341 research outputs found
On the expressivity of feature logics with negation, functional uncertainty, and sort equations
Feature logics are the logical basis for so-called unification grammars studied in computational linguistics. We investigate the expressivity of feature terms with complements and the functional uncertainty construct needed for the description of long-distance dependencies and obtain the following results: satisfiability of feature terms is undecidable, sort equations can be internalized, consistency of sort equations is decidable if there is at least one atom, and consistency of sort equations is undecidable if there is no atom
On the expressivity of feature logics with negation, functional uncertainty, and sort equations
Feature logics are the logical basis for so-called unification grammars studied in computational linguistics. We investigate the expressivity of feature terms with complements and the functional uncertainty construct needed for the description of long-distance dependencies and obtain the following results: satisfiability of feature terms is undecidable, sort equations can be internalized, consistency of sort equations is decidable if there is at least one atom, and consistency of sort equations is undecidable if there is no atom
TDL : a type description language for HPSG. - Part 1: Overview
Unification-based grammar formalisms have become the predominant paradigm in natural language processing NLP and computational linguistics CL. Their success stems from the fact that they can be seen as high-level declarative programming languages for linguists, which allow them to express linguistic knowledge in a monotonic fashion. More over, such formalisms can be given a precise set theoretical semantics. This paper presents mathcal{TDL}, a typed featurebased language and inference system, which is specically designed to support highly lexicalized grammar theories like HPSG, FUG, or CUG. mathcal{TDL} allows the user to define possibly recursive hierarchically ordered types consisting of type constraints and feature constraints over the boolean connectives wedge, vee, and neg. mathcal{TDL} distinguishes between avm types (open-world reasoning), sort types (closed-world reasoning), built-in types and atoms, and allows the declaration of partitions and incompatible types. Working with partially as well as with fully expanded types is possible, both at definition time and at run time. mathcal{TDL} is incremental, i.e., it allows the redefinition of types and the use of undefined types. Efficient reasoning is accomplished through four specialized reasoners
Reasoning with Individuals for the Description Logic SHIQ
While there has been a great deal of work on the development of reasoning
algorithms for expressive description logics, in most cases only Tbox reasoning
is considered. In this paper we present an algorithm for combined Tbox and Abox
reasoning in the SHIQ description logic. This algorithm is of particular
interest as it can be used to decide the problem of (database) conjunctive
query containment w.r.t. a schema. Moreover, the realisation of an efficient
implementation should be relatively straightforward as it can be based on an
existing highly optimised implementation of the Tbox algorithm in the FaCT
system.Comment: To appear at CADE-1
Towards the integration of functions, relations and types in an AI programming language
This paper describes the design and implementation of the programming language PC-Life. This language integrates the functional and the Logic-oriented programming style and feature types supporting inheritance. This combination yields a language particularly suited to knowledge representation, especially for application in computational linguistics
Practical Reasoning for Very Expressive Description Logics
Description Logics (DLs) are a family of knowledge representation formalisms
mainly characterised by constructors to build complex concepts and roles from
atomic ones. Expressive role constructors are important in many applications,
but can be computationally problematical. We present an algorithm that decides
satisfiability of the DL ALC extended with transitive and inverse roles and
functional restrictions with respect to general concept inclusion axioms and
role hierarchies; early experiments indicate that this algorithm is well-suited
for implementation. Additionally, we show that ALC extended with just
transitive and inverse roles is still in PSPACE. We investigate the limits of
decidability for this family of DLs, showing that relaxing the constraints
placed on the kinds of roles used in number restrictions leads to the
undecidability of all inference problems. Finally, we describe a number of
optimisation techniques that are crucial in obtaining implementations of the
decision procedures, which, despite the worst-case complexity of the problem,
exhibit good performance with real-life problems
A hybrid approach for modeling uncertainty in terminological logics
This paper proposes a probabilistic extension of terminological logics. The extension maintains the original performance of drawing inferences in a hierarchy of terminological definitions. It enlarges the range of applicability to real world domains determined not only by definitional but also by uncertain knowledge. First, we introduce the propositionally complete terminological language ALC. On the basis of the language construct "probabilistic implication" it is shown how statistical information on concept dependencies can be represented. To guarantee (terminological and probabilistic) consistency, several requirements have to be met. Moreover, these requirements allow one to infer implicitly existent probabilistic relationships and their quantitative computation. By explicitly introducing restrictions for the ranges derived by instantiating the consistency requirements, exceptions can also be handled. In the categorical cases this corresponds to the overriding of properties in non monotonic inheritance networks. Consequently, our model applies to domains where both term descriptions and non-categorical relations between term extensions have to be represented
Relational extensions to feature logic: applications to constraint based grammars
This thesis investigates the logical and computational foundations of unification-based
or more appropriately constraint based grammars. The thesis explores extensions to
feature logics (which provide the basic knowledge representation services to constraint
based grammars) with multi-valued or relational features. These extensions are useful
for knowledge representation tasks that cannot be expressed within current feature
logics.The approach bridges the gap between concept languages (such as KL-ONE), which
are the mainstay of knowledge representation languages in AI, and feature logics. Va¬
rious constraints on relational attributes are considered such as existential membership,
universal membership, set descriptions, transitive relations and linear precedence con¬
straints.The specific contributions of this thesis can be summarised as follows:
1. Development of an integrated feature/concept logic
2. Development of a constraint logic for so called partial set descriptions
3. Development of a constraint logic for expressing linear precedence constraints
4. The design of a constraint language CL-ONE that incorporates the central ideas
provided by the above study
5. A study of the application of CL-ONE for constraint based grammarsThe thesis takes into account current insights in the areas of constraint logic programming, object-oriented languages, computational linguistics and knowledge representation
A Complete and Recursive Feature Theory
Various feature descriptions are being employed in logic programming
languages and constrained-based grammar formalisms. The common notational
primitive of these descriptions are functional attributes called features. The
descriptions considered in this paper are the possibly quantified first-order
formulae obtained from a signature of binary and unary predicates called
features and sorts, respectively. We establish a first-order theory FT by means
of three axiom schemes, show its completeness, and construct three elementarily
equivalent models. One of the models consists of so-called feature graphs, a
data structure common in computational linguistics. The other two models
consist of so-called feature trees, a record-like data structure generalizing
the trees corresponding to first-order terms. Our completeness proof exhibits a
terminating simplification system deciding validity and satisfiability of
possibly quantified feature descriptions.Comment: Short version appeared in the 1992 Annual Meeting of the Association
for Computational Linguistic
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