David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 80 (2-3):321 - 346 (2005)
Certain extensions of Nelson's constructive logic N with strong negation have recently become important in arti.cial intelligence and nonmonotonic reasoning, since they yield a logical foundation for answer set programming (ASP). In this paper we look at some extensions of Nelson's .rst-order logic as a basis for de.ning nonmonotonic inference relations that underlie the answer set programming semantics. The extensions we consider are those based on 2-element, here-and-there Kripke frames. In particular, we prove completeness for .rst-order here-and-there logics, and their minimal strong negation extensions, for both constant and varying domains. We choose the constant domain version, which we denote by QNc5, as a basis for de.ning a .rst-order nonmonotonic extension called equilibrium logic. We establish several metatheoretic properties of QNc5, including Skolem forms and Herbrand theorems and Interpolation, and show that the .rst-oder version of equilibrium logic can be used as a foundation for answer set inference.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
|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
No citations found.
Similar books and articles
Riccardo Rosati (1999). Reasoning About Minimal Knowledge in Nonmonotonic Modal Logics. Journal of Logic, Language and Information 8 (2):187-203.
Marcus Kracht (1998). On Extensions of Intermediate Logics by Strong Negation. Journal of Philosophical Logic 27 (1):49-73.
Matthew Spinks & Robert Veroff (2008). Constructive Logic with Strong Negation is a Substructural Logic. I. Studia Logica 88 (3):325 - 348.
Charles B. Cross (2003). Nonmonotonic Inconsistency. Artificial Intelligence 149 (2):161-178.
Agustín Arrieta (1995). Comentarios Sobre la Relación Entre la Programación Logica Y Las Lógicas No Monótonas. Theoria 10 (3):181-198.
Aleksander Peczenik (1996). Jumps and Logic in the Law. Artificial Intelligence and Law 4 (3-4):297-329.
Henry E. Kyburg (2001). Real Logic is Nonmonotonic. Minds and Machines 11 (4):577-595.
Henry E. Kyburg Jr (2001). Real Logic is Nonmonotonic. Minds and Machines 11 (4):577-595.
Dimiter Vakarelov (2005). Nelson's Negation on the Base of Weaker Versions of Intuitionistic Negation. Studia Logica 80 (2-3):393 - 430.
Added to index2009-01-28
Total downloads7 ( #213,451 of 1,679,345 )
Recent downloads (6 months)1 ( #183,761 of 1,679,345 )
How can I increase my downloads?