Lori Lorigo

In Google We Trust: Users’ Decisions on Rank, Position, and Relevance

An eye tracking experiment revealed that college student users have substantial trust in Google’s ability to rank results by their true relevance to the query. When the participants selected a link to follow from Google’s result pages, their decisions were strongly biased towards links higher in position even if the abstracts themselves were less relevant. While the participants reacted to artificially reduced retrieval quality by greater scrutiny, they failed to achieve the same success rate. This demonstrated trust in Google has implications for the search engine’s tremendous potential influence on culture, society, and user traffic on the Web.

Innovations in computational type theory using Nuprl

Abstract For twenty years the Nuprl (“new pearl”) system has been used to develop software systems and formal theories of computational mathematics. It has also been used to explore and implement computational type theory (CTT)—a formal theory of computation closely related to Martin-Lofs intuitionistic type theory (ITT) and to the calculus of inductive constructions (CIC) implemented in the Coq prover. This article focuses on the theory and practice underpinning our use of Nuprl for much of the last decade. We discuss innovative elements of type theory, including new type constructors such as unions and dependent intersections, our theory of classes, and our theory of event structures. We also discuss the innovative architecture of Nuprl as a distributed system and as a transactional database of formal mathematics using the notion of abstract object identifiers. The database has led to an independent project called the Formal Digital Library, FDL, now used as a repository for Nuprl results as well as selected results from HOL, MetaPRL, and PVS. We discuss Howes set theoretic semantics that is used to relate such disparate theories and systems as those represented by these provers.

The Nuprl Open Logical Environment

The Nuprl system is a framework for reasoning about mathematics and programming. Over the years its design has been substantially improved to meet the demands of large-scale applications. Nuprl LPE, the newest release, features an open, distributed architecture centered around a flexible knowledge base and supports the cooperation of independent formal tools. This paper gives a brief overview of the system and the objectives that are addressed by its new architecture.

MetaPRL – A Modular Logical Environment

MetaPRL is the latest system to come out of over twenty five years of research by the Cornell PRL group. While initially created at Cornell, MetaPRL is currently a collaborative project involving several universities in several countries. The MetaPRL system combines the properties of an interactive LCF-style tactic-based proof assistant, a logical framework, a logical programming environment, and a formal methods programming toolkit. MetaPRL is distributed under an open-source license and can be downloaded from http://metaprl.org/. This paper provides an overview of the system focusing on the features that did not exist in the previous generations of PRL systems.

JProver: Integrating Connection-Based Theorem Proving into Interactive Proof Assistants

JProver is a first-order intuitionistic theorem prover that creates sequent-style proof objects and can serve as a proof engine in interactive proof assistants with expressive constructive logics. This paper gives a brief overview of JProvers proof technique, the generation of proof objects, and its integration into the Nuprl proof development system.

A Graph-Based Approach Towards Discerning Inherent Structures in a Digital Library of Formal Mathematics

As the amount of online formal mathematical content grows, for example through active efforts such as the Mathweb [21], MOWGLI [4], Formal Digital Library, or FDL [1], and others, it becomes increasingly valuable to find automated means to manage this data and capture semantics such as relatedness and significance. We apply graph-based approaches, such as HITS, or Hyperlink Induced Topic Search, [11] used for World Wide Web document search and analysis, to formal mathematical data collections. The nodes of the graphs we analyze are theorems and definitions, and the links are logical dependencies. By exploiting this link structure, we show how one may extract organizational and relatedness information from a collection of digital formal math. We discuss the value of the information we can extract, yielding potential applications in math search tools, theorem proving, and education.

Using Formal Reference to Enhance Authority and Integrity in Online Mathematical Texts

The amount and variety of digital information readily available to the public has become one of the defining features of the intellectual and scientific landscape. Digital information is bringing to the forefront new questions for computing and information science, e.g., how should this information be organized, searched, and evaluated. Universities, publishers, government, and other esteemed professionals bring unique and essential value to this enterprise that goes beyond their support of research – namely, intellectual authority. The imprimatur given to the information resources they own or sponsor is essential in helping individuals assess the validity of what they encounter on the Web.