David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
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
Lionel Shapiro (2015). Naive Structure, Contraction and Paradox. Topoi 34 (1):75-87.
Sato Kentaro (2008). Proper Semantics for Substructural Logics, From a Stalker Theoretic Point of View. Studia Logica 88 (2):295 - 324.
Sato Kentaro (2008). Proper Semantics for Substructural Logics, From a Stalker Theoretic Point of View. Studia Logica 88 (2):295-324.
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.
Robert Goldblatt & Michael Kane (2010). An Admissible Semantics for Propositionally Quantified Relevant Logics. Journal of Philosophical Logic 39 (1):73 - 100.
Ken-etsu Fujita (1998). On Proof Terms and Embeddings of Classical Substructural Logics. Studia Logica 61 (2):199-221.
Greg Restall (1994). Subintuitionistic Logics. Notre Dame Journal of Formal Logic 35 (1):116-129.
Norihiro Kamide (2002). Kripke Semantics for Modal Substructural Logics. Journal of Logic, Language and Information 11 (4):453-470.
Lou Goble (2007). Combinatory Logic and the Semantics of Substructural Logics. Studia Logica 85 (2):171 - 197.
Greg Restall (1930). Models for Substructural Arithmetics. Australasian Journal of Philosophy 8:82-99.
Greg Restall (forthcoming). Substructural Logics. Stanford Encyclopedia of Philosophy.
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 downloads65 ( #67,599 of 1,911,418 )
Recent downloads (6 months)2 ( #319,111 of 1,911,418 )
How can I increase my downloads?