L-Fuzzy Structured Query Language

Lattice valued fuzziness is more general than crispness or fuzziness based on the unit interval. In this work, we present a query language for a lattice based fuzzy database. We define a Lattice Fuzzy Structured Query Language (LFSQL) taking its membership values from an arbitrary lattice L. LFSQL can handle, manage and represent crisp values, linear ordered membership degrees and also allows membership degrees from lattices with non-comparable values. This gives richer membership degrees, and hence makes LFSQL more flexible than FSQL or SQL. In order to handle vagueness or imprecise information, every entry into an L-fuzzy database is an L-fuzzy set instead of crisp values. All of this makes LFSQL an ideal query language to handle imprecise data where some factors are non-comparable. After defining the syntax of the language formally, we provide its semantics using L-fuzzy sets and relations. The semantics can be used in future work to investigate concepts such as functional dependencies. Last but not least, we present a parser for LFSQL implemented in Haskell.

Henry Hope & Sons of Canada Ltd. Letter, 1916

Henry Hope & Sons of Canada Ltd. were located at 45 King Street West, Toronto, Ont. at the writing of this letter in 1916. The company specialized in “weathertight casements in iron steel or gun-metal, unbreakable steel windows, fanlight opening-gear, leaded lights and stained glass, patent glass roofing, locks and door furniture, rainwater goods in cast lead and cast iron”. The letter is addressed to Mr. H.Y. [Harry Young] Grant, c/o Fenwick Farm, Lundy’s Lane, Niagara Falls, Ont. from R.W. Smith. The letter is in reply to a query about casement windows. Harry Young Grant (1860-1934), son of Sir James Alexander Grant and Maria Malloch of Ottawa, Ont. was a medical doctor specializing in the treatment of the eye, ear, nose and throat. After his retirement he became a member of the Niagara Parks Commission. He was married to Grace A. Smith, daughter of James R. Smith of Buffalo.

Armory and Lineages of Canada 1914

A book called "Armory and Lineages Of Canada 1914" with the copyright year 1913. The book is signed by H.K. Woodruff and it is also signed by Margaret Woodruff Band. Within the back pages is a list of dates of births, weddings and deaths. The full text is available in the Brock University Special Collections and Archives. There are other full text copies of later editions available in the Internet Archive: https://archive.org/search.php?query=title%3A%28armory%20and%20lineages%20of%20canada%29

An Abstract Algebraic Theory of L-Fuzzy Relations for Relational Databases

Classical relational databases lack proper ways to manage certain real-world situations including imprecise or uncertain data. Fuzzy databases overcome this limitation by allowing each entry in the table to be a fuzzy set where each element of the corresponding domain is assigned a membership degree from the real interval [0…1]. But this fuzzy mechanism becomes inappropriate in modelling scenarios where data might be incomparable. Therefore, we become interested in further generalization of fuzzy database into L-fuzzy database. In such a database, the characteristic function for a fuzzy set maps to an arbitrary complete Brouwerian lattice L. From the query language perspectives, the language of fuzzy database, FSQL extends the regular Structured Query Language (SQL) by adding fuzzy specific constructions. In addition to that, L-fuzzy query language LFSQL introduces appropriate linguistic operations to define and manipulate inexact data in an L-fuzzy database. This research mainly focuses on defining the semantics of LFSQL. However, it requires an abstract algebraic theory which can be used to prove all the properties of, and operations on, L-fuzzy relations. In our study, we show that the theory of arrow categories forms a suitable framework for that. Therefore, we define the semantics of LFSQL in the abstract notion of an arrow category. In addition, we implement the operations of L-fuzzy relations in Haskell and develop a parser that translates algebraic expressions into our implementation.