David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Notre Dame Journal of Formal Logic 40 (3):352-374 (1999)
In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalise to partial and paraconsistent logics once the right set-up is chosen. Our logic L4 has a semantics that also underlies Belnap’s  and is related to the logic of bilattices. L4 is in focus most of the time, but it is also shown how results obtained for L4 can be transferred to several variants.
|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
Jørgen Villadsen (2005). Supra-Logic: Using Transfinite Type Theory with Type Variables for Paraconsistency. Journal of Applied Non-Classical Logics 15 (1):45-58.
Similar books and articles
Newton C. A. da Costa & Décio Krause, Remarks on the Applications of Paraconsistent Logic to Physics.
Marcelo E. Coniglio & Newton M. Peron (2009). A Paraconsistentist Approach to Chisholm's Paradox. Principia 13 (3):299-326.
O. Arieli, A. Avron & A. Zamansky (2011). Ideal Paraconsistent Logics. Studia Logica 99 (1-3):31-60.
Gemma Robles & José M. Méndez (2010). Paraconsistent Logics Included in Lewis’ S4. Review of Symbolic Logic 3 (03):442-466.
Sergei P. Odintsov (2005). The Class of Extensions of Nelson's Paraconsistent Logic. Studia Logica 80 (2-3):291 - 320.
Greg Restall (2002). Paraconsistency Everywhere. Notre Dame Journal of Formal Logic 43 (3):147-156.
Dominic Hyde & Mark Colyvan (2008). Paraconsistent Vagueness: Why Not? Australasian Journal of Logic 6:107-121.
Juliana Bueno-Soler (2010). Two Semantical Approaches to Paraconsistent Modalities. Logica Universalis 4 (1):137-160.
Bryson Brown (1999). Yes, Virginia, There Really Are Paraconsistent Logics. Journal of Philosophical Logic 28 (5):489-500.
Added to index2009-01-28
Total downloads21 ( #88,188 of 1,139,993 )
Recent downloads (6 months)1 ( #157,514 of 1,139,993 )
How can I increase my downloads?