A first order nonmonotonic extension of constructive logic

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)
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 23,217
External links
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
David Nelson (1949). Constructible Falsity. Journal of Symbolic Logic 14 (1):16-26.

View all 12 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

17 ( #267,544 of 1,932,454 )

Recent downloads (6 months)

2 ( #332,988 of 1,932,454 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.