224
Mathematical Aspects of Logic Programming Semantics
Wide Web Consortium
7 for this purpose. One of them, called RIF,
8 is essentially a logic programming language, and other ontology languages can also
be understood as logic programming variants.
9
In the light of such recent developments, theoretical investigations into
logic programming, as provided in this book, gain further interest. It can be
conjectured that the methods developed in this book may be used for design
and analysis of new KR languages suitable for application purposes.
Conceptually interesting from this point of view is the observation that
the methods of analysis provided herein are close to a denotational semantics approach and thus complement the historically model-theory-driven semantics in KR languages. In particular, there may be scope for the study
of decidability and/or semi-decidability of KR languages based on the levelmappings approach discussed in Chapter 2,
10 a topic which has so far been
largely neglected for logic programming, although it has played a major role in
the development of the currently main ontology language, the Web Ontology
Language OWL.
11
8.5 Clarifying Logic Programming Semantics
In this book, we have covered the most important semantics for normal
logic programs. However, many more different semantics for normal logic programs and generalizations of this paradigm have been defined in the literature.
The rationale behind these various semantics has been manifold, depending
on one’s point of view, which may be that of a programmer or inspired by
commonsense reasoning. Consequently, the constructions which lead to these
semantics are technically very diverse, and the exact relationships between
them have not yet been fully understood.
Our work, and in particular the treatment in Chapter 2, but also Section 5.2, provides a uniform perspective of different logic programming semantics, and it should be clear from the proofs that the approach adopted there
can be lifted to other fixed-point semantics, in particular to those involving
monotonic operators. It thus reconciles these semantics within an overarching
framework which can be used for easy comparison of semantics with respect
to syntactic structures that can be employed with them, that is, to determine the extent to which a semantics is able to break up positive or negative
dependencies or loops between atoms in programs.
7 W3C, http://www.w3.org/
8 See [Boley and Kifer, 2010, Hitzler et al., 2009b].
9 OWL RL [Hitzler et al., 2009a, Reynolds, 2010], ELP [Kr¨ otzsch et al., 2008], or F-Logic
[Kifer et al., 1995], for example.
10 For a preliminary investigation into this, see [Cherchago et al., 2007].
11 See [Hitzler et al., 2009a, Hitzler et al., 2009b].
Mathematical Aspects of Logic Programming Semantics
Wide Web Consortium
7 for this purpose. One of them, called RIF,
8 is essentially a logic programming language, and other ontology languages can also
be understood as logic programming variants.
9
In the light of such recent developments, theoretical investigations into
logic programming, as provided in this book, gain further interest. It can be
conjectured that the methods developed in this book may be used for design
and analysis of new KR languages suitable for application purposes.
Conceptually interesting from this point of view is the observation that
the methods of analysis provided herein are close to a denotational semantics approach and thus complement the historically model-theory-driven semantics in KR languages. In particular, there may be scope for the study
of decidability and/or semi-decidability of KR languages based on the levelmappings approach discussed in Chapter 2,
10 a topic which has so far been
largely neglected for logic programming, although it has played a major role in
the development of the currently main ontology language, the Web Ontology
Language OWL.
11
8.5 Clarifying Logic Programming Semantics
In this book, we have covered the most important semantics for normal
logic programs. However, many more different semantics for normal logic programs and generalizations of this paradigm have been defined in the literature.
The rationale behind these various semantics has been manifold, depending
on one’s point of view, which may be that of a programmer or inspired by
commonsense reasoning. Consequently, the constructions which lead to these
semantics are technically very diverse, and the exact relationships between
them have not yet been fully understood.
Our work, and in particular the treatment in Chapter 2, but also Section 5.2, provides a uniform perspective of different logic programming semantics, and it should be clear from the proofs that the approach adopted there
can be lifted to other fixed-point semantics, in particular to those involving
monotonic operators. It thus reconciles these semantics within an overarching
framework which can be used for easy comparison of semantics with respect
to syntactic structures that can be employed with them, that is, to determine the extent to which a semantics is able to break up positive or negative
dependencies or loops between atoms in programs.
7 W3C, http://www.w3.org/
8 See [Boley and Kifer, 2010, Hitzler et al., 2009b].
9 OWL RL [Hitzler et al., 2009a, Reynolds, 2010], ELP [Kr¨ otzsch et al., 2008], or F-Logic
[Kifer et al., 1995], for example.
10 For a preliminary investigation into this, see [Cherchago et al., 2007].
11 See [Hitzler et al., 2009a, Hitzler et al., 2009b].