Unified Foundations of Team Semantics via Semirings

Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse contexts such as databases, quantum mechanics, and statistics by extending first-order logic with atoms that describe dependencies between variables. Combining these two, we propose a unifying approach for analysing the concepts of dependence and independence via a novel semiring team semantics, which subsumes all the previously considered variants for first-order team semantics. In particular, we study the preservation of satisfaction of dependencies and formulae between different semirings. In addition we create links to reasoning tasks such as provenance, counting, and repairs

Reasoning about embedded dependencies using inclusion dependencies

The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded dependencies that is based on the chase and uses inclusion dependencies and implicit existential quantification in the intermediate steps of deductions

Theoretical framework of temporal databases.

by Lam Wing Hee.Thesis (M.Phil.)--Chinese University of Hong Kong, 1991.Bibliography: leaves [56]-59.List of Figures --- p.vAcknowledgements --- p.viChapter 1. --- Introduction --- p.1Chapter 1.1 --- Historical Data and Temporal Databases --- p.1Chapter 1.2 --- Valid Time and Transaction Time --- p.3Chapter 1.2.1 --- Snapshot Databases --- p.3Chapter 1.2.2 --- Rollback Databases --- p.4Chapter 1.2.3 --- Historical Databases --- p.6Chapter 1.2.4 --- Temporal Databases --- p.7Chapter 1.3 --- Literature Review --- p.8Chapter 1.3.1 --- Data Models --- p.9Chapter 1.3.2 --- Query Languages --- p.11Chapter 1.3.3 --- Logical Design --- p.13Chapter 2. --- The Temporal Relational Data Model --- p.14Chapter 2.1 --- The Temporal Relational Data Model - Informal Description --- p.14Chapter 2.2 --- The Temporal Relational Data Model - Formal Description --- p.15Chapter 2.2.1 --- Valid and Transaction Time Intervals --- p.16Chapter 2.2.2 --- "Attributes, Tuples and Temporal Relations" --- p.16Chapter 2.3 --- What is a Key in Temporal Relations? --- p.17Chapter 3. --- The Temporal Relational Algebra --- p.20Chapter 3.1 --- Operations in the Temporal Relational Algebra --- p.20Chapter 3.1.1 --- Union and Set Difference --- p.21Chapter 3.1.2 --- Selection --- p.21Chapter 3.1.3 --- Projection --- p.23Chapter 3.1.4 --- Join --- p.24Chapter 3.1.4.1 --- Natural Join --- p.25Chapter 3.2 --- Temporal Relational Algebra and TempSQL --- p.30Chapter 4. --- Classical Data Dependencies in Temporal Relations --- p.32Chapter 4.1 --- Functional Dependency in the Temporal Relational Model --- p.32Chapter 4.2 --- Multivalued Dependency in the Temporal Relational Model --- p.33Chapter 4.3 --- Relationship with Snapshot Data Dependencies --- p.34Chapter 4.4 --- Lossless Decomposition --- p.35Chapter 5. --- Asynchronous Dependency --- p.39Chapter 5.1 --- Asynchronous Dependency --- p.40Chapter 5.2 --- Asynchronous Normal Form --- p.41Chapter 5.3 --- Generalized Form of Data Dependency --- p.42Chapter 5.3.1 --- Embedded Implicational Dependency --- p.43Chapter 5.3.2 --- Algebraic Dependency --- p.45Chapter 5.4 --- Asynchronous Dependency versus Synchronous Dependency --- p.46Chapter 6. --- Conclusions --- p.48Chapter 6.1 --- Summary of the Thesis --- p.48Chapter 6.2 --- Unsolved Problems and Research Directions --- p.49Chapter 6.2.1 --- Equivalent Representations in the Temporal Relational Model --- p.49Chapter 6.2.2 --- The Notion of 'Completeness' of Temporal Query Languages --- p.50Chapter 6.2.3 --- Logical Basis for Temporal Data Models and Languages --- p.51Chapter 6.2.4 --- Other Temporal Dependencies --- p.51Chapter 6.2.5 --- Research Directions in Topics other than Theory --- p.52Appendix Proofs of Theorems --- p.53Bibliography --- p.5