David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
This essay is structured around the bifurcation between proofs and models: The first section discusses Proof Theory of relevant and substructural logics, and the second covers the Model Theory of these logics. This order is a natural one for a history of relevant and substructural logics, because much of the initial work — especially in the Anderson–Belnap tradition of relevant logics — started by developing proof theory. The model theory of relevant logic came some time later. As we will see, Dunn’s algebraic models [76, 77] Urquhart’s operational semantics [267, 268] and Routley and Meyer’s relational semantics [239, 240, 241] arrived decades after the initial burst of activity from Alan Anderson and Nuel Belnap. The same goes for work on the Lambek calculus: although inspired by a very particular application in linguistic typing, it was developed first proof-theoretically, and only later did model theory come to the fore. Girard’s linear logic is a different story: it was discovered though considerations of the categorical models of coherence..
|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
Sato Kentaro (2008). Proper Semantics for Substructural Logics, From a Stalker Theoretic Point of View. Studia Logica 88 (2):295 - 324.
Lionel Shapiro (2015). Naive Structure, Contraction and Paradox. Topoi 34 (1):75-87.
Ivor Grattan-Guinness (2008). Levels of Criticism: Handling Popperian Problems in a Popperian Way. [REVIEW] Axiomathes 18 (1):37-48.
Similar books and articles
Kosta Došen (1992). Modal Translations in Substructural Logics. Journal of Philosophical Logic 21 (3):283 - 336.
Greg Restall (forthcoming). Substructural Logics. Stanford Encyclopedia of Philosophy.
Greg Restall (1930). Models for Substructural Arithmetics. Australasian Journal of Philosophy 8:82-99.
Lou Goble (2007). Combinatory Logic and the Semantics of Substructural Logics. Studia Logica 85 (2):171 - 197.
Norihiro Kamide (2002). Kripke Semantics for Modal Substructural Logics. Journal of Logic, Language and Information 11 (4):453-470.
Greg Restall (1994). Subintuitionistic Logics. Notre Dame Journal of Formal Logic 35 (1):116-129.
Ken-etsu Fujita (1998). On Proof Terms and Embeddings of Classical Substructural Logics. Studia Logica 61 (2):199-221.
Robert Goldblatt & Michael Kane (2010). An Admissible Semantics for Propositionally Quantified Relevant Logics. Journal of Philosophical Logic 39 (1):73 - 100.
Greg Restall (1998). Displaying and Deciding Substructural Logics 1: Logics with Contraposition. Journal of Philosophical Logic 27 (2):179-216.
Added to index2009-01-28
Total downloads59 ( #57,882 of 1,726,249 )
Recent downloads (6 months)9 ( #74,830 of 1,726,249 )
How can I increase my downloads?