arXiv subjects

Zoran Majkic

Publications and source records attributed to Zoran Majkic.

24 records · Page 2Linked to original sources

arXiv2011

Sound and Complete Query Answering in Intensional P2P Data Integration

Contemporary use of the term 'intension' derives from the traditional logical doctrine that an idea has both an extension and an intension. In this paper we introduce an intensional FOL (First-order-logic) for P2P systems by fusing the Bealer's intensional algebraic FOL with the S5 possible-world semantics of the Montague, we define the intensional equivalence relation for this logic and the weak deductive inference for it. The notion of ontology has become widespread in semantic Web. The meaning of concepts and views defined over some database ontology can be considered as intensional objects which have particular extension in some possible world: for instance in the actual world. Thus, non invasive mapping between completely independent peer databases in a P2P systems can be naturally specified by the set of couples of intensionally equivalent views, which have the same meaning (intension), over two different peers. Such a kind of mapping has very different semantics from the standard view-based mappings based on the material implication commonly used for Data Integration. We show how a P2P database system may be embedded into this intensional modal FOL, and how we are able to obtain a weak non-omniscient inference, which can be effectively implemented. For a query answering we consider non omniscient query agents and we define object-oriented class for them which implements as method the query rewriting algorithm. Finally, we show that this query answering algorithm is sound and complete w.r.t. the weak deduction of the P2P intensional logic.

cs.DB↗

arXiv2011

A New Representation Theorem for Many-valued Modal Logics

We propose a new definition of the representation theorem for many-valued logics, with modal operators as well, and define the stronger relationship between algebraic models of a given logic and relational structures used to define the Kripke possible-world semantics for it. Such a new framework offers a new semantics for many-valued logics based on the truth-invariance entailment. Consequently, it is substantially different from current definitions based on a matrix with a designated subset of logic values, used for the satisfaction relation, often difficult to fix. In the case when the many-valued modal logics are based on the set of truth-values that are complete distributive lattices we obtain a compact autoreferential Kripke-style canonical representation. The Kripke-style semantics for this subclass of modal logics have the joint-irreducible subset of the carrier set of many-valued algebras as set of possible worlds. A significant member of this subclass is the paraconsistent fuzzy logic extended by new logic values in order to also deal with incomplete and inconsistent information. This new theory is applied for the case of autoepistemic intuitionistic many-valued logic, based on Belnap's 4-valued bilattice, as a minimal extension of classical logic used to manage incomplete and inconsistent information as well.

cs.LO↗

arXiv2011

DB Category: Denotational Semantics for View-based Database Mappings

We present a categorical denotational semantics for a database mapping, based on views, in the most general framework of a database integration/exchange. Developed database category DB, for databases (objects) and view-based mappings (morphisms) between them, is different from Set category: the morphisms (based on a set of complex query computations) are not functions, while the objects are database instances (sets of relations). The logic based schema mappings between databases, usually written in a highly expressive logical language (ex. LAV, GAV, GLAV mappings, or tuple generating dependency) may be functorially translated into this "computation" category DB. A new approach is adopted, based on the behavioral point of view for databases, and behavioral equivalences for databases and their mappings are established. By introduction of view-based observations for databases, which are computations without side-effects, we define a fundamental (Universal algebra) monad with a power-view endofunctor T. The resulting 2-category DB is symmetric, so that any mapping can be represented as an object (database instance) as well, where a higher-level mapping between mappings is a 2-cell morphism. Database category DB has the following properties: it is equal to its dual, complete and cocomplete. Special attention is devoted to practical examples: a query definition, a query rewriting in GAV Database-integration environment, and the fixpoint solution of a canonical data integration model.

cs.DB↗

arXiv2011

Data Base Mappings and Monads: (Co)Induction

In this paper we presented the semantics of database mappings in the relational DB category based on the power-view monad T and monadic algebras. The objects in this category are the database-instances (a database-instance is a set of n-ary relations, i.e., a set of relational tables as in standard RDBs). The morphisms in DB category are used in order to express the semantics of view-based Global and Local as View (GLAV) mappings between relational databases, for example those used in Data Integration Systems. Such morphisms in this DB category are not functions but have the complex tree structures based on a set of complex query computations between two database-instances. Thus DB category, as a base category for the semantics of databases and mappings between them, is different from the Set category used dominantly for such issues, and needs the full investigation of its properties. In this paper we presented another contributions for an intensive exploration of properties and semantics of this category, based on the power-view monad T and the Kleisli category for databases. Here we stressed some Universal algebra considerations based on monads and relationships between this DB category and the standard Set category. Finally, we investigated the general algebraic and induction properties for databases in this category, and we defined the initial monadic algebras for database instances.

cs.DB↗

arXiv2011

Matching, Merging and Structural Properties of Data Base Category

Main contribution of this paper is an investigation of expressive power of the database category DB. An object in this category is a database-instance (set of n-ary relations). Morphisms are not functions but have complex tree structures based on a set of complex query computations. They express the semantics of view-based mappings between databases. The higher (logical) level scheme mappings between databases, usually written in some high expressive logical language, may be functorially translated into this base "computation" DB category . The behavioral point of view for databases is assumed, with behavioural equivalence of databases corresponding to isomorphism of objects in DB category. The introduced observations, which are view-based computations without side-effects, are based (from Universal algebra) on monad endofunctor T, which is the closure operator for objects and for morphisms also. It was shown that DB is symmetric (with a bijection between arrows and objects) 2-category, equal to its dual, complete and cocomplete. In this paper we demonstrate that DB is concrete, locally small and finitely presentable. Moreover, it is enriched over itself monoidal symmetric category with a tensor products for matching, and has a parameterized merging database operation. We show that it is an algebraic lattice and we define a database metric space and a subobject classifier: thus, DB category is a monoidal elementary topos.

cs.DB↗

arXiv2011

On Paraconsistent Weakening of Intuitionistic Negation

In [1], systems of weakening of intuitionistic negation logic called Z_n and CZ_n were developed in the spirit of da Costa's approach(c.f. [2]) by preserving, differently from da Costa, its fundamental properties: antitonicity, inversion and additivity for distributive lattices. However, according to [3], those systems turned out to be not paraconsistent but extensions of intuitionistic logic. Taking into account of this result, we shall here make some observations on the modified systems of Z_n and CZ_n, that are paraconsistent as well.

cs.LO↗