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100
Understanding Open Source Software Evolution
 Applying, Breaking, and Rethinking the Laws of Software Evolution
, 2003
"... This chapter examines the evolution of open source software and how their evolutionary patterns compare to prior studies of software evolution of proprietary (or closed source) software. Free or open source software (F/OSS) development focuses attention to systems like the GNU/Linux operating system ..."
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Cited by 18 (5 self)
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This chapter examines the evolution of open source software and how their evolutionary patterns compare to prior studies of software evolution of proprietary (or closed source) software. Free or open source software (F/OSS) development focuses attention to systems like the GNU/Linux operating system, Apache Web server, and Mozilla Web browser,
Variations by complexity theorists on three themes of
 Computational Complexity
, 2005
"... This paper surveys some connections between geometry and complexity. A main role is played by some quantities —degree, Euler characteristic, Betti numbers — associated to algebraic or semialgebraic sets. This role is twofold. On the one hand, lower bounds on the deterministic time (sequential and pa ..."
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Cited by 12 (4 self)
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This paper surveys some connections between geometry and complexity. A main role is played by some quantities —degree, Euler characteristic, Betti numbers — associated to algebraic or semialgebraic sets. This role is twofold. On the one hand, lower bounds on the deterministic time (sequential and parallel) necessary to decide a set S are established as functions of these quantities associated to S. The optimality of some algorithms is obtained as a consequence. On the other hand, the computation of these quantities gives rise to problems which turn out to be hard (or complete) in different complexity classes. These two kind of results thus turn the quantities above into measures of complexity in two quite different ways. 1
Formal proof—theory and practice
 Notices AMS
, 2008
"... Aformal proof is a proof written in a precise artificial language that admits only a fixed repertoire of stylized steps. This formal language is usually designed so that there is a purely mechanical process by which the correctness of a proof in the language can be verified. Nowadays, there are nume ..."
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Aformal proof is a proof written in a precise artificial language that admits only a fixed repertoire of stylized steps. This formal language is usually designed so that there is a purely mechanical process by which the correctness of a proof in the language can be verified. Nowadays, there are numerous computer programs known as proof assistants that can check, or even partially construct, formal proofs written in their preferred proof language. These can be considered as practical, computerbased realizations of the traditional systems of formal symbolic logic and set theory proposed as foundations for mathematics. Why should we wish to create formal proofs?
On dynamically presenting a topology course
 Annals of Mathematics and Artificial Intelligence
, 2001
"... www.cs.mdx.ac.uk/imp Authors of traditional mathematical texts often have difficulty balancing the amount of contextual information and proof detail. We propose a simple hypermedia framework that can assist in the organisation and presentation of mathematical theorems and definitions. We describe th ..."
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Cited by 10 (5 self)
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www.cs.mdx.ac.uk/imp Authors of traditional mathematical texts often have difficulty balancing the amount of contextual information and proof detail. We propose a simple hypermedia framework that can assist in the organisation and presentation of mathematical theorems and definitions. We describe the application of the framework to convert an existing course in general topology to a webbased set of materials. A pilot study of the materials indicated a high level of user satisfaction. We discuss further lines of investigation, in particular, the presentation of larger bodies of work. 1
CHIRON: Planning in an Opentextured Domain
, 1994
"... Most work in artificial intelligence and law has concentrated on modelling the type of reasoning done by trial lawyers. In fact, most lawyers' work involves planning  for example, wills and trusts, real estate deals, and business mergers and acquisitions. Certain planning issues, such as the use o ..."
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Cited by 10 (4 self)
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Most work in artificial intelligence and law has concentrated on modelling the type of reasoning done by trial lawyers. In fact, most lawyers' work involves planning  for example, wills and trusts, real estate deals, and business mergers and acquisitions. Certain planning issues, such as the use of underspecified, or "opentextured" rules, are illustrated especially clearly in this domain. In this thesis, I set forth the characteristic features of planning in law, place it in the context of past artificial intelligence work in both law and planning, and describe CHIRON, a system that I have developed implementing my theory of opentextured planning in the domain of personal income tax law.
Qualitative Reasoning beyond the Physics Domain: The Density Dependence Theory of Organizational Ecology
 Proceedings of QR95
, 1995
"... Abstract: Qualitative reasoning is traditionally associated with the domain of physics, although the domain of application is, in fact, much broader. This paper investigates the application of qualitative reasoning beyond the domain of physics. It presents a case study of application in the social s ..."
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Abstract: Qualitative reasoning is traditionally associated with the domain of physics, although the domain of application is, in fact, much broader. This paper investigates the application of qualitative reasoning beyond the domain of physics. It presents a case study of application in the social sciences: the density dependence theory of organizational ecology. It discusses how the different nature of soft science domains will complicate the process of model building. Furthermore, it shows that the “model building ” process can also help making theoretically important decisions, and, as a result, have an impact on the original theory. This will require a shift in focus from the “model simulation ” process towards the “model building ” process. 1
Mathematical proofs at a crossroad
 Theory Is Forever, Lectures Notes in Comput. Sci. 3113
, 2004
"... Abstract. For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomaticdeductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimen ..."
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Abstract. For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomaticdeductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimental, psychological and social aspects, yesterday only marginal, but now changing radically the very essence of proof. In this paper, we try to organize this evolution, to distinguish its different steps and aspects, and to evaluate its advantages and shortcomings. Axiomaticdeductive proofs are not a posteriori work, a luxury we can marginalize nor are computerassisted proofs bad mathematics. There is hope for integration! 1
Formal Theory Building Using Automated Reasoning Tools
 In
, 1998
"... The merits of representing scientific theories in formal logic are wellknown. Expressing a scientific theory in formal logic explicates the theory as a whole, and the logic provides formal criteria for evaluating the theory, such as soundness and consistency. On the one hand, these criteria corresp ..."
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Cited by 6 (6 self)
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The merits of representing scientific theories in formal logic are wellknown. Expressing a scientific theory in formal logic explicates the theory as a whole, and the logic provides formal criteria for evaluating the theory, such as soundness and consistency. On the one hand, these criteria correspond to natural questions to be asked about the theory: is the theory contradictionfree? (is the theory logically consistent?) is the theoretical argumentation valid? (can a theorem be soundly derived from the premises?) and other such questions. On the other hand, testing for these criteria amounts to making many specific proof attempts or model searches: respectively, does the theory have a model? can we find a proof of a particular theorem? As a result, testing for these criteria quickly defies manual processing. Fortunately, automated reasoning provides some valuable tools for this endeavor. This paper discusses the use of firstorder logic and existing automated rea...
Computers, Reasoning and Mathematical Practice
"... ion in itself is not the goal: for Whitehead [117]"it is the large generalisation, limited by a happy particularity, which is the fruitful conception." As an example consider the theorem in ring theory, which states that if R is a ring, f(x) is a polynomial over R and f(r) = 0 for every element of ..."
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ion in itself is not the goal: for Whitehead [117]"it is the large generalisation, limited by a happy particularity, which is the fruitful conception." As an example consider the theorem in ring theory, which states that if R is a ring, f(x) is a polynomial over R and f(r) = 0 for every element of r of R then R is commutative. Special cases of this, for example f(x) is x 2 \Gamma x or x 3 \Gamma x, can be given a first order proof in a few lines of symbol manipulation. The usual proof of the general result [20] (which takes a semester's postgraduate course to develop from scratch) is a corollary of other results: we prove that rings satisfying the condition are semisimple artinian, apply a theorem which shows that all such rings are matrix rings over division rings, and eventually obtain the result by showing that all finite division rings are fields, and hence commutative. This displays von Neumann's architectural qualities: it is "deep" in a way in which the symbol manipulati...