590 research outputs found
Bayesian Logic Programs
Bayesian networks provide an elegant formalism for representing and reasoning
about uncertainty using probability theory. Theyare a probabilistic extension
of propositional logic and, hence, inherit some of the limitations of
propositional logic, such as the difficulties to represent objects and
relations. We introduce a generalization of Bayesian networks, called Bayesian
logic programs, to overcome these limitations. In order to represent objects
and relations it combines Bayesian networks with definite clause logic by
establishing a one-to-one mapping between ground atoms and random variables. We
show that Bayesian logic programs combine the advantages of both definite
clause logic and Bayesian networks. This includes the separation of
quantitative and qualitative aspects of the model. Furthermore, Bayesian logic
programs generalize both Bayesian networks as well as logic programs. So, many
ideas developedComment: 52 page
The inheritance of dynamic and deontic integrity constraints or: Does the boss have more rights?
In [18,23], we presented a language for the specification of static, dynamic and deontic integrity constraints (IC's) for conceptual models (CM's). An important problem not discussed in that paper is how IC's are inherited in a taxonomic network of types. For example, if students are permitted to perform certain actions under certain preconditions, must we repeat these preconditions when specializing this action for the subtype of graduate students, or are they inherited, and if so, how? For static constraints, this problem is relatively trivial, but for dynamic and deontic constraints, it will turn out that it contains numerous pitfalls, caused by the fact that common sense supplies presuppositions about the structure of IC inheritance that are not warranted by logic. In this paper, we unravel some of these presuppositions and show how to avoid the pitfalls. We first formulate a number of general theorems about the inheritance of necessary and/or sufficient conditions and show that for upward inheritance, a closure assumption is needed. We apply this to dynamic and deontic IC's, where conditions arepreconditions of actions, and show that our common sense is sometimes mistaken about the logical implications of what we have specified. We also show the connection of necessary and sufficient preconditions of actions with the specification of weakest preconditions in programming logic. Finally, we argue that information analysts usually assume constraint completion in the specification of (pre)conditions analogous to predicate completion in Prolog and circumscription in non-monotonic logic. The results are illustrated with numerous examples and compared with other approaches in the literature
SLT-Resolution for the Well-Founded Semantics
Global SLS-resolution and SLG-resolution are two representative mechanisms
for top-down evaluation of the well-founded semantics of general logic
programs. Global SLS-resolution is linear for query evaluation but suffers from
infinite loops and redundant computations. In contrast, SLG-resolution resolves
infinite loops and redundant computations by means of tabling, but it is not
linear. The principal disadvantage of a non-linear approach is that it cannot
be implemented using a simple, efficient stack-based memory structure nor can
it be easily extended to handle some strictly sequential operators such as cuts
in Prolog.
In this paper, we present a linear tabling method, called SLT-resolution, for
top-down evaluation of the well-founded semantics. SLT-resolution is a
substantial extension of SLDNF-resolution with tabling. Its main features
include: (1) It resolves infinite loops and redundant computations while
preserving the linearity. (2) It is terminating, and sound and complete w.r.t.
the well-founded semantics for programs with the bounded-term-size property
with non-floundering queries. Its time complexity is comparable with
SLG-resolution and polynomial for function-free logic programs. (3) Because of
its linearity for query evaluation, SLT-resolution bridges the gap between the
well-founded semantics and standard Prolog implementation techniques. It can be
implemented by an extension to any existing Prolog abstract machines such as
WAM or ATOAM.Comment: Slight modificatio
Nominal Logic Programming
Nominal logic is an extension of first-order logic which provides a simple
foundation for formalizing and reasoning about abstract syntax modulo
consistent renaming of bound names (that is, alpha-equivalence). This article
investigates logic programming based on nominal logic. We describe some typical
nominal logic programs, and develop the model-theoretic, proof-theoretic, and
operational semantics of such programs. Besides being of interest for ensuring
the correct behavior of implementations, these results provide a rigorous
foundation for techniques for analysis and reasoning about nominal logic
programs, as we illustrate via examples.Comment: 46 pages; 19 page appendix; 13 figures. Revised journal submission as
of July 23, 200
Independence in constraint logic programs
Studying independence of literals, variables, and substitutions has proven very useful in the context of logic programming (LP). Here we study independence in the broader context of constraint logic programming (CLP). We show that a naive extrapolation of the LP definitions of independence to CLP is unsatisfactory (in fact, wrong) for two reasons. First, because interaction between variables through constraints is more complex than in the case of logic programming. Second, in order to ensure the efUciency of several optimizations not only must independence of the search space be considered, but also an orthogonal issue - "independence of constraint solving." We clarify these issues by proposing various types of search independence
and constraint solver independence, and show how they can be combined to allow different independence-related optimizations, from parallelism to intelligent backtracking. Sufficient conditions for independence which can be evaluated "a-priori" at run-time are also proposed. Our results suggest that independence, provided a suitable definition is chosen, is even more useful in CLP than in LP
Parameter Learning of Logic Programs for Symbolic-Statistical Modeling
We propose a logical/mathematical framework for statistical parameter
learning of parameterized logic programs, i.e. definite clause programs
containing probabilistic facts with a parameterized distribution. It extends
the traditional least Herbrand model semantics in logic programming to
distribution semantics, possible world semantics with a probability
distribution which is unconditionally applicable to arbitrary logic programs
including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM
algorithm, the graphical EM algorithm, that runs for a class of parameterized
logic programs representing sequential decision processes where each decision
is exclusive and independent. It runs on a new data structure called support
graphs describing the logical relationship between observations and their
explanations, and learns parameters by computing inside and outside probability
generalized for logic programs. The complexity analysis shows that when
combined with OLDT search for all explanations for observations, the graphical
EM algorithm, despite its generality, has the same time complexity as existing
EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside
algorithm for PCFGs, and the one for singly connected Bayesian networks that
have been developed independently in each research field. Learning experiments
with PCFGs using two corpora of moderate size indicate that the graphical EM
algorithm can significantly outperform the Inside-Outside algorithm
Extended RDF: Computability and Complexity Issues
ERDF stable model semantics is a recently proposed semantics for
ERDF ontologies and a faithful extension of RDFS semantics on RDF graphs.
In this paper, we elaborate on the computability and complexity issues of the
ERDF stable model semantics. Based on the undecidability result of ERDF
stable model semantics, decidability under this semantics cannot be achieved,
unless ERDF ontologies of restricted syntax are considered. Therefore, we
propose a slightly modified semantics for ERDF ontologies, called ERDF #n-
stable model semantics. We show that entailment under this semantics is, in
general, decidable and also extends RDFS entailment. Equivalence statements
between the two semantics are provided. Additionally, we provide algorithms
that compute the ERDF #n-stable models of syntax-restricted and general
ERDF ontologies. Further, we provide complexity results for the ERDF #nstable
model semantics on syntax-restricted and general ERDF ontologies.
Finally, we provide complexity results for the ERDF stable model semantics
on syntax-restricted ERDF ontologies
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