Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic via Linear Nested Sequents

This paper employs the linear nested sequent framework to design a new cut-free calculus LNIF for intuitionistic fuzzy logic--the first-order G\"odel logic characterized by linear relational frames with constant domains. Linear nested sequents--which are nested sequents restricted to linear structures--prove to be a well-suited proof-theoretic formalism for intuitionistic fuzzy logic. We show that the calculus LNIF possesses highly desirable proof-theoretic properties such as invertibility of all rules, admissibility of structural rules, and syntactic cut-elimination.Comment: Appended version of the paper "Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic via Linear Nested Sequents", accepted to the International Symposium on Logical Foundations of Computer Science (LFCS 2020

On Spatial Conjunction as Second-Order Logic

Spatial conjunction is a powerful construct for reasoning about dynamically allocated data structures, as well as concurrent, distributed and mobile computation. While researchers have identified many uses of spatial conjunction, its precise expressive power compared to traditional logical constructs was not previously known. In this paper we establish the expressive power of spatial conjunction. We construct an embedding from first-order logic with spatial conjunction into second-order logic, and more surprisingly, an embedding from full second order logic into first-order logic with spatial conjunction. These embeddings show that the satisfiability of formulas in first-order logic with spatial conjunction is equivalent to the satisfiability of formulas in second-order logic. These results explain the great expressive power of spatial conjunction and can be used to show that adding unrestricted spatial conjunction to a decidable logic leads to an undecidable logic. As one example, we show that adding unrestricted spatial conjunction to two-variable logic leads to undecidability. On the side of decidability, the embedding into second-order logic immediately implies the decidability of first-order logic with a form of spatial conjunction over trees. The embedding into spatial conjunction also has useful consequences: because a restricted form of spatial conjunction in two-variable logic preserves decidability, we obtain that a correspondingly restricted form of second-order quantification in two-variable logic is decidable. The resulting language generalizes the first-order theory of boolean algebra over sets and is useful in reasoning about the contents of data structures in object-oriented languages.Comment: 16 page

Moa and the multi-model architecture: a new perspective on XNF2

Advanced non-traditional application domains such as geographic information systems and digital library systems demand advanced data management support. In an effort to cope with this demand, we present the concept of a novel multi-model DBMS architecture which provides evaluation of queries on complexly structured data without sacrificing efficiency. A vital role in this architecture is played by the Moa language featuring a nested relational data model based on XNF2, in which we placed renewed interest. Furthermore, extensibility in Moa avoids optimization obstacles due to black-box treatment of ADTs. The combination of a mapping of queries on complexly structured data to an efficient physical algebra expression via a nested relational algebra, extensibility open to optimization, and the consequently better integration of domain-specific algorithms, makes that the Moa system can efficiently and effectively handle complex queries from non-traditional application domains

NOSQL design for analytical workloads: Variability matters

Big Data has recently gained popularity and has strongly questioned relational databases as universal storage systems, especially in the presence of analytical workloads. As result, co-relational alternatives, commonly known as NOSQL (Not Only SQL) databases, are extensively used for Big Data. As the primary focus of NOSQL is on performance, NOSQL databases are directly designed at the physical level, and consequently the resulting schema is tailored to the dataset and access patterns of the problem in hand. However, we believe that NOSQL design can also benefit from traditional design approaches. In this paper we present a method to design databases for analytical workloads. Starting from the conceptual model and adopting the classical 3-phase design used for relational databases, we propose a novel design method considering the new features brought by NOSQL and encompassing relational and co-relational design altogether.Peer ReviewedPostprint (author's final draft

User Defined Types and Nested Tables in Object Relational Databases

Bernadette Byrne, Mary Garvey, ‘User Defined Types and Nested Tables in Object Relational Databases’, paper presented at the United Kingdom Academy for Information Systems 2006: Putting Theory into Practice, Cheltenham, UK, 5-7 June, 2006.There has been much research and work into incorporating objects into databases with a number of object databases being developed in the 1980s and 1990s. During the 1990s the concept of object relational databases became popular, with object extensions to the relational model. As a result, several relational databases have added such extensions. There has been little in the way of formal evaluation of object relational extensions to commercial database systems. In this work an airline flight logging system, a real-world database application, was taken and a database developed using a regular relational database and again using object relational extensions, allowing the evaluation of the relational extensions.Peer reviewe

06472 Abstracts Collection - XQuery Implementation Paradigms

From 19.11.2006 to 22.11.2006, the Dagstuhl Seminar 06472 ``XQuery Implementation Paradigms'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Deductive Optimization of Relational Data Storage

Optimizing the physical data storage and retrieval of data are two key database management problems. In this paper, we propose a language that can express a wide range of physical database layouts, going well beyond the row- and column-based methods that are widely used in database management systems. We use deductive synthesis to turn a high-level relational representation of a database query into a highly optimized low-level implementation which operates on a specialized layout of the dataset. We build a compiler for this language and conduct experiments using a popular database benchmark, which shows that the performance of these specialized queries is competitive with a state-of-the-art in memory compiled database system

Solving equations in the relational algebra

Enumerating all solutions of a relational algebra equation is a natural and powerful operation which, when added as a query language primitive to the nested relational algebra, yields a query language for nested relational databases, equivalent to the well-known powerset algebra. We study \emph{sparse} equations, which are equations with at most polynomially many solutions. We look at their complexity, and compare their expressive power with that of similar notions in the powerset algebra.Comment: Minor revision, accepted for publication in SIAM Journal on Computin

On Deriving Nested Calculi for Intuitionistic Logics from Semantic Systems

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated labelled calculus