On Implicational Dependency Families Possessing Finite Armstrong Relations

Let X ≠ 0 be a finite collection of nonempty relations over the relation scheme R(A1, A2 , ... , A,.); then the closure of X under embedding and direct product (up to isomorphism) is a finitely generated Implicational Dependency family (ID-family) generated by X. In this paper, we show that the class of finitely generated ID-families is identical to the class of those ID-families which possess a finite Armstrong relation

Intelligent query answering in rule based systems

AbstractWe propose that in large knowledge bases which are collections of atomic facts and general rules (Horn clauses), the rules should be allowed to occur in the answer for a query. We introduce a new concept of the answer for a query which includes both atomic facts and general rules. We provide a method of transforming rules by relational algebra expressions built from projection, join, and selection and demonstrate how the answers consisting of both facts and general rules can be generated

Model-theoretic Characterizations of Existential Rule Languages

Existential rules, a.k.a. dependencies in databases, and Datalog+/- in knowledge representation and reasoning recently, are a family of important logical languages widely used in computer science and artificial intelligence. Towards a deep understanding of these languages in model theory, we establish model-theoretic characterizations for a number of existential rule languages such as (disjunctive) embedded dependencies, tuple-generating dependencies (TGDs), (frontier-)guarded TGDs and linear TGDs. All these characterizations hold for arbitrary structures, and most of them also work on the class of finite structures. As a natural application of these characterizations, complexity bounds for the rewritability of above languages are also identified.Comment: 17 pages, 2 figures, the full version of a paper submitted to IJCAI 202

An Inheritance-Based Theory of the Lexicon in Combinatory Categorial Grammar

Institute for Communicating and Collaborative SystemsThis thesis proposes an extended version of the Combinatory Categorial Grammar (CCG) formalism, with the following features: 1. grammars incorporate inheritance hierarchies of lexical types, defined over a simple, feature-based constraint language 2. CCG lexicons are, or at least can be, functions from forms to these lexical types This formalism, which I refer to as ‘inheritance-driven’ CCG (I-CCG), is conceptualised as a partially model-theoretic system, involving a distinction between category descriptions and their underlying category models, with these two notions being related by logical satisfaction. I argue that the I-CCG formalism retains all the advantages of both the core CCG framework and proposed generalisations involving such things as multiset categories, unary modalities or typed feature structures. In addition, I-CCG: 1. provides non-redundant lexicons for human languages 2. captures a range of well-known implicational word order universals in terms of an acquisition-based preference for shorter grammars This thesis proceeds as follows: Chapter 2 introduces the ‘baseline’ CCG formalism, which incorporates just the essential elements of category notation, without any of the proposed extensions. Chapter 3 reviews parts of the CCG literature dealing with linguistic competence in its most general sense, showing how the formalism predicts a number of language universals in terms of either its restricted generative capacity or the prioritisation of simpler lexicons. Chapter 4 analyses the first motivation for generalising the baseline category notation, demonstrating how certain fairly simple implicational word order universals are not formally predicted by baseline CCG, although they intuitively do involve considerations of grammatical economy. Chapter 5 examines the second motivation underlying many of the customised CCG category notations — to reduce lexical redundancy, thus allowing for the construction of lexicons which assign (each sense of) open class words and morphemes to no more than one lexical category, itself denoted by a non-composite lexical type. Chapter 6 defines the I-CCG formalism, incorporating into the notion of a CCG grammar both a type hierarchy of saturated category symbols and an inheritance hierarchy of constrained lexical types. The constraint language is a simple, feature-based, highly underspecified notation, interpreted against an underlying notion of category models — this latter point is crucial, since it allows us to abstract away from any particular inference procedure and focus on the category notation itself. I argue that the partially model-theoretic I-CCG formalism solves the lexical redundancy problem fairly definitively, thereby subsuming all the other proposed variant category notations. Chapter 7 demonstrates that the I-CCG formalism also provides the beginnings of a theory of the CCG lexicon in a stronger sense — with just a small number of substantive assumptions about types, it can be shown to formally predict many implicational word order universals in terms of an acquisition-based preference for simpler lexical inheritance hierarchies, i.e. those with fewer types and fewer constraints. Chapter 8 concludes the thesis

Supervenience, Dependence, Disjunction

This paper explores variations on and connections between the topics mentioned in its title, using as something of an anchor the discussion in Valentin Goranko and Antti Kuusisto’s “Logics for propositional determinacy and independence”, a venture into what the authors call the logic of determinacy, which they contrast with (a demodalized version of) Jouko Väänänen’s modal dependence logic. As they make clear in their discussion, these logics are closely connected with the topics of noncontingency and supervenience. Two opening sections of the present paper address some of these connections, including related earlier logical work by the present author as well as very recent work by Jie Fan. The Väänänen-inspired treatment is presented in a third section, and then, in Sections 4 and 5, as a kind of centerpiece for the discussion, we follow Goranko and Kuusisto in elaborating one principal reason offered for preferring their own approach over that treatment, which concerns some anomalies over the behaviour of disjunction in the latter treatment. Sections 6 and 7 look at dependence and (several different versions of) disjunction in inquisitive logic, especially as presented by Ivano Ciardelli. Section 8 revisits the less formal property-supervenience literature with issues from the first two sections of the paper in mind, and we conclude with a Postscript addressing a further conceptual issue pertaining to the relation between modal and quantificational dependence logics

Integration of Information System Database Module Schemas

Paralelan i nezavisan rad više projektanata na različitim modulima (podsistemima) nekog informacionog sistema, identifikovanim saglasno početnoj funkcionalnoj dekompoziciji realnog sistema, nužno dovodi do međusobno nekonzistentnih rešenja šema modula baze podataka. Rad se bavi pitanjima identifikacije i razrešavanja problema, vezanih za automatsko otkrivanje kolizija, koje nastaju pri paralelnom projektovanju različitih šema modula i problema vezanih za integraciju šema modula u jedinstvenu šemu baze podataka informacionog sistema. Identifikovani su mogući tipovi kolizija šema modula, formulisan je i dokazan potreban i dovoljan uslov stroge i intenzionalne kompatibilnosti šema modula, što je omogućilo da se, u formi algoritama, prikažu postupci za ispitivanje stroge i intenzionalne kompatibilnosti šema modula. Formalizovan je i postupak integracije kompatibilnih šema u jedinstvenu (strogo pokrivajuću) šemu baze podataka. Dat je, takođe, prikaz metodologije primene algoritama za testiranje kompatibilnosti i integraciju šema modula u jedinstvenu šemu baze podataka informacionog sistema.Parallel and independent work of a number of designers on different information system modules (i.e. subsystems), identified by the initial real system functional decomposition, necessarily leads to mutually inconsistent database (db) module schemas. The thesis considers the problems concerning automatic detection of collisions, that can appear during the simultaneous design of different db module schemas, and integration of db module schemas into the unique information system db schema. All possible types of db module schema collisions have been identified. Necessary and sufficient condition of strong and intensional db module schema compatibility has been formu-lated and proved. It has enabled to formalize the process of db module schema strong and intensional compatibility checking and to construct the appropriate algorithms. The integration process of the unique (strong covering) db schema, on the basis of compatible db module schemas, is formalized, as well. The methodology of applying the algorithms for compatibility checking and unique db schema integration is also presented