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A Framework for Defining Logics
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1993
"... The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of arities. T ..."
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Cited by 696 (39 self)
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The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of arities. The treatment of rules and proofs focuses on his notion of a judgement. Logics are represented in LF via a new principle, the judgements as types principle, whereby each judgement is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurrence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higherorder judgements and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logicindependent tools such as proof editors and proof checkers can be constructed.
Some Theories With Positive Induction of Ordinal Strength ...
 JOURNAL OF SYMBOLIC LOGIC
, 1996
"... This paper deals with: (i) the theory ID # 1 which results from c ID 1 by restricting induction on the natural numbers to formulas which are positive in the fixed point constants, (ii) the theory BON() plus various forms of positive induction, and (iii) a subtheory of Peano arithmetic with ord ..."
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Cited by 7 (3 self)
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This paper deals with: (i) the theory ID # 1 which results from c ID 1 by restricting induction on the natural numbers to formulas which are positive in the fixed point constants, (ii) the theory BON() plus various forms of positive induction, and (iii) a subtheory of Peano arithmetic with ordinals in which induction on the natural numbers is restricted to formulas which are \Sigma in the ordinals. We show that these systems have prooftheoretic strength '!0.
The µ Quantification Operator in Explicit Mathematics With Universes and Iterated Fixed Point Theories With Ordinals
, 1998
"... This paper is about two topics: 1. systems of explicit mathematics with universes and a nonconstructive quantification operator ¯; 2. iterated fixed point theories with ordinals. We give a prooftheoretic treatment of both families of theories; in particular, ordinal theories are used to get upper ..."
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Cited by 5 (3 self)
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This paper is about two topics: 1. systems of explicit mathematics with universes and a nonconstructive quantification operator ¯; 2. iterated fixed point theories with ordinals. We give a prooftheoretic treatment of both families of theories; in particular, ordinal theories are used to get upper bounds for explicit theories with finitely many universes. 1 Introduction The two major frameworks for explicit mathematics that were introduced in Feferman [4, 5] are the theories T 0 and T 1 . T 1 results from T 0 by strengthening the applicative axioms by the socalled nonconstructive ¯ operator. Although highly nonconstructive, ¯ is predicatively acceptable and makes quantification over the natural numbers explicit. While the proof theory of T 0 is wellknown since the early eighties (cf. Feferman [4, 5], Feferman and Sieg [10], Jager [14], Jager and Pohlers [17]), the corresponding investigations of subystems of T 1 have been completed only recently by Feferman and Jager [9, 8] and G...
The Unfolding of NonFinitist Arithmetic
, 2000
"... The unfolding of schematic formal systems is a novel concept which was initiated in Feferman [6]. This paper is mainly concerned with the prooftheoretic analysis of various unfolding systems for nonnitist arithmetic NFA. In particular, we examine two restricted unfoldings U 0 (NFA) and U 1 (NFA ..."
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Cited by 5 (3 self)
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The unfolding of schematic formal systems is a novel concept which was initiated in Feferman [6]. This paper is mainly concerned with the prooftheoretic analysis of various unfolding systems for nonnitist arithmetic NFA. In particular, we examine two restricted unfoldings U 0 (NFA) and U 1 (NFA), as well as a full unfolding, U(NFA). The principal results then state: (i) U 0 (NFA) is equivalent to PA; (ii) U 1 (NFA) is equivalent to RA<! ; (iii) U(NFA) is equivalent to RA< 0 . Thus U(NFA) is prooftheoretically equivalent to predicative analysis.
Business marketing: Present and future
 Journal oflt~dustrial Marketing and Purclrasittg
, 1987
"... Industrial marketing or the new term, business marketing, is the marketing of goods and services to industrial customers for use, in turn, in their own production of goods and services. The marketing of business goods and consumer goods have two attributes in common: a purchase is the usual outcome ..."
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Cited by 4 (1 self)
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Industrial marketing or the new term, business marketing, is the marketing of goods and services to industrial customers for use, in turn, in their own production of goods and services. The marketing of business goods and consumer goods have two attributes in common: a purchase is the usual outcome of the process and the result derives from some decisionmaking activities. In spite of these superficial similarities, business or industrial marketing problems must be handled differently from consumer marketing for several important reasons outlined below. (In what follows, we use the terms "business " and "industrial " marketing interchangeably.) This paper highlights areas of progress in structuring industrial marketing problems and outlines prospects for important new developments in the near future. The reasons for the consumer market/industrial market differences include the following: Derived Demand. One characteristic of the industrial goods market is
The NonConstructive µ Operator, Fixed Point Theories With Ordinals, and the Bar Rule
, 2000
"... This paper deals with the proof theory of first order applicative theories with nonconstructive operator and a form of the bar rule, yielding systems of ordinal strength 0 and '20, respectively. Relevant use is made of fixed point theories with ordinals plus bar rule. ..."
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Cited by 2 (2 self)
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This paper deals with the proof theory of first order applicative theories with nonconstructive operator and a form of the bar rule, yielding systems of ordinal strength 0 and '20, respectively. Relevant use is made of fixed point theories with ordinals plus bar rule.
On the Proof Theory of Applicative Theories
 PHD THESIS, INSTITUT FÜR INFORMATIK UND ANGEWANDTE MATHEMATIK, UNIVERSITÄT
, 1996
"... ..."
Fixed Point Theories and Dependent Choice
, 2000
"... In this paper we establish the prooftheoretic equivalence of (i) ATR and c ID ! , (ii) ATR 0 + (\Sigma 1 1 DC) and c ID !! ! , and (iii) ATR + (\Sigma 1 1 DC) and c ID !"0 . ..."
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Cited by 1 (0 self)
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In this paper we establish the prooftheoretic equivalence of (i) ATR and c ID ! , (ii) ATR 0 + (\Sigma 1 1 DC) and c ID !! ! , and (iii) ATR + (\Sigma 1 1 DC) and c ID !"0 .
Design, Analysis and Reasoning about Tools: Abstracts from the Second Workshop
, 1992
"... Introduction The secondDAR T workshoptookplaceonThursday August20'thandFriday August21'statLimfjordshotelletinAalborg.The primaryaimofthe workshopwastoincreasetheawarenessofDAR T participantsforeach other's work,andtostimulatecollaborationbetweenthedifierentgroups.Inadditiontothis, theThursday prog ..."
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Introduction The secondDAR T workshoptookplaceonThursday August20'thandFriday August21'statLimfjordshotelletinAalborg.The primaryaimofthe workshopwastoincreasetheawarenessofDAR T participantsforeach other's work,andtostimulatecollaborationbetweenthedifierentgroups.Inadditiontothis, theThursday programmewasplannedsoastobe ofinterest alsotocomputerscientistsnotparticipatinginDAR T; hencea numberof surveytalksaboutrecen tresearch werepresentedby thecontactpersonsfor each area. A briefoverviewofDAR T willbegivenintheremainderofthisIntroduction; foramoredetaileddescriptionpleaseconsultSection3of[95].Theremaining sectionslisttheabstractsofthetalksgiven(Section2),reportonthecurrent stateofactivities(Sections3 and 4)and give an overviewofallresearch publicationsfromDAR T participants(Section5). The DART projectconcernsthe\Design,Analysisand Reasoningabout Tools ".Itisfundedby theDanishResearch Councilsuntil1994andcomprisesresearchersatAarhusUniversity, University ofCopenhagenandAalborgUnivers
Joint Center for Housing Studies Harvard University Behaviorally Informed Home Mortgage Credit Regulation
, 2008
"... given to the source. ..."