245 research outputs found
Combining Enumeration and Deductive Techniques in order to Increase the Class of Constructible Infinite Models
AbstractA new method for building infinite models for first-order formulae is presented. The method combines enumeration techniques with existing deductive (in a broad sense) ones. Its soundness and completeness w.r.t. the class of models that can be represented by equational constraints are proven. This shows that the use of enumeration techniques strictly increases the power of existing methods for building Herbrand models that are not complete in this sense. Some strategies are proposed to reduce the search space. We give examples and show how to use this approach for building interactively a model of a formula introduced by Goldfarb in his proof of the undecidability of the Gödel class with identity. This formula is satisfiable but has no finite model
Handling Conflicts in Depth-First Search for LTL Tableau to Debug Compliance Based Languages
Providing adequate tools to tackle the problem of inconsistent compliance
rules is a critical research topic. This problem is of paramount importance to
achieve automatic support for early declarative design and to support evolution
of rules in contract-based or service-based systems. In this paper we
investigate the problem of extracting temporal unsatisfiable cores in order to
detect the inconsistent part of a specification. We extend conflict-driven
SAT-solver to provide a new conflict-driven depth-first-search solver for
temporal logic. We use this solver to compute LTL unsatisfiable cores without
re-exploring the history of the solver.Comment: In Proceedings FLACOS 2011, arXiv:1109.239
Type-elimination-based reasoning for the description logic SHIQbs using decision diagrams and disjunctive datalog
We propose a novel, type-elimination-based method for reasoning in the
description logic SHIQbs including DL-safe rules. To this end, we first
establish a knowledge compilation method converting the terminological part of
an ALCIb knowledge base into an ordered binary decision diagram (OBDD) which
represents a canonical model. This OBDD can in turn be transformed into
disjunctive Datalog and merged with the assertional part of the knowledge base
in order to perform combined reasoning. In order to leverage our technique for
full SHIQbs, we provide a stepwise reduction from SHIQbs to ALCIb that
preserves satisfiability and entailment of positive and negative ground facts.
The proposed technique is shown to be worst case optimal w.r.t. combined and
data complexity and easily admits extensions with ground conjunctive queries.Comment: 38 pages, 3 figures, camera ready version of paper accepted for
publication in Logical Methods in Computer Scienc
Independence in CLP Languages
Studying independence of goals has proven very useful in the context of logic programming. In particular, it has provided a formal basis for powerful automatic parallelization tools, since independence ensures that two goals may be evaluated in parallel while preserving correctness and eciency. We extend the concept of independence to constraint logic programs (CLP) and
prove that it also ensures the correctness and eciency of the parallel evaluation of independent goals. Independence for CLP languages is more complex than for logic programming as search space preservation is necessary but no longer sucient for ensuring correctness and eciency. Two
additional issues arise. The rst is that the cost of constraint solving may depend upon the order constraints are encountered. The second is the need to handle dynamic scheduling. We clarify these issues by proposing various types of search independence and constraint solver independence, and show how they can be combined to allow dierent optimizations, from parallelism to intelligent
backtracking. Sucient conditions for independence which can be evaluated \a priori" at run-time are also proposed. Our study also yields new insights into independence in logic programming languages. In particular, we show that search space preservation is not only a sucient but also a necessary condition for ensuring correctness and eciency of parallel execution
Module extraction for inexpressive description logics
Module extraction is an important reasoning task, aiding in the design, reuse and maintenance
of ontologies. Reasoning services such as subsumption testing and MinA extraction have been
shown to bene t from module extraction methods. Though various syntactic traversal-based
module extraction algorithms exist for extracting modules, many only consider the subsumee
of a subsumption statement as a selection criterion for reducing the axioms in the module.
In this dissertation we extend the bottom-up reachability-based module extraction heuristic
for the inexpressive Description Logic EL, by introducing a top-down version of the heuristic
which utilises the subsumer of a subsumption statement as a selection criterion to minimize
the number of axioms in a module. Then a combined bidirectional heuristic is introduced
which uses both operands of a subsumption statement in order to extract very small modules.
We then investigate the relationship between MinA extraction and bidirectional reachabilitybased
module extraction. We provide empirical evidence that bidirectional reachability-based
module extraction for subsumption entailments in EL provides a signi cant reduction in the
size of modules for almost no additional costs in the running time of the original algorithms.Computer ScienceM. Sc. (Computer Science
- …