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Scritical Pairs and Sunification
"... A general critical pair theory is given for rewriting many sorted terms with overloaded operations modulo equations. A main notion is sunification, which yields a set of scritical pairs, such that a set of rules is locally confluent iff they all converge. We prove a sufficient condition for overlaps ..."
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A general critical pair theory is given for rewriting many sorted terms with overloaded operations modulo equations. A main notion is sunification, which yields a set of scritical pairs, such that a set of rules is locally confluent iff they all converge. We prove a sufficient condition for overlaps to work instead of sunification, show that complete sunifier sets always exist, and are finite in important special cases. We also sketch a generalization based on category theory, for rewriting in free objects, e.g., algebras with additional structure, such as many sorts, ordered sorts, equationally defined subsorts, or continuity.
NOTES FOR THE CONCEPTUAL DESIGN OF INTERFACES
"... This paper presents a design method for user interfaces based on some ideas from conversation analysis. The method uses interaction diagram and it is conceived to design way, as an architectural prolegomenon to the designer’s choice of the actual interface elements that will be used. 1 Introduction. ..."
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This paper presents a design method for user interfaces based on some ideas from conversation analysis. The method uses interaction diagram and it is conceived to design way, as an architectural prolegomenon to the designer’s choice of the actual interface elements that will be used. 1 Introduction. The art of design is an art of abstraction. A design is the specification of certain structural relations between components; a specification that abstracts, on one hand, from the characteristics of the components that are not relevant for the structure of the whole and, on the other hand, from those structural relations that can be dispensed with at the level of
Webbased Multimedia Support for Distributed Cooperative Software Engineering
 In Proceedings, International Symposium on Multimedia Software Engineering
, 2000
"... The Tatami project is building a system to support software engineering over the internet, exploiting recent advances in web technology, interface design, and specification. Our effort to improve the usability of such systems led us into algebraic semiotics, while our effort to develop better formal ..."
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The Tatami project is building a system to support software engineering over the internet, exploiting recent advances in web technology, interface design, and specification. Our effort to improve the usability of such systems led us into algebraic semiotics, while our effort to develop better formal methods for distributed concurrent systems led us into hidden algebra. We discuss the Tatami system design, especially user interface issues, and sketch an extension of algebraic semiotics for interface dynamics. 1 Introduction The Tatami project has pursued three main goals: 1. explore novel multimedia interface design principles, for easing the use of complex interactive systems; 2. build and use a generic distributed environment for cooperative work; and 3. verify distributed concurrent software. We discuss these goals in turn. The first is motivated by the difficulties many practicing engineers have with formal methods tools. We have taken theorem provers as a typically difficult c...
1 9/4/05 Mathematics and Narrative
"... For over two millennia, it has seemed irresistible to imagine that the essence of all reality lies in numbers, and that a transcendent system of mathematics, if we could only know it synoptically, cosmically, would provide the answers to our questions. The Pythagorean insight that the capacious and ..."
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For over two millennia, it has seemed irresistible to imagine that the essence of all reality lies in numbers, and that a transcendent system of mathematics, if we could only know it synoptically, cosmically, would provide the answers to our questions. The Pythagorean insight that the capacious and sensory world of music is an avatar of ratios of numbers, and that, as a result, melody and harmony carry mathematical patterns, must have seemed like a revelation. The idea that mathematics lies somehow behind everything has motivated inquiry since the Ancient Greeks. If music—from Pythagoras to fractals—can be mathematics, and the heavens and their motions can be mathematics, perhaps human biology and even the soul are mathematical systems, to be tuned like stringed instruments to their perfect order. This impulse to seek the essence of reality in mathematics is compelling. As an undergraduate student, I hoped to find within mathematics some technical instruments sufficient to describe the human central nervous system and the brain. The impulse to do so was not mystical or merely reductionistic. The human brain has on the order of 10 to
Systems Synthesis: Towards a new paradigm and discipline for knowledge, software, and system development and maintenance
, 2001
"... This paper motivates and describes a new paradigm and discipline for knowledge, software, and system development and maintenance. This paradigm promises to improve system quality and make systems development and maintenance faster and cheaper. ..."
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This paper motivates and describes a new paradigm and discipline for knowledge, software, and system development and maintenance. This paradigm promises to improve system quality and make systems development and maintenance faster and cheaper.
On HighLevel LowLevel Programming
, 2002
"... The current solution for ecient highlevel parallel programming in the industry is to use directives to the compiler. However these directives pose two problems: rst, they are often designed in an ad hoc manner and their subtleties are less easy to understand than the rest of the language; second, ..."
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The current solution for ecient highlevel parallel programming in the industry is to use directives to the compiler. However these directives pose two problems: rst, they are often designed in an ad hoc manner and their subtleties are less easy to understand than the rest of the language; second, the degree of stringency of the directives is not xed, so that evaluating the eciency of the directives he writes is not easy for the programmer. This article proposes a methodology for addressing these issues. The data mapping directives of the language High Performance Fortran are used as an example; in particular, it is shown how the use of formal semantics can help clarify and structure the issues.
Signs and Representations: Semiotics
 In Procs. Workshop in Computing
, 1998
"... The use of semiotics has been proposed in studying the ways in which information is mediated in computer systems, particularly in user interfaces. ..."
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The use of semiotics has been proposed in studying the ways in which information is mediated in computer systems, particularly in user interfaces.
Unformatted version of the paper. Final formatting done
, 2002
"... this articles accept the latter view, and argue that, on such a view, it is inconceivable to research intelligence (natural or artificial) without studying creativity ..."
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this articles accept the latter view, and argue that, on such a view, it is inconceivable to research intelligence (natural or artificial) without studying creativity
470 1 Some Considerations Regarding Mathematical Semiosis
"... Abstract: The discussion on the possibility of machines to achieve semiosis (meaning process) is a very controversial debate within Artificial Intelligence and Cognitive Science. In this work, we define meaning process in an entirely mathematical framework. We call the “transposition ” of the Peirce ..."
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Abstract: The discussion on the possibility of machines to achieve semiosis (meaning process) is a very controversial debate within Artificial Intelligence and Cognitive Science. In this work, we define meaning process in an entirely mathematical framework. We call the “transposition ” of the Peircean theory to an abstract mathematical model as “Mathematical Semiosis”. By doing this, we aim at growing a more understandable theory for explaining what is to mean, in a strictly mathematical sense, avoiding complications related to the connection of signs to a real world. The main application of such a theory would be in order to develop machines with these capabilities. In such a regard, what we are calling here "Mathematical Semiosis " would be a kind of purely mathematical abstraction for what is "Semiosis" in the real world.