Probabilistic Justification Logic

We present a probabilistic justification logic, PPJ, to study rational belief, degrees of belief and justifications. We establish soundness and completeness for PPJ and show that its satisfiability problem is decidable. In the last part we use PPJ to provide a solution to the lottery paradox.

Sermon notes compiled by Warham Williams, 1716-1718

Parchment-bound notebook containing notes kept by Warham Williams on sermons he attended between May 20, 1716 and April 20, 1718, while he was an undergraduate at Harvard College. The notebook includes two chronological tables, at the front and end of the volume, that list the town, lecturer (generally Harvard tutors), biblical text, year, month, day, and part of the day of sermons attended by Williams. The volume contains one-to-two page entries on specific sermons and provides the biblical text and related questions and conclusions. From the front of the volume, the pages contain entries for sermons attended between May 20, 1716 through February 13, 1717. Sermon entries for April 7, 1717 to April 20 1718 are written tête-bêche from the other end of the volume.

Student essay composed by Edmund Toppan, 1795

Four-page handwritten student essay composed in English by Edmund Toppan as a Harvard undergraduate. The verso of the last page is inscribed "Toppan June 22'd 1795." The essay is titled with a quote from Horace: "Qui non moderabitur irae, Infectum volet esse, dolor quod suaserit et mens." The essay discusses the destructive force of uncontrolled passion and begins, "Last evening, having a very disagreeable head-ache, I early retired to bed."

Sermon on redemption by David Tappan, 1781

Sewn notebook containing a forty-six page handwritten sermon composed by David Tappan based on the Biblical text Isaiah 65: 17, 18 and the subject of redemption. Tappan delivered the sermon multiple times as evidenced by the note on the first page, "March 11, 18, 25 Spring April 1781 Frisbee July 1782, Byfield July 1783, Lynn, Kimball. Dr. Huntington, Deerfield, French, Merrill, Dana."

New Hampshire, 1816 (Image 3 of 6) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: New Hampshire by recent survey : made under the supreme authority and published according to law by Philip Carrigain ; J.J. Barralet, del. ; W. Harrison, sct., Philada. It was published by Philip Carrigain in 1816. Scale [ca. 1:200,000]. This layer is image 3 of 6 total images, representing the southeast portion of the six sheet source map. The image inside the map neatline is georeferenced to the surface of the earth and fit to the New Hampshire State Plane coordinate system (NAD 1983 in Feet) (Fipszone 2800). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, drainage, public buildings, schools, churches, industry locations (e.g. mills, factories, mines, etc.), selected private buildings with names of property owners, town boundaries, land grants, and more. Relief shown pictorially and by hachures. Includes area notes, text, and table of population. Also includes illustrations: View of the Great Boars Head and Hampton Beach -- The Cap of the White Mountains -- View of the White Mountains from Shelburne; inset maps: States of the Union east of the Hudson with the adjacent British colonies. Scale [ca. 1:1,920,000] -- The middle, southern and western sections of the United States with the territories. Scale [ca. 1:4,900,000]. Includes: ms. additions with updated county boundary & township names.This layer is part of a selection of digitally scanned and georeferenced historic maps of New England from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of regions, originators, ground condition dates, scales, and map purposes.

New Hampshire, 1816 (Image 4 of 6) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: New Hampshire by recent survey : made under the supreme authority and published according to law by Philip Carrigain ; J.J. Barralet, del. ; W. Harrison, sct., Philada. It was published by Philip Carrigain in 1816. Scale [ca. 1:200,000]. This layer is image 4 of 6 total images, representing the southwest portion of the six sheet source map. The image inside the map neatline is georeferenced to the surface of the earth and fit to the New Hampshire State Plane coordinate system (NAD 1983 in Feet) (Fipszone 2800). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, drainage, public buildings, schools, churches, industry locations (e.g. mills, factories, mines, etc.), selected private buildings with names of property owners, town boundaries, land grants, and more. Relief shown pictorially and by hachures. Includes area notes, text, and table of population. Also includes illustrations: View of the Great Boars Head and Hampton Beach -- The Cap of the White Mountains -- View of the White Mountains from Shelburne; inset maps: States of the Union east of the Hudson with the adjacent British colonies. Scale [ca. 1:1,920,000] -- The middle, southern and western sections of the United States with the territories. Scale [ca. 1:4,900,000]. Includes: ms. additions with updated county boundary & township names.This layer is part of a selection of digitally scanned and georeferenced historic maps of New England from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of regions, originators, ground condition dates, scales, and map purposes.

Rockingham County, New Hampshire, 1857 (Image 3 of 4) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Map of Rockingham Co., New Hampshire, by actual surveys by J. Chace, Junr. It was published by Smith and Coffin in 1857. Scale [ca 1:15,840]. This layer is image 3 of 4 total images, representing the southwest portion of the four sheet source map. The image inside the map neatline is georeferenced to the surface of the earth and fit to the New Hampshire State Plane coordinate system (NAD 1983 in Feet) (Fipszone 2800). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, railroads, drainage, public buildings, schools, churches, cemeteries, industry locations (e.g. mills, factories, mines, etc.), private buildings with names of property owners, town boundaries, and more. It includes many cadastral insets of individual county towns and villages. It also includes illustrations, business directories, and tables of statistics and distances.This layer is part of a selection of digitally scanned and georeferenced historic maps of New England from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of regions, originators, ground condition dates, scales, and map purposes.

Rockingham County, New Hampshire, 1857 (Image 4 of 4) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Map of Rockingham Co., New Hampshire, by actual surveys by J. Chace, Junr. It was published by Smith and Coffin in 1857. Scale [ca 1:15,840]. This layer is image 4 of 4 total images, representing the northwest portion of the four sheet source map. The image inside the map neatline is georeferenced to the surface of the earth and fit to the New Hampshire State Plane coordinate system (NAD 1983 in Feet) (Fipszone 2800). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, railroads, drainage, public buildings, schools, churches, cemeteries, industry locations (e.g. mills, factories, mines, etc.), private buildings with names of property owners, town boundaries, and more. It includes many cadastral insets of individual county towns and villages. It also includes illustrations, business directories, and tables of statistics and distances.This layer is part of a selection of digitally scanned and georeferenced historic maps of New England from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of regions, originators, ground condition dates, scales, and map purposes.

Franklin County, Massachusetts, 1858 (Image 1 of 3) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Map of Franklin County, Massachusetts : based upon the trigonometrical survey of the state, the details from actual surveys under the direction of H.F. Walling, supt. of the state map. It was published by Smith & Ingraham in 1858. Scale [ca. 1:47,520]. This layer is image 1 of 3 total images, representing the northwest portion of the four sheet source map. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Massachusetts State Plane Coordinate System, Mainland Zone (in Feet) (Fipszone 2001). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, railroads, drainage, public buildings, schools, churches, cemeteries, industry locations (e.g. mills, factories, mines, etc.), private buildings with names of property owners, town and school district boundaries, and more. Relief shown by hachures. It includes many cadastral insets of individual county towns and villages. It also includes illustrations, business directories, and tables of statistics and distances.This layer is part of a selection of digitally scanned and georeferenced historic maps of Massachusetts from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of regions, originators, ground condition dates (1755-1922), scales, and purposes. The digitized selection includes maps of: the state, Massachusetts counties, town surveys, coastal features, real property, parks, cemeteries, railroads, roads, public works projects, etc.

Franklin County, Massachusetts, 1858 (Image 3 of 3) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Map of Franklin County, Massachusetts : based upon the trigonometrical survey of the state, the details from actual surveys under the direction of H.F. Walling, supt. of the state map. It was published by Smith & Ingraham in 1858. Scale [ca. 1:47,520]. This layer is image 3 of 3 total images, representing the northeast portion of the four sheet source map. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Massachusetts State Plane Coordinate System, Mainland Zone (in Feet) (Fipszone 2001). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, railroads, drainage, public buildings, schools, churches, cemeteries, industry locations (e.g. mills, factories, mines, etc.), private buildings with names of property owners, town and school district boundaries, and more. Relief shown by hachures. It includes many cadastral insets of individual county towns and villages. It also includes illustrations, business directories, and tables of statistics and distances.This layer is part of a selection of digitally scanned and georeferenced historic maps of Massachusetts from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of regions, originators, ground condition dates (1755-1922), scales, and purposes. The digitized selection includes maps of: the state, Massachusetts counties, town surveys, coastal features, real property, parks, cemeteries, railroads, roads, public works projects, etc.

Greenfield, Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic of the historic 15-minute USGS topographic map of the Greenfield, Massachusetts quadrangle. The survey date (ground condition) of this map is 1886 and 1887; the edition date is September, 1894. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map. The names of quadrangles which border this one appear on the map collar in their respective positions (N,S,E,W) in relation to this map.

Northampton, Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic of the historic 15-minute USGS topographic map of the Northampton, Massachusetts quadrangle. The survey date (ground condition) of the original paper map is 1884-1885, the edition date is July, 1895 and this map has a reprint date of April 1909. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map.

Massachusetts drainage basin studies : from field surveys and data /

no. 1. Blackstone River -- no. 3. Farmington River -- no. 4. Millers River -- no. 5. Deerfield River -- no. 6. Westfield River -- no. 7. Chicopee River.