David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 63 (3):831-859 (1998)
We show that the elimination rule for the multiplicative (or intensional) conjunction $\wedge$ is admissible in many important multiplicative substructural logics. These include LL m (the multiplicative fragment of Linear Logic) and RMI m (the system obtained from LL m by adding the contraction axiom and its converse, the mingle axiom.) An exception is R m (the intensional fragment of the relevance logic R, which is LL m together with the contraction axiom). Let SLL m and SR m be, respectively, the systems which are obtained from LL m and R m by adding this rule as a new rule of inference. The set of theorems of SR m is a proper extension of that of R m , but a proper subset of the set of theorems of RMI m . Hence it still has the variable-sharing property. SR m has also the interesting property that classical logic has a strong translation into it. We next introduce general algebraic structures, called strong multiplicative structures, and prove strong soundness and completeness of SLL m relative to them. We show that in the framework of these structures, the addition of the weakening axiom to SLL m corresponds to the condition that there will be exactly one designated element, while the addition of the contraction axiom corresponds to the condition that there will be exactly one nondesignated element (in the first case we get the system BCK m , in the second - the system SR m ). Various other systems in which multiplicative conjunction functions as a true conjunction are studied, together with their algebraic counterparts
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Arnon Avron (2014). What is Relevance Logic? Annals of Pure and Applied Logic 165 (1):26-48.
Similar books and articles
Wolfgang Spohn & Matthias Hild (2008). The Measurement of Ranks and the Laws of Iterated Contraction. Artificial Intelligence 172:1195-1218.
Andreja Prijatelj (1995). Connectification Forn-Contraction. Studia Logica 54 (2):149 - 171.
Yves Lafont (1996). The Undecidability of Second Order Linear Logic Without Exponentials. Journal of Symbolic Logic 61 (2):541-548.
Romà J. Adillon & Ventura Verdú (2000). On a Contraction-Less Intuitionistic Propositional Logic with Conjunction and Fusion. Studia Logica 65 (1):11-30.
Eiji Kiriyama & Hlroakira Ono (1991). The Contraction Rule and Decision Problems for Logics Without Structural Rules. Studia Logica 50 (2):299 - 319.
Mitsuhiro Okada & Kazushige Terui (1999). The Finite Model Property for Various Fragments of Intuitionistic Linear Logic. Journal of Symbolic Logic 64 (2):790-802.
Peter W. O'Hearn & David J. Pym (1999). The Logic of Bunched Implications. Bulletin of Symbolic Logic 5 (2):215-244.
Andreja Prijatelj (1996). Bounded Contraction and Gentzen-Style Formulation of Łukasiewicz Logics. Studia Logica 57 (2-3):437 - 456.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads1 ( #437,916 of 1,100,838 )
Recent downloads (6 months)1 ( #289,727 of 1,100,838 )
How can I increase my downloads?