198 (2021): 5315–5352. DOI: http://dx.doi.org/10.1007/s11229-019-02344-0

Cintula, P., and F. Paoli, “Is multiset consequence trivial?”, Synthese 199 (2021): 741–765. DOI: http://dx.doi.org/10.1007/s11229-016-1209-7

Cobreros, P., P. Egré, D. Ripley, and R. van Rooij, “Reaching transparent truth”, Mind 122, 488 (2013): 841–866. https://www.jstor.org/stable/24489584

Cobreros, P., P. Egré, D. Ripley, and R. van Rooij, “Vagueness, truth and permissive consequence”, pages 409–430 in T. Achourioti, H. Galinon, J. Martínez Fernández, and K. Fujimoto (eds.), Unifying the Philosophy of Truth. Logic, Epistemology, and the Unity of Science, Springer, Dordrecht, 2015.

Copilowish, I. M., “Matrix Development of the Calculus of Relations”, The Journal of Symbolic Logic 13, 4 (1948): 193–203. DOI: http://dx.doi.org/10.2307/2267134

Frankowski, S., “Formalization of a plausible inference”, Bulletin of the Section of Logic 33, 1 (2004): 41–52. DOI: http://dx.doi.org/10.2307/2267134

French, R., “Structural reflexivity and the paradoxes of self-reference”, Ergo 3, 5 (2016): 113–131. DOI: http://dx.doi.org/10.3998/ergo.12405314.0003.005

Halldén, S., The Logic of Nonsense, Ph.D. Tesis, Uppsala Universitets Arsskrift, Uppsala, 1949.

Kleene, S., Introduction to Metamathematics, North-Holland, Amsterdam, 1952.

Kripke, S., “Outline of a theory of truth”, Journal of Philosophy 72, 19 (1975): 690–716. DOI: http://dx.doi.org/10.1007/s11229-019-02344-0

Malinowski, G., “Q-consequence operation”, Reports on Mathematical Logic 24, 1 (1990): 49–59.

Pailos, F., “Disjoint logics”, Logic and Logical Philosophy 30, 1 (2021): 109–137. DOI: http://dx.doi.org/10.12775/LLP.2020.014

Pailos, F., “Empty logics”, Journal of Philosophical Logic (2021). DOI: http://dx.doi.org/10.1007/s10992-021-09622-8

Priest, G., “The logic of paradox”, Journal of Philosophical Logic 8 (1979): 219–241. DOI: http://dx.doi.org/10.1007/BF00258428

Ripley, D., “Conservatively extending classical logic with transparent truth”, Review of Symbolic Logic 5, 2 (2012): 354–378. DOI: http://dx.doi.org/10.1017/S1755020312000056

Ripley, D., “A toolkit for metainferential logics”, Manuscript.

Roffé, A. and J. Toranzo Calderón, “mapped_logics”, in A. Roffé, logics, version 1.0.1, 2021. URL: github.com/ariroffe/logics (last time consulted: 2022-03-25)

Scambler, C., “Classical Logic and the strict tolerant hierarchy”, Journal of Philosophical Logic 49 (2020): 351–3870. DOI: http://dx.doi.org/10.1007/s10992-019-09520-0

Sharvit, Y., “A note on (Strawson) entailment”, Semantics and Pragmatics 10, 1 (2017): 1–38. DOI: http://dx.doi.org/10.3765/sp.10.1

Szmuc, D., “Defining LFIs and LFUs in extensions of infectious logics”, Journal of Applied Non-Classical Logics 26, 4 (2017): 286–314. DOI: http://dx.doi.org/10.1080/11663081.2017.1290488

Tarski, A., “On some fundamental concepts of metamathematics”, pages 30–37 in J. Corcoran (ed.), Logic, Semantics Metamathematics, Indianapolis: Hackett Publishing Company, 1983 (1930).

Logic and Logical Philosophy

Downloads

  • PDF

Published

2022-04-11

How to Cite

1.
TORANZO CALDERÓN, Joaquín & PAILOS, Federico. Beyond Mixed Logics. Logic and Logical Philosophy [online]. 11 April 2022, T. 31, nr 4, s. 637–664. [accessed 24.3.2023]. DOI 10.12775/LLP.2022.014.
  • PN-ISO 690 (Polish)
  • ACM
  • ACS
  • APA
  • ABNT
  • Chicago
  • Harvard
  • IEEE
  • MLA
  • Turabian
  • Vancouver
Download Citation
  • Endnote/Zotero/Mendeley (RIS)
  • BibTeX

Issue

Vol. 31 No. 4 (2022): December

Section

Articles

License

Copyright (c) 2022 Joaquín Toranzo Calderón, Federico Pailos

Creative Commons License

This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

Stats

Number of views and downloads: 1053
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:

many-valued logics, mixed consequence relations, mapping matrix, multiple conclusions interpretations
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