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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Marcelino, Sérgio and Caleiro, Carlos 2016. On the characterization of fibred logics, with applications to conservativity and finite-valuedness. Journal of Logic and Computation, p. exw023.


    Williamson, Timothy 2014. Logic, Metalogic and Neutrality. Erkenntnis, Vol. 79, Issue. S2, p. 211.


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JUXTAPOSITION: A NEW WAY TO COMBINE LOGICS

  • JOSHUA SCHECHTER (a1)
  • DOI: http://dx.doi.org/10.1017/S1755020311000219
  • Published online: 12 October 2011
Abstract

This paper develops a new framework for combining propositional logics, called “juxtaposition.” Several general metalogical theorems are proved concerning the combination of logics by juxtaposition. In particular, it is shown that under reasonable conditions, juxtaposition preserves strong soundness. Under reasonable conditions, the juxtaposition of two consequence relations is a conservative extension of each of them. A general strong completeness result is proved. The paper then examines the philosophically important case of the combination of classical and intuitionist logics. Particular attention is paid to the phenomenon of collapse. It is shown that there are logics with two stocks of classical or intuitionist connectives that do not collapse. Finally, the paper briefly investigates the question of which rules, when added to these logics, lead to collapse.

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*DEPARTMENT OF PHILOSOPHY, BROWN UNIVERSITY, BOX 1918, PROVIDENCE, RI 02912. E-mail: joshua_schechter@brown.edu
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C. Caleiro , W. Carnielli , J. Rasga , & C. Sernadas (2005). Fibring of logics as a universal construction. In Handbook of Philosophical Logic (second edition), Vol. 13. Dordrecht, The Netherlands: Springer, pp. 123187.

C. Caleiro , & J. Ramos (2007). From fibring to cryptofibring: A solution to the collapsing problem. Logica Universalis, 1, 7192.

W. Carnielli , M. Coniglio , D. M. Gabbay , P. Gouveia , & C. Sernadas (2008). Analysis and Synthesis of Logics: How to Cut and Paste Reasoning Systems. Dordrecht, The Netherlands: Springer.

M. Coniglio (2007). Recovering a logic from its fragments by meta-fibring. Logica Universalis, 1, 377416.

L. Cruz-Filipe , A. Sernadas , & C. Sernadas (2007). Heterogenous fibring of deductive systems via abstract proof systems. Logic Journal of the IGPL, 16, 121153.

J. Czelakowski (1981). Equivalential logics (I), (II). Studia Logica, 40, 227236; 355–372.

J. Czelakowski (2003). The Suszko operator I. Studia Logica, 74, 181231.

J. Czelakowski , & D. Pigozzi (2004). Fregean logics. Annals of Pure and Applied Logic, 127, 1776.

L. F. del Cerro , & A. Herzig (1996). Combining classical and intuitionistic logic, or: Intuitionistic implication as a conditional. In F. Baader , and K. Schultz , editors. Frontiers of Combining Systems. Dordrecht, The Netherlands: Kluwer Academic Publishers, pp. 93102.

G Gentzen . (1934/1935). Untersuchungen über das logische schließen. Mathematische Zeitschrift, 39, 176210; 405–431.

M. Hand (1993). Negations in conflict. Erkenntnis, 38, 115129.

J. H Harris . (1982). What’s so logical about the ‘logical axioms’? Studia Logica, 41, 159171.

V. McGee (1997). How we learn mathematical language. The Philosophical Review, 106(1), 3568.

H. Rasiowa (1974). An Algebraic Approach to Non-Classical Logics. Warsaw, Poland: Polish Scientific Publishers.

W. Rautenberg (1981). 2-element matrices. Studia Logica, 40, 315353.

A. Sernadas , C. Sernadas , & C. Caleiro (1999). Fibring of logics as a categorial construction. Journal of Logic and Computation, 9(2), 149179.

R. Wójcicki (1988). Theory of Logical Calculi: Basic Theory of Consequence Operations. Dordrecht, The Netherlands: Kluwer Academic Publishers.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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