A System for Models of First Order Theories

If you want to know whether a property is true or not in a specific algebraic structure,you need to test that property on the given structure. This can be done by hand, which can be cumbersome and erroneous. In addition, the time consumed in testing depends on the size of the structure where the property is applied. We present an implementation of a system for finding counterexamples and testing properties of models of first-order theories. This system is supposed to provide a convenient and paperless environment for researchers and students investigating or studying such models and algebraic structures in particular. To implement a first-order theory in the system, a suitable first-order language.( and some axioms are required. The components of a language are given by a collection of variables, a set of predicate symbols, and a set of operation symbols. Variables and operation symbols are used to build terms. Terms, predicate symbols, and the usual logical connectives are used to build formulas. A first-order theory now consists of a language together with a set of closed formulas, i.e. formulas without free occurrences of variables. The set of formulas is also called the axioms of the theory. The system uses several different formats to allow the user to specify languages, to define axioms and theories and to create models. Besides the obvious operations and tests on these structures, we have introduced the notion of a functor between classes of models in order to generate more co~plex models from given ones automatically. As an example, we will use the system to create several lattices structures starting from a model of the theory of pre-orders.

Letter to Mr. Walsh, Registrar Office, 1836

The man to whom the letter is addressed is Francis Leigh Walsh who was a land surveyor and registrar. Mr. Walsh was born on March 12, 1789 in Harford County, Maryland to Thomas Welsh, a United Empire Loyalist. In 1793, his family moved to Norfolk County and in 1810, Francis succeeded his father as registrar for Norfolk County. During the War of 1812 he served in the local militia and became a captain in 1824. He was the representative for Norfolk in the legislative assembly of Upper Canada from 1820 to 1828 and 1834 to 1836. He became justice of the peace in the London district in 1821 and 1838 in the Talbot district. He died in Simcoe on Oct. 14th, 1884. His son, Aquila Walsh served in the Legislative Assembly of the Province of Canada and in the Canadian House of Commons. Benjamin Hardison was born in Berwick in the Thirteen Colonies (British colonies on the Atlantic Coast of North America) on April 2, 1757 to Thomas Hardison and Mary Chadbourne. He was a farmer, miller and political figure. He was the representative for 4th Lincoln and Norfolk in the Legislative Assembly of Upper Canada from 1797-1800. On January 21, 1800 he married Jane Warren. He served with the American forces during the American Revolution at which time he was taken prisoner and sent to Canada. Later, he settled in Fort Erie where he was a captain in the militia and a justice of the peace for the Niagara district. He operated mills and a distillery in Fort Erie and died there on July 26, 1823. Source: http://en.vionto.com/show/me/Francis+Leigh+Walsh http://en.wikipedia.org/wiki/Benjamin_Hardison

Dr. Stuart D. Scott Papers, 1837-2010 (non-inclusive)

Dr. Stuart D. Scott has written extensively in the fields of prehistory and history. As an archaeologist, he has traveled to some of the most significant sites in the world, including Pompeii, Stonehenge, the Valley of the Kings, Egypt’s pyramids and the Taj Mahal. He spent nine months excavating with the Tikal Project in Guatemala before returning to the University of Arizona where he received a Ph.D. in 1963. He excavated in New Zealand as a Fulbright scholar in 1963-1964. In the fall of 1964, Dr. Scott started a long career in the Anthropology Department of the State University of New York. He taught graduate and undergraduate archaeology courses and continued his archaeological and historical research. In 1979, Scott established the Old Fort Niagara Archaeology in Progress Project at Old Fort Niagara in Youngstown, New York. For many years, he became involved with historical archaeology in western New York. It was during this work that he became interested in the Upper Canada Rebellion of 1837-1838 and its aftermath. Dr. Scott and his wife, Patricia Kay Scott, would use Christmas breaks, summer vacations, and sabbatical years to travel. They were repeatedly lured back to the South Pacific, conducting research in New Zealand, Australia and many of the Micronesian and Polynesian islands. To tell the whole story of the Rebellion and the prison exiles, they traveled extensively in Canada, the United States, England and Tasmania to collect archival research and to experience the scenes of this remarkable narrative. In 2004, Dr. Scott published To the Outskirts of Habitable Creation: Americans and Canadians Transported to Tasmania in the 1840s, which told the story of the men captured, tried, convicted, and exiled as a result of the Rebellion, also called the Patriot War. Other contributions include: • A collaboration with Dr. Charles Cazeau on the book Exploring the Unknown, Great Mysteries Reexamined published by Plenum Press in 1979 • The Patriot Game: New Yorkers and the Canadian Rebellion of 1837-1838, which appeared in New York History, Vol. 68, No.3. 1987 • A Frontier Spirit: The Life of James Gemmell published in Australiasian Canadian Studies, Vol. 25, No. 2 2007 • To the Outskirts of Habitable Creation which appeared in the Friends of the National Archives, Vol. 20, No. 1 2009 • Numerous academic journal publications • Service on conference panels • Various research papers and proposals Before retiring in 1997 and while still a resident of Buffalo, N.Y., Dr. Scott spent considerable time with Brock University President Emeritus James A. Gibson and History Professor Colin Duquemin. The three shared a love of Rebellion history. It was largely because of this connection that Brock University was chosen as the recipient of Dr. Scott’s research materials.

Copy of poster advertising “Grand Buffalo Hunt at Niagara Falls” with Bill Hickok, August, 1872

James Butler Hickok (1837-1876), also known as “Wild Bill” Hickok, was an American gun-fighter, scout and spy. He was involved in altercations with others while working for the famous express company Russell, Majors and Waddell (in 1861), and later while working as a wagon master, scout, and spy for the Union forces during the Civil War. These altercations resulted in the deaths of 4 people, but Hickok was acquitted in all cases. An embellished article written about him in Harper’s magazine helped contribute to his reputation as a western hero. He served as a deputy U.S. marshal and sheriff in Kansas in the late 1860’s, helping to bring law and order to a previously lawless area. He gambled considerably, and during a card game on August 2, 1876, was shot and killed. The cards he was holding (two aces, two eights, and a jack) became known as the "dead man's hand."

An Investigation of the Role of Attention in the Cross-Race Effect: An Ecological Approach

The current set of studies was conducted to examine the cross-race effect (CRE), a phenomenon commonly found in the face perception literature. The CRE is evident when participants display better own-race face recognition accuracy than other-race recognition accuracy (e.g. Ackerman et al., 2006). Typically the cross-race effect is attributed to perceptual expertise, (i.e., other-race faces are processed less holistically; Michel, Rossion, Han, Chung & Caldara, 2006), and the social cognitive model (i.e., other-race faces are processed at the categorical level by virtue of being an out-group member; Hugenberg, Young, Bernstein, & Sacco, 2010). These effects may be mediated by differential attention. I investigated whether other-race faces are disregarded and, consequently, not remembered as accurately as own-race (in-group) faces. In Experiment 1, I examined how the magnitude of the CRE differed when participants learned individual faces sequentially versus when they learned multiple faces simultaneously in arrays comprising faces and objects. I also examined how the CRE differed when participants recognized individual faces presented sequentially versus in arrays of eight faces. Participants’ recognition accuracy was better for own-race faces than other-race faces regardless of familiarization method. However, the difference between own- and other-race accuracy was larger when faces were familiarized sequentially in comparison to familiarization with arrays. Participants’ response patterns during testing differed depending on the combination of familiarization and testing method. Participants had more false alarms for other-race faces than own-race faces if they learned faces sequentially (regardless of testing strategy); if participants learned faces in arrays, they had more false alarms for other-race faces than own-races faces if ii i they were tested with sequentially presented faces. These results are consistent with the perceptual expertise model in that participants were better able to use the full two seconds in the sequential task for own-race faces, but not for other-race faces. The purpose of Experiment 2 was to examine participants’ attentional allocation in complex scenes. Participants were shown scenes comprising people in real places, but the head stimuli used in Experiment 1 were superimposed onto the bodies in each scene. Using a Tobii eyetracker, participants’ looking time for both own- and other-race faces was evaluated to determine whether participants looked longer at own-race faces and whether individual differences in looking time correlated with individual differences in recognition accuracy. The results of this experiment demonstrated that although own-race faces were preferentially attended to in comparison to other-race faces, individual differences in looking time biases towards own-race faces did not correlate with individual differences in own-race recognition advantages. These results are also consistent with perceptual expertise, as it seems that the role of attentional biases towards own-race faces is independent of the cognitive processing that occurs for own-race faces. All together, these results have implications for face perception tasks that are performed in the lab, how accurate people may be when remembering faces in the real world, and the accuracy and patterns of errors in eyewitness testimony.

Letter - Mrs. Olive Diefenbaker to Sean O'Sullivan, 6 December 1966

A handwritten letter from Olive Diefenbaker to Sean O'Sullivan, 6 December 1966. Mrs. Diefenbaker remarks about a phone call she received from a Hamiltonian who had met O'Sullivan at "the Convention" and had "'tried to help him over his disillusion"'. Mrs. Diefenbaker took offense to the comments and responded to the individual "I wouldn't worry about Sean. He is mature and wise, and will think his way through like the rest of us".

Elisha B. Sherwood letter, February 26, 1845

Elisha Barber Sherwood (1810-1905) was a Presbyterian minister. He began his career as a minister in the Church at Wilson, Niagara County, N.Y., subsequently becoming pastor at various churches in New York, Michigan, and Missouri. He is the author of Fifty Years on the Skirmish Line, a review of his ministerial work.

Wrestling Card - John Katan

The wrestler's name is John Katan and the number stamped on the reverse is 341. He was born in the Ukraine and moved to Lethbridge, Alberta and became a coal miner. He wrestled after work until he was discovered and went pro. He bought two wrestling franchises based in Hamilton and became a promoter when he retired from active wrestling. His honours include the Canadian Wrestling Hall of Fame.