Indenture between Orson Phelps and Calista M. Phelps and Owen Clifford

Indenture of bargain and sale between Orson Phelps formerly of St. Catharines, but at the time of the transaction, was living in Buffalo, New York and Calista M. Phelps (his wife) and Owen Clifford of Grantham for lots numbered 12 and 13 in the 8th Concession in Grantham Township. The instrument no. is 3411, July 11, 1851.

Indenture between Owen Clifford and Margaret Clifford to Samuel D. Woodruff

Indenture of mortgage deed between Owen Clifford and Margaret Clifford of the Township of Grantham to Samuel D. Woodruff of St. Catharines regarding 36 3/4 acres in Lots numbered 12 and 13 in the 8th Concession in the Township of Grantham - instrument no. 187. This was registered at the Registry Office for Lincoln on April 30, 1867 in Liber I, March 29, 1867.

Indenture between Owen Clifford and Margaret Clifford to John Charles Rykert and William B. Gilleland

Indenture of mortgage deed between Owen Clifford and Margaret Clifford of the Township of Grantham to John Charles Rykert and William B. Gilleland of St. Catharines regarding parts of Lots no. 10 and 11 in the 9th Concession of the Township of Grantham. Registered in the Township of Grantham Register on September 15, 1870 - instrument no. 804 and registered in the Township of Grantham Register of February 8, 1872 - instrument no. 1104, September 15, 1870.

Indenture between Margaret Clifford and Samuel D. Woodruff

Indenture of deed of land between Margaret Clifford of Grantham and Samuel D. Woodruff of St. Catharines for lots 12 and 13 in the 8th Concession in the Township of Grantham. This was registered February 7, 1872 - instrument no. 19112 [?], February 2, 1872.

Statement from the Sheriff’s Office, Lincoln that there are no writs of execution or extent against Owen Clifford

Statement from the Sheriff’s Office, Lincoln that there are no writs of execution or extent against Owen Clifford. This is signed by Joseph A. Woodruff, March 5, 1869.

Last Will and Testament of Owen Clifford (copy) of the Township of Grantham

Last Will and Testament of Owen Clifford (copy) of the Township of Grantham, Sept. 23, 1870.

ReAlM - a system to manipulate relations

Given a heterogeneous relation algebra R, it is well known that the algebra of matrices with coefficient from R is relation algebra with relational sums that is not necessarily finite. When a relational product exists or the point axiom is given, we can represent the relation algebra by concrete binary relations between sets, which means the algebra may be seen as an algebra of Boolean matrices. However, it is not possible to represent every relation algebra. It is well known that the smallest relation algebra that is not representable has only 16 elements. Such an algebra can not be put in a Boolean matrix form.[15] In [15, 16] it was shown that every relation algebra R with relational sums and sub-objects is equivalent to an algebra of matrices over a suitable basis. This basis is given by the integral objects of R, and is, compared to R, much smaller. Aim of my thesis is to develop a system called ReAlM - Relation Algebra Manipulator - that is capable of visualizing computations in arbitrary relation algebras using the matrix approach.

Generating finite integral relation algebras

Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

Second Welland Canal - Book 2, Survey Map 2 - Locks 9 and 10 in Grantham

Survey map of the Second Welland Canal created by the Welland Canal Company showing the Grantham Township between the Town of St. Catharines and Merritton. Identified structures associated with the Canal include Locks 9 and 10, waste weirs, the towing path, a 2nd towing path, and the Canal waterway itself. The surveyors' measurements and notes can be seen in red and black ink and pencil. Local area landmarks are also identified and include roads (ex. Road to Centreville), hydraulic race, and the Centreville Mill. Properties and property owners of note are: Concession 8 Lots 12 and 12, Lewis Traver, Richard Ash, John Bradley, Owen Clifford, Orson Phelps, C. Bradley, the W. C. Loan Company, and T. Towers Mill Lot.

Second Welland Canal - Book 2, Survey Map 3 - Locks 8, 9 and 10 in Grantham

Survey map of the Second Welland Canal created by the Welland Canal Company showing the Grantham Township between the Town of St. Catharines and Merritton. Identified structures associated with the Canal include Locks 8, 9, and 10, waste weirs, the towing path, and several floating bridges. The surveyors' measurements and notes can be seen in red and black ink and pencil. Several stones and tree stumps likely used in the measurements are identified on the map. Local area landmarks are also identified and include streets and roads(ex. Macadamized Road to Thorold), J. Hamilton's Hotel, a school house, McCoy's Farm House, Bradley's House, O. Phelps Saw Mill, Disher and Hait's Woolen Mill, Centreville Mills, a bridge, several barns, and a number of structures (possibly houses, cabins, or shops) belonging to: P. McCoy, E. McLachlan, T. Wilson, W. Wilson, M. Bradley, S. Bradley, P. Boyle, J. Bradley, E. Grant, and W. Church. Lock 12 and 15 of the original canal are also identified. Properties and property owners of note are: Concession 8 Lots 12, 13 and 14, O. J. Phelps, P. McCoy, A. Bradley, C. Bradley, T. Reed, O. Clifford, J. Bradley, W. C. Loan Company, Duffin, and T. Towers Mill Lot.

Second Welland Canal - Book 2, Survey Map 4 - Locks 11, 12, 13, 14 and 15 in Grantham

Survey map of the Second Welland Canal created by the Welland Canal Company showing the Grantham Township along the outskirts of Merritton. Identified structures associated with the Canal include Locks 11, 12, 13, 14, and 15, Lock House Lot, and the towing path. The surveyors' measurements and notes can be seen in red and black ink and pencil. Several stones likely used in the measurements are identified on the map. Local area landmarks are also identified and include streets and roads(ex. Hartzel Road and Macadamized Road), the Great Western Railroad, Swing Bridge, Thorold Station and its structures (ex. freight house, office, water tank, and wood house), Gordon and Mackay Houses, Gordon and Mackay's Cotton Mill, hydraulic race, a wharf, pond, and an unnamed bridge. Properties and property owners of note are: Concession 9 Lots 12 and 13, A. Bradley, John O'Coner, G. Grant, J. Bradley, J. Vanderburgh, O. Clifford and a parcel of land leased Gordon and Mackay.

RelMDD-A Library for Manipulating Relations Based on MDDs

Relation algebras is one of the state-of-the-art means used by mathematicians and computer scientists for solving very complex problems. As a result, a computer algebra system for relation algebras called RelView has been developed at Kiel University. RelView works within the standard model of relation algebras. On the other hand, relation algebras do have other models which may have different properties. For example, in the standard model we always have L;L=L (the composition of two (heterogeneous) universal relations yields a universal relation). This is not true in some non-standard models. Therefore, any example in RelView will always satisfy this property even though it is not true in general. On the other hand, it has been shown that every relation algebra with relational sums and subobjects can be seen as matrix algebra similar to the correspondence of binary relations between sets and Boolean matrices. The aim of my research is to develop a new system that works with both standard and non-standard models for arbitrary relations using multiple-valued decision diagrams (MDDs). This system will implement relations as matrix algebras. The proposed structure is a library written in C which can be imported by other languages such as Java or Haskell.

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.

Certificate of Baptism - Margaret Elizabeth Woodruff

Certificate of Baptism for Margaret Elizabeth Woodruff, the child of Percy Carruthers and Margaret Julia Band who was baptized at St. George's Church, St. Catharines, June 14, 1935. The sponsors listed are: Maude Band Mabee, Alice Eaton, and Clifford Scott Howard.

Indenture between Samuel DeVeaux Woodruff and Alexander Pettigrew

Indenture regarding articles of agreement between Samuel DeVeaux Woodruff of St. Catharines and Alexander Pettigrew of Merritton for parts of building lots 17, 18 and 19 of the Clifford Tract in Merritton (2 copies), Oct. 21, 1899.