Databases Reference
In-Depth Information
Another ASP extension suitable for preference handling has been presented in [84].
There, standard ASP has been enriched by introducing consistency-restoring rules (cr-
rules) and preferences, leading to the CR-Prolog language. Basically, in this language,
besides standard ASP rules one may specify CR-rules, that are expressions of the form:
r
:
a
1
∨
1). The intuitive meaning of CR-rule
r
is: if
body
is true then one of
a
1
,...,a
n
is “possibly” believed to be true. Importantly, the name
of CR-prolog rules can be directly exploited to specify preferences among them. In
particular, if the fact
prefer
(
r
1
,r
2
) is added to a CR-program, then rule
r
1
is preferred
over rule
r
2
. This allows one to encode partial orderings among preferred answer sets
by explicitly writing preferences among CR-rules.
...
∨
a
n
←
+
body
(
n
≥
Other Extensions.
ASP has been extended in other directions in order to meet require-
ments of different application domains, hence there is a number of interesting languages
having the roots on ASP. For instance, ASP has been exploited for defining and im-
plementing
action languages
(i.e., languages conceived for dealing with actions and
change)
[86]; while, in [87] a framework for
abduction with penaliza-
tion
has been proposed and implemented as a front-end for the ASP system DLV. A
logic language called
ID-Logic
[88] has been introduced to deal with classical logic
with inductive definitions (which correspond semantically to logic rules). Other ASP
extensions have been conceived to deal with
Ontologies
(i.e., abstract models of a com-
plex domain). In particular, in [89] an ASP-based language for ontology specification
and reasoning has been proposed, which extends ASP in order to deal with complex
real-world entities, like classes, objects, compound objects, axioms, and taxonomies.
In [90] an open world semantics for ASP programs has been proposed. Moreover, in
[91] an extension of ASP, called
HEX-Programs
, which supports higher-order atoms
as well as external atoms has been proposed. External atoms allows for embedding
external sources of computation in a logic program. Thus, HEX-programs are useful
for various tasks, including meta-reasoning, data type manipulations, and reasoning on
top of Description Logic (DL) [92] ontologies.
Template predicates
have been intro-
duced in [93]. Template predicates are special intensional predicates defined by means
of generic reusable subprograms, which have been conceived for easing coding and im-
proving readability and compactness of programs. Finally, nested programs, allowing
for nested logical expressions to occur in rules have also been studied [94,95].
K
[85], and
E
4
Knowledge Representation and Reasoning in ASP
ASP has been used in several domains, ranging from artificial intelligence over tradi-
tional databases to semantic web applications. ASP can be used to encode problems
in a declarative fashion; indeed, the power of disjunctive rules allows for expressing
problems which are more complex than NP, and the (optional) separation of a fixed,
non-ground program from an input database allows one to obtain uniform solutions
over varying instances.
More in detail, many problems of comparatively high computational complexity can
be solved in a natural manner by following a “Guess&Check” programming method-
ology, originally introduced in [96] and refined in [42]. The idea behind this method
