|
This article is cited in 22 scientific papers (total in 22 papers)
Predicate and set-theoretic calculi based on logic without contractions
V. N. Grishin
Abstract:
In this paper the author studies the effect of eliminating the contraction rules from the Gentzen predicate calculus, and also from set-theoretic systems based on this calculus. It turns out that the predicate calculus without contraction rules is complete relative to finite models, and eliminating contraction rules from set-theoretic systems does not change the number of derivable formulas as long as the systems contain certain natural axioms.
Bibliography: 4 titles.
 Full text:
PDF file (2001 kB)
References:
PDF file
HTML file
English version:
Mathematics of the USSR-Izvestiya, 1982, 18:1, 41–59
Bibliographic databases:
 
UDC:
51.01.16
MSC: Primary 03B20; Secondary 03G25
Received: 14.05.1980
Citation:
V. N. Grishin, “Predicate and set-theoretic calculi based on logic without contractions”, Izv. Akad. Nauk SSSR Ser. Mat., 45:1 (1981), 47–68; Math. USSR-Izv., 18:1 (1982), 41–59
Citation in format AMSBIB
\Bibitem{Gri81}
\by V.~N.~Grishin
\paper Predicate and set-theoretic calculi based on logic without contractions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 1
\pages 47--68
\mathnet{http://mi.mathnet.ru/izv1547}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=607576}
\zmath{https://zbmath.org/?q=an:0478.03009|0464.03027}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 18
\issue 1
\pages 41--59
\crossref{https://doi.org/10.1070/IM1982v018n01ABEH001382}
Linking options:
http://mi.mathnet.ru/eng/izv1547 http://mi.mathnet.ru/eng/izv/v45/i1/p47
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
Andrzej Wroński, “Remarks on a survey article on many valued logic by A. Urquhart”, Stud Logica, 46:3 (1987), 275
-
Jean-Yves Girard, “Light Linear Logic”, Information and Computation, 143:2 (1998), 175
-
V. N. Grishin, “On the weight of the comprehension axiom in a theory based on logic without contractions”, Math. Notes, 66:5 (1999), 533–540
   -
Francesco Paoli, “★-autonomous Lattices”, Stud Logica, 79:2 (2005), 283
-
Shunsuke Yatabe, Hiroyuki Inaoka, “On Evans's Vague Object from Set Theoretic Viewpoint”, J Philos Logic, 35:4 (2006), 423
-
Joan Gispert, Antoni Torrens, “Bounded BCK-algebras and their generated variety”, MLQ - Math Log Quart, 53:2 (2007), 206
-
Joan Gispert, Antoni Torrens, “Boolean representation of bounded BCK-algebras”, Soft Comput, 12:10 (2008), 941
-
Kai Brünnler, Dieter Probst, Thomas Studer, “On contraction and the modal fragment”, MLQ - Math Log Quart, 54:4 (2008), 345
-
Richard McKinley, “Soft Linear Set Theory”, Journal of Logic and Algebraic Programming, 76:2 (2008), 226
-
Antoni Torrens, “Semisimplicity and the discriminator in bounded BCK-algebras”, Algebra univers, 2010
-
Diego Castaño, José Patricio Díaz Varela, Antoni Torrens, “Indecomposability of free algebras in some subvarieties of residuated lattices and their bounded subreducts”, Soft Comput, 2010
-
Patrick Baillot, Damiano Mazza, “Linear logic by levels and bounded time complexity”, Theoretical Computer Science, 411:2 (2010), 470
-
Andrew Bacon, “Non-classical Metatheory for Non-classical Logics”, J Philos Logic, 2012
-
Edwin Mares, Francesco Paoli, “Logical Consequence and the Paradoxes”, J Philos Logic, 2013
-
S. Yatabe, “On the crispness of and arithmetic with a bisimulation in a constructive naive set theory”, Logic Journal of IGPL, 2013
-
Andrew Bacon, “Paradoxes of Logical Equivalence and Identity”, Topoi, 2013
-
MAJID ALIZADEH, FARZANEH DERAKHSHAN, HIROAKIRA ONO, “UNIFORM INTERPOLATION IN SUBSTRUCTURAL LOGICS”, The Review of Symbolic Logic, 2014, 1
-
L. Tranchini, “Proof-theoretic semantics, paradoxes and the distinction between sense and denotation”, Journal of Logic and Computation, 2014
-
ROHAN FRENCH, DAVID RIPLEY, “CONTRACTIONS OF NONCONTRACTIVE CONSEQUENCE RELATIONS”, The Review of Symbolic Logic, 2014, 1
-
DAVID RIPLEY, “NAIVE SET THEORY AND NONTRANSITIVE LOGIC”, The Review of Symbolic Logic, 2015, 1
-
David Ripley, “Contraction and closure”, Thought: A Journal of Philosophy, 4:2 (2015), 131
-
T.F.jetland Øgaard, “Paths to Triviality”, J Philos Logic, 2015
|
| Number of views: |
| This page: | 759 | | Full text: | 174 | | References: | 62 | | First page: | 4 |
|
Terms of Use