CONTENTS

KNOWLEDGE ENGINEERING: PRINCIPLES AND TECHNIQUES
Proceedings of the International Conference on Knowledge Engineering,
Principles and Techniques, KEPT2009
Cluj-Napoca (Romania), July 2–4, 2009, pp. 231–234
SKEPTICAL REASONING IN CONSTRAINED DEFAULT LOGIC
USING SEQUENT CALCULUS
MIHAIELA LUPEA (1)
Abstract. Constrained default logic is a version of Reiter’s classical default logic
satisfying desirable formal properties as supraclassicality, semi-monotonicity, commitment
to assumptions. In this paper we propose an axiomatic system called
skeptical constrained default sequent calculus, based on sequent and anti-sequent
calculi from classical logics. This system is used to formalize and study from
theoretical point of view the skeptical nonmonotonic reasoning process modelled
by constrained default logic.
1. Introduction
Constrained default logic [7], as a version of Reiter’s default logic [6], models the
nonmonotonic reasoning using special inference rules called defaults, to overcome the
lack of information.
The defaults extend a given set of facts obtaining one or more sets called extensions
which contain the nonmonotonic consequences(beliefs). The extensions represent
possible belief sets of an agent reasoning about the initial theory. A credulous
reasoning perspective means that an agents’ beliefs belong to at least one extension.
Skeptical consequences are more robust beliefs because they belong to all extensions of
a theory. In the papers [2, 8] the properties of the nonmonotonic credulous/skeptical
inference relations in default logics are studied.
Theoretical studies in the direction of the axiomatization of the credulous/ skeptical
nonmonotonic inference process modelled by different versions of default logic
are presented in the papers [1, 3, 5].
In this paper we propose an axiomatic system called skeptical constrained default
sequent calculus. This system is used to formalize and study the skeptical nonmonotonic
inference modelled by constrained default logic.
2. Constrained default logic
Definition 2.1. A default theory ∆ = (D, W ) contains a set W of consistent
formulas (facts) of first order logic and a set D of default rules. A default has the
2000 Mathematics Subject Classification. 03B79, 68T15, 68T27, 68T20.
Key words and phrases. constrained default logic, skeptical default inference, sequent and antisequent
calculi.
231
c○2009 Babe¸s-Bolyai University, Cluj-Napoca