6 research outputs found
Deciding Second-order Logics using Database Evaluation Techniques
We outline a novel technique that maps the satisfiability problems of
second-order logics, in particular WSnS (weak monadic second-order
logic with n successors), S1S (monadic second-order logic with one
successor), and of μ-calculus, to the problem of query evaluation
of Complex-value Datalog queries. In this dissertation, we propose
techniques that use database evaluation and optimization techniques
for automata-based decision procedures for the above logics. We show
how the use of advanced implementation techniques for Deductive
databases and for Logic Programs, in particular the use of tabling,
yields a considerable improvement in performance over more traditional
approaches. We also explore various optimizations of the proposed
technique, in particular we consider variants of tabling and goal
reordering. We then show that the decision problem for S1S can be
mapped to the problem of query evaluation of
Complex-value Datalog queries.
We explore optimizations that
can be applied to various types of formulas. Last, we propose
analogous techniques that allow us to approach μ-calculus
satisfiability problem in an incremental fashion and without the need
for re-computation. In addition, we outline a top-down evaluation
technique to drive our incremental procedure and propose heuristics
that guide the problem partitioning to reduce the size of the problems
that need to be solved
Set Unification
The unification problem in algebras capable of describing sets has been
tackled, directly or indirectly, by many researchers and it finds important
applications in various research areas--e.g., deductive databases, theorem
proving, static analysis, rapid software prototyping. The various solutions
proposed are spread across a large literature. In this paper we provide a
uniform presentation of unification of sets, formalizing it at the level of set
theory. We address the problem of deciding existence of solutions at an
abstract level. This provides also the ability to classify different types of
set unification problems. Unification algorithms are uniformly proposed to
solve the unification problem in each of such classes.
The algorithms presented are partly drawn from the literature--and properly
revisited and analyzed--and partly novel proposals. In particular, we present a
new goal-driven algorithm for general ACI1 unification and a new simpler
algorithm for general (Ab)(Cl) unification.Comment: 58 pages, 9 figures, 1 table. To appear in Theory and Practice of
Logic Programming (TPLP
Approximate inference in graphical models
Probability theory provides a mathematically rigorous yet conceptually flexible calculus of uncertainty, allowing the construction of complex hierarchical models for real-world inference tasks. Unfortunately, exact inference in probabilistic models is often computationally expensive or even intractable. A close inspection in such situations often reveals that computational bottlenecks are confined to certain aspects of the model, which can be circumvented by approximations without having to sacrifice the model's interesting aspects. The conceptual framework of graphical models provides an elegant means of representing probabilistic models and deriving both exact and approximate inference algorithms in terms of local computations. This makes graphical models an ideal aid in the development of generalizable approximations. This thesis contains a brief introduction to approximate inference in graphical models (Chapter 2), followed by three extensive case studies in which approximate inference algorithms are developed for challenging applied inference problems. Chapter 3 derives the first probabilistic game tree search algorithm. Chapter 4 provides a novel expressive model for inference in psychometric questionnaires. Chapter 5 develops a model for the topics of large corpora of text documents, conditional on document metadata, with a focus on computational speed. In each case, graphical models help in two important ways: They first provide important structural insight into the problem; and then suggest practical approximations to the exact probabilistic solution.This work was supported by a scholarship from Microsoft Research, Ltd
The Relationlog system prototype
The Relationlog system is a novel persistent deductive database system for advanced data and knowledgebased applications. It directly supports the storage and inference of data with complex structures, especially data supported in nested relational and complex-object models. The Relationlog system supports the Relationlog query language, which is a typed extension of Datalog with tuples and sets and stands in the same relationship to the nested relational and complex-object models as Datalog stands to the relational model. It also supports an SQL-like data definition language and a declarative data manipulation language. This article introduces the Relationlog language, discusses the system architecture, the design decisions incorporated within its implementation, and our experience in developing the system. Copyright © 2001 John Wiley & Sons, Ltd