  In this thesis, we present two approaches to a rigorous mathematical and
algorithmic foundation of quantitative and statistical inference in
constraint-based natural language processing. The first approach, called
quantitative constraint logic programming, is conceptualized in a clear logical
framework, and presents a sound and complete system of quantitative inference
for definite clauses annotated with subjective weights. This approach combines
a rigorous formal semantics for quantitative inference based on subjective
weights with efficient weight-based pruning for constraint-based systems. The
second approach, called probabilistic constraint logic programming, introduces
a log-linear probability distribution on the proof trees of a constraint logic
program and an algorithm for statistical inference of the parameters and
properties of such probability models from incomplete, i.e., unparsed data. The
possibility of defining arbitrary properties of proof trees as properties of
the log-linear probability model and efficiently estimating appropriate
parameter values for them permits the probabilistic modeling of arbitrary
context-dependencies in constraint logic programs. The usefulness of these
ideas is evaluated empirically in a small-scale experiment on finding the
correct parses of a constraint-based grammar. In addition, we address the
problem of computational intractability of the calculation of expectations in
the inference task and present various techniques to approximately solve this
task. Moreover, we present an approximate heuristic technique for searching for
the most probable analysis in probabilistic constraint logic programs.
