CP-logic is a probabilistic extension of the logic FO(ID). Unlike ASP, both
of these logics adhere to a Tarskian informal semantics, in which
interpretations represent objective states-of-affairs. In other words, these
logics lack the epistemic component of ASP, in which interpretations represent
the beliefs or knowledge of a rational agent. Consequently, neither CP-logic
nor FO(ID) have the need for two kinds of negations: there is only one
negation, and its meaning is that of objective falsehood. Nevertheless, the
formal semantics of this objective negation is mathematically more similar to
ASP's negation-as-failure than to its classical negation. The reason is that
both CP-logic and FO(ID) have a constructive semantics in which all atoms start
out as false, and may only become true as the result of a rule application.
This paper investigates the possibility of adding the well-known ASP feature of
allowing negation in the head of rules to CP-logic. Because CP-logic only has
one kind of negation, it is of necessity this ''negation-as-failure like''
negation that will be allowed in the head. We investigate the intuitive meaning
of such a construct and the benefits that arise from it.

本文研究了将 ASP 特征引入到 CP-logic 中的可能性，提出了一种允许在规则头部进行否定的构造，并探讨其直观含义和带来的好处。

CP-logic 规则头部的否定

Negation in the Head of CP-logic Rules

In this paper, we present two alternative approaches to defining answer sets
for logic programs with arbitrary types of abstract constraint atoms (c-atoms).
These approaches generalize the fixpoint-based and the level mapping based
answer set semantics of normal logic programs to the case of logic programs
with arbitrary types of c-atoms. The results are four different answer set
definitions which are equivalent when applied to normal logic programs. The
standard fixpoint-based semantics of logic programs is generalized in two
directions, called answer set by reduct and answer set by complement. These
definitions, which differ from each other in the treatment of
negation-as-failure (naf) atoms, make use of an immediate consequence operator
to perform answer set checking, whose definition relies on the notion of
conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The other
two definitions, called strongly and weakly well-supported models, are
generalizations of the notion of well-supported models of normal logic programs
to the case of programs with c-atoms. As for the case of fixpoint-based
semantics, the difference between these two definitions is rooted in the
treatment of naf atoms. We prove that answer sets by reduct (resp. by
complement) are equivalent to weakly (resp. strongly) well-supported models of
a program, thus generalizing the theorem on the correspondence between stable
models and well-supported models of a normal logic program to the class of
programs with c-atoms. We show that the newly defined semantics coincide with
previously introduced semantics for logic programs with monotone c-atoms, and
they extend the original answer set semantics of normal logic programs. We also
study some properties of answer sets of programs with c-atoms, and relate our
definitions to several semantics for logic programs with aggregates presented
in the literature.

本文提出了两种方法来定义任意类型抽像限制原子（c-atoms）的逻辑程序的答案集，这些定义泛化了正常逻辑程序的修正点和级别映射基础的答案集语义，其中包括四种不同的答案集定义，这四种在应用于正常逻辑程序时是相等的。