N-ary Relations Research Articles

The decision problem for some logics for finite words on infinite alphabets

This paper is a follow-up to a previous paper where the logical characterization of n-ary synchronous relations due to Eilenbeig, Elgot, and Shepherdson was investigated in the case where the alphabet has infinitely many letters. Here we show that modifying one of the predicates leads to a completely different picture for infinite alphabets, though it does not change the expressive power for finite alphabets. Indeed, roughly speaking, being able to express the fact that two words end with the same symbol leads to an undecidable theory, already for the Σ2 fragment. Finally, we show that the existential fragment is decidable. Bibliography: 19 titles.

YAGO: A Large Ontology from Wikipedia and WordNet

This article presents YAGO, a large ontology with high coverage and precision. YAGO has been automatically derived from Wikipedia and WordNet. It comprises entities and relations, and currently contains more than 1.7 million entities and 15 million facts. These include the taxonomic Is-A hierarchy as well as semantic relations between entities. The facts for YAGO have been extracted from the category system and the infoboxes of Wikipedia and have been combined with taxonomic relations from WordNet. Type checking techniques help us keep YAGO’s precision at 95%—as proven by an extensive evaluation study. YAGO is based on a clean logical model with a decidable consistency. Furthermore, it allows representing n-ary relations in a natural way while maintaining compatibility with RDFS. A powerful query model facilitates access to YAGO’s data.

Querying over fuzzy description logic

Description logics (DLs) play an important role in representing and reasoning domain knowledge. Conjunctive queries stemmed from the domain of relational databases, and have attracted more attentions in semantic Web recently. To acquire a tractable DL for query answering, DL-Lite is proposed. Due to the large amount of imprecision and uncertainty in the real world, it is essential to extend DLs to deal with these vague and imprecise information. We thus propose a new fuzzy DL f-DLR-Liteℱ⊓, which allows for the presence of n-ary relations and the occurrence of concept conjunction on the left land of inclusion axioms. We also suggest an improved fuzzy query language, which supports the presence of thresholds and user defined weights. We also show that the query answering algorithm over the extended DL is still FOL reducible and shows polynomial data complexity. DL f-DLR-Liteℱ⊓ can make up for the disadvantages of knowledge representation and reasoning of classic DLs, and the enhanced query language expresses user intentions more precisely and reasonably.

ALGORITHMS FOR THE JOIN AND AUTO-INTERSECTION OF MULTI-TAPE WEIGHTED FINITE-STATE MACHINES

A weighted finite-state machine with n tapes describes a rational relation on n strings. We recall some basic operations on n-ary rational relations, recast the important join operation in terms of "auto-intersection", and propose restricted algorithms for both operations. If two rational relations are joined on more than one tape, it can unfortunately lead to non-rational relations with undecidable properties. As a consequence, there cannot be a fully general algorithm, able to compile any rational join or auto-intersection. We define a class of triples 〈A,i,j〉 for which we are able to compile the auto-intersection of the machine A w.r.t. tapes i and j. We hope that this class is sufficient for many practical applications.

TRACTARIAN SÄTZE, EGYPTIAN HIEROGLYPHS, AND THE VERY IDEA OF SCRIPT AS PICTURE

Is it possible for a writing system to be based on pictures? In the philosophical literature, the hieroglyphic writing system of the Ancient Egyptians is sometimes taken as the example par excellence of a purely pictorial script. The hieroglyphs are assumed to be signs that do not indicate how they are supposed to be pronounced, as do the signs of the alphabets of, among other, the Indo-European languages; instead, they depict what they mean. Most prominently, Ludwig Wittgenstein draws an analogy between the pictorial semantics of the Tractatus Logico-Philosophicus and the alleged pictorial script of hieroglyphic writing:

YAGO: A Large Ontology from Wikipedia Andwordnet

This article presents YAGO, a large ontology with high coverage and precision. YAGO has been automatically derived from Wikipedia and WordNet. It comprises entities and relations, and currently contains more than 1.7 million entities and 15 million facts. These include the taxonomic Is-A hierarchy as well as semantic relations between entities. The facts for YAGO have been extracted from the category system and the infoboxes of Wikipedia and have been combined with taxonomic relations from WordNet. Type checking techniques help us keep YAGO's precision at 95% - as proven by an extensive evaluation study. YAGO is based on a clean logical model with a decidable consistency. Furthermore, it allows representing n-ary relations in a natural way while maintaining compatibility with RDFS. A powerful query model facilitates access to YAGO's data.

The multilevel hypernetwork dynamics of complex systems of robot soccer agents

A mathematical formalism is sketched for representing relational structure between agents. n -ary relations, n > 2, require hypernetworks, which generalize binary relation networks. n -ary relations on sets create structure at higher levels of representation to the elements in multilevel systems. The state of a system is represented by its multilevel relational structure. The dynamics of a system are represented by state changes through time. These can be continuous with no change in the hypernetwork topology, but often they are not. Controlling such systems involves taking actions intended to result in desirable state changes. The concept of multilevel hypernetwork can be applied to multiagent systems in general.

Ontology schema for an agent belief store

In this paper we explore the use of a formal ontology as a constraining framework for the belief store of a rational agent. The static beliefs of the agent are the axioms of the ontology. The dynamic beliefs are the descriptions of the individuals that are instances of the ontology classes. The individuals all have a unique identifier, an associated set of named classes to which they are believed to belong, and a set of property values. The ontology axioms act as a schema for the dynamic beliefs. Belief updates not conforming to the axioms lead to either rejection of the update or some other revision of the dynamic belief store to maintain consistency. Partial descriptions are augmented by inferences of property values and class memberships licensed by the axioms. For concreteness we sketch how such an ontology based agent belief store could be implemented in a multi-threaded logic programming language with action rules and object oriented programming features called Go!. This language was specifically designed for implementing communicating rational agent applications. We shall see that its logic rules allow us to extend an ontology of classes and properties with rule defined n-ary relations and functions. Its action rules enable us to implement a consistency maintenance system that takes into account justifications for beliefs. The pragmatics of consistency maintenance is an issue not normally considered by the ontology community. The paper assumes some familiarity with ontology specification using languages such as OWL DL and its subsets, and with logic programming.

Context-based Retrieval for Explainable Reasoning

On the background of mobile, ubiquitous, and pervasive applications, context determination and assignment is a necessary factor to provide IT solutions suited to a user and the user's current situation. In this paper, context is seen as n-ary relationship. Context gets embedded into ontologies, which are used to structure application specific knowledge. We present an integrative, case-based modelling approach for context and context management. We discuss the incorporation of context-based reasoning and explanation. And finally, we show how to apply our approach for trust management.

Normal Forms for Characteristic Functions on n-ary Relations

Functions of type $lt;n$gt; are characteristic functions on n-ary relations. Keenan established their importance for natural language semantics, by showing that natural language has many examples of irreducible type $lt;n$gt; functions, i.e. functions of type $lt;n$gt; that cannot be represented as compositions of unary functions. Keenan proposed some tests for reducibility, and Dekker improved on these by proposing an invariance condition that characterizes the functions with a reducible counterpart with the same behaviour on product relations. The present paper generalizes the notion of reducibility (a quantifier is reducible if it can be represented as a composition of quantifiers of lesser, but not necessarily unary, types), proposes a direct criterion for reducibility, and establishes a diamond theorem and a normal form theorem for reduction. These results are then used to show that every positive $lt;n$gt; function has a unique representation as a composition of positive irreducible functions, and to give an algorithm for finding this representation. With these formal tools it can be established that natural language has examples of n ary quantificational expressions that cannot be reduced to any composition of quantifiers of lesser degree.

Extracting the extended entity-relationship model from a legacy relational database

The maintenance of an existing database depends on the depth of understanding of its characteristics. Such an understanding is easily lost when the developers disperse. The situation becomes worse when the related documentation is missing. This paper addresses this issue by extracting the extended entity-relationship schema from the relational schema. We developed algorithms that investigate characteristics of an existing legacy database in order to identify candidate keys of all relations in the relational schema, to locate foreign keys, and to decide on the appropriate links between the given relations. Based on this analysis, a graph consistent with the entity-relationship diagram is derived to contain all possible uniary and binary relationships between the given relations. The minimum and maximum cardinalities of each link in the mentioned graph are determined, and extra links within the graph are identified and categorized, if any. The latter information is necessary to optimize foreign keys related information. Finally, the last steps in the process involve~(when applicable) suggesting improvements on the original conceptual design, deciding on relationships with attributes, many-to-many and n-ary ( n⩾3) relationships, and identifying is-a links. User involvement in the process is minimized to the case of having multiple choices, where the system does not have the semantic knowledge required to decide on a certain choice.

Online Learning of Binary and n-ary Relations over Clustered Domains

We consider the online learning problem for binary relations defined over two finite sets, each clustered into a relatively small number k,l of types (such a relation is termed a ( k,l)-binary relation), extending the models of S. Goldman, R. Rivest, and R. Schapire (1993, SIAM J. Comput. 22, 1006–1034). We investigate the learning complexity of ( k,l)-binary relations with respect to both the self-directed and adversary-directed learning models. We also generalize this problem to the learning problem for ( k 1,…, k d )- d-ary relations. In the self-directed model, we exhibit an efficient learning algorithm which makes at most kl+( n− k)log k+( m− l)log l mistakes, where n and m are the number of rows and columns, roughly twice the lower bound we show for this problem, 1 4 ⌊log k⌋⌊log l⌋+ 1 2 ( n− k) ⌊log k⌋+ 1 2 ( m− l) ⌊log l⌋. In the adversary-directed model, we exhibit an efficient algorithm for the (2,2)-binary relations, which makes at most n+ m+2 mistakes, only two more than the lower bound we show for this problem, n+ m. As for ( k 1,…, k d )- d-ary relations, we obtain lower bounds and upper bounds on the number of mistakes in the self-directed model, teacher-directed model, and adversary-directed model. Finally we show that, although the sample consistency problem for (2,2)-binary relations is solvable in polynomial time, the same problem for (2,2,2)-ternary relations is already NP-complete.

Robustness beyond shallowness: incremental deep parsing

Robustness is a key issue for natural language processing in general and parsing in particular, and many approaches have been explored in the last decade for the design of robust parsing systems. Among those approaches is shallow or partial parsing, which produces minimal and incomplete syntactic structures, often in an incremental way. We argue that with a systematic incremental methodology one can go beyond shallow parsing to deeper language analysis, while preserving robustness. We describe a generic system based on such a methodology and designed for building robust analyzers that tackle deeper linguistic phenomena than those traditionally handled by the now widespread shallow parsers. The rule formalism allows the recognition of n-ary linguistic relations between words or constituents on the basis of global or local structural, topological and/or lexical conditions. It offers the advantage of accepting various types of inputs, ranging from raw to chunked or constituent-marked texts, so for instance it can be used to process existing annotated corpora, or to perform a deeper analysis on the output of an existing shallow parser. It has been successfully used to build a deep functional dependency parser, as well as for the task of co-reference resolution, in a modular way.

From ternary relationship to relational tables

The transformation from n-ary relationships to a relational database schema has never been really fully analyzed. This paper presents one of the several ternary cases ignored by the ER-to-RM literature. The case shows that the following common belief is wrong: Given a set of FDs over a table resulting in a non-3NF situation, it is always possible to obtain a fully equivalent set of 3NF tables, without adding other restrictions than candidate keys and elementary inclusion dependencies.

Improving SMIL with NCM Facilities

SMIL is an XML-based language for specifying documents with temporal and spatial synchronization relationships, recommended by the W3C. However, SMIL has some limitations as a hypermedia authoring language. In order to overcome these limitations, this work presents the integration of SMIL documents with HyperProp, a hypermedia system based on an object-oriented model called NCM (Nested Context Model). As benefits, the integration makes both NCM facilities and HyperProp authoring and formatting tools available for SMIL documents. Furthermore, this work presents how the SMIL language can be extended to incorporate NCM facilities through the inclusion of new XML elements and attributes found in NCL, the NCM declarative language. Among the facilities, we can highlight the possibility of reusing document components and their presentation characteristics, offering flexibility in temporal specifications, adapting a document presentation according to user navigation and specifying n-ary relationships expressing causality or constraint among components.

Relational database reverse engineering: Algorithms to extract cardinality constraints

This paper presents algorithms which build SQL queries to improve the reverse engineering of relational databases. Our process extracts the current cardinality constraints of n-ary relationships through a combination of data dictionary, data schema and data instance analysis. Our results can be applied to semantic data models with cardinalities constraints based either on the ER model or to semantic data models with cardinality constraints on participation constraints (MERISE, ECR, ERC +, OMT, ODMG). The process we propose can also refine conceptual diagrams of commercial tools with reverse-engineering options (AMC ∗Designer ™, ORACLE TM Designer 2000, etc.). From our algorithms a PRO*C program using dynamic SQL has been implemented.

Complete rules for n-ary relationship cardinality constraints

An extended approach is presented for modeling data relationships that involve multiple entities. This approach unifies the relationship cardinality constraints defined by a variety of existing approaches into a common framework and extends the types of constraints captured. A concise tabular notation for specifying such constraints is introduced. The result is a modeling technique that captures more completely the nature of data relationships. Rules are defined for identifying inconsistencies among cardinality constraints specified for a given data relationship. Specific subsets of these rules are shown to be complete for four of the most commonly used variations of cardinality constraints. These rules extend work done in axiomatization of functional and numerical dependencies for relational databases into the area of conceptual data models.

An approach for decomposingN-ary data relationships

One of the most significant challenges in the use of entity relationship data models is in deciding whether to use a single relationship between several entities or a set of simpler relationships to represent a complex association. A practical eight-step approach is presented for analysis of n-ary relationships and decomposition into simpler relationships where appropriate. Relational database design concepts form the basis for this approach. An extended specification of cardinality constraints is used to support the decomposition approach and to ensure applicability to a variety of modeling styles. This approach defines a fundamental analysis skill for data modeling practitioners. © 1998 John Wiley & Sons, Ltd.

An approach for decomposing N-ary data relationships

One of the most significant challenges in the use of entity relationship data models is in deciding whether to use a single relationship between several entities or a set of simpler relationships to represent a complex association. A practical eight-step approach is presented for analysis of n-ary relationships and decomposition into simpler relationships where appropriate. Relational database design concepts form the basis for this approach. An extended specification of cardinality constraints is used to support the decomposition approach and to ensure applicability to a variety of modeling styles. This approach defines a fundamental analysis skill for data modeling practitioners. © 1998 John Wiley & Sons, Ltd.

A q -deformed differential calculus at roots of unity

We present main results obtained and published recently, concerning the derivation satisfying d N = 0, and the algebras defined by N-ary relations imposed by such condition. We show the covariant version of this calculus, and interpret the irreducible parts of the tensorial products of N such differentials in terms of generalized curvature and torsion.