A First Order Nonmonotonic Extension of Constructive Logic

Studia Logica 80 (2-3):321-346 (2005)

Abstract
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
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DOI 10.1007/s11225-005-8473-8
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References found in this work BETA

Constructible Falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
On Extensions of Intermediate Logics by Strong Negation.Marcus Kracht - 1998 - Journal of Philosophical Logic 27 (1):49-73.
A Semantical Study of Constructible Falsity.Richmond H. Thomason - 1969 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 15 (16-18):247-257.
Intuitionistic Logic with Strong Negation.Yuri Gurevich - 1977 - Studia Logica 36 (1-2):49 - 59.

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