CONTENTS

234 MIHAIELA LUPEA (1)
For reducing Π12 we apply the rule (S3). No extension of the initial theory satisfies
the constraint L¬T , so the default sequent Π12 is reduced to a basic anti-sequent and
therefore is a true sequent according to the following:
Q,R,T,H,¬P ⇒¬T
Π12:{M(P ∧S),L¬T };({Q,R},{d3= R:¬P
H
,d4= H:T
T });{ Q
S } ↦−→T (S3)
Π2 can also be reduced to basic sequent/anti-sequents, therefore the initial sequent:
∅; ({Q, R} , {d1, d2, d3, d4}); ∅ ↦−→ T is true and thus T is a skeptical constrained
default consequence of ∆.
5. Conclusions
In this paper we have introduced an axiomatic system which formalizes the skeptical
nonmonotonic inference in constrained default logic. This system is based on
sequent and anti-sequent calculi for classical logics and uses specific rules for the
defaults. Using the monotonic rules called residues and constraints for the applied
defaults, the default reasoning process becomes a monotonic one.
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(1) Babes¸-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-
Napoca, Romania
E-mail address: lupea@cs.ubbcluj.ro