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AN OVERVIEW OF MODERN UNIVERSAL ALGEBRA
"... This article, aimed specifically at young mathematical logicians, gives a gentle introduction to some of the central achievements and problems of universal algebra during the last 25 years. ..."
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This article, aimed specifically at young mathematical logicians, gives a gentle introduction to some of the central achievements and problems of universal algebra during the last 25 years.
Article revision 2007/08/18 A Tool for Logicians
"... Abstract turnstile is a LATEX package that allows typesetting of the mathematical logic symbol, “turnstile”, in all of the various ways it is used. This package was developed because there was no easy way in LATEX to typeset this symbol in its various forms, and place expressions above and below the ..."
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Abstract turnstile is a LATEX package that allows typesetting of the mathematical logic symbol, “turnstile”, in all of the various ways it is used. This package was developed because there was no easy way in LATEX to typeset this symbol in its various forms, and place expressions above and below
The emergence of firstorder logic
 University of Minnesota Press, Minneapolis
, 1988
"... To most mathematical logicians working in the 1980s, firstorder logic is the proper and natural framework for mathematics. Yet it was not always so. In 1923, when a young Norwegian mathematician named Thoralf Skolem argued that set theory should be based on firstorder logic, it was ..."
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Cited by 5 (0 self)
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To most mathematical logicians working in the 1980s, firstorder logic is the proper and natural framework for mathematics. Yet it was not always so. In 1923, when a young Norwegian mathematician named Thoralf Skolem argued that set theory should be based on firstorder logic, it was
Notation, Logical (see: Notation, Mathematical)
"... Notation is a conventional written system for encoding a formal axiomatic system. Notation governs: • the rules for assignment of written symbols to elements of the axiomatic system • the writing and interpretation rules for wellformed formulae in the axiomatic system • the derived writing and inte ..."
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of most mathematicians) that branch of mathematics (logicians, by contrast, tend to think of mathematics as a branch of logic; both metaphors are correct, in the appropriate formal axiomatic system) most concerned with many questions that arise in natural language,
Does Mathematics Need New Axioms?
 American Mathematical Monthly
, 1999
"... this article I will be looking at the leading question from the point of view of the logician, and for a substantial part of that, from the perspective of one supremely important logician: Kurt Godel. From the time of his stunning incompleteness results in 1931 to the end of his life, Godel called f ..."
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Cited by 23 (2 self)
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this article I will be looking at the leading question from the point of view of the logician, and for a substantial part of that, from the perspective of one supremely important logician: Kurt Godel. From the time of his stunning incompleteness results in 1931 to the end of his life, Godel called
Spider diagrams
"... The use of diagrams in mathematics has traditionally been restricted to guiding intuition and communication. With rare exceptions such as Peirce’s α and β systems, purely diagrammatic formal reasoning has not been in the mathematicians or logicians toolkit. This paper develops a purely diagrammatic ..."
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Cited by 94 (34 self)
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The use of diagrams in mathematics has traditionally been restricted to guiding intuition and communication. With rare exceptions such as Peirce’s α and β systems, purely diagrammatic formal reasoning has not been in the mathematicians or logicians toolkit. This paper develops a purely diagrammatic
Mathematical logic for life science ontologies
 DE QUEIROZ (EDS.), LOGIC, LANGUAGE, INFORMATION AND COMPUTATION, 16TH INT. WORKSHOP, WOLLIC 2009
, 2009
"... We discuss how concepts and methods introduced in mathematical logic can be used to support the engineering and deployment of life science ontologies. The required applications of mathematical logic are not straighforward and we argue that such ontologies provide a new and rich family of logical th ..."
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Cited by 4 (2 self)
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We discuss how concepts and methods introduced in mathematical logic can be used to support the engineering and deployment of life science ontologies. The required applications of mathematical logic are not straighforward and we argue that such ontologies provide a new and rich family of logical
Knowledge Representation and Classical Logic
, 2007
"... Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspe ..."
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Cited by 11 (5 self)
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Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from
Getting beyond Boole
 Information Processing & Management
, 1988
"... AbstractAlthough most computerbased information search systems in current use employ a Boolean search strategy, there is by no means a clear consensus throughout the information retrieval research community that the conventional Boolean approach is best. The wellknown drawbacks of the Boolean des ..."
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Cited by 25 (0 self)
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as Boolean combinations of document descriptors. This suggestion seemed to meet with the immediate approval of most mathematicians, computer scientists, and technically oriented information professionals. At that time only BarHillel, a mathematical logician, objected strenuously [I].
Alan Turing and the Mathematical Objection
 Minds and Machines 13(1
, 2003
"... Abstract. This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet accord ..."
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Cited by 5 (3 self)
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Abstract. This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet
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