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316
A Mathematical Framework for the Study of Coevolution
 Foundations of Genetic Algorithms 7
, 2003
"... Despite achieving compelling results in engineering and optimization problems, coevolutionary algorithms remain difficult to understand, with most knowledge to date coming from practical successes and failures, not from theoretical understanding. Thus, explaining why coevolution succeeds is still ..."
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Cited by 35 (11 self)
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Despite achieving compelling results in engineering and optimization problems, coevolutionary algorithms remain difficult to understand, with most knowledge to date coming from practical successes and failures, not from theoretical understanding. Thus, explaining why coevolution succeeds is still more art than science. In this paper, we present a theoretical framework for studying coevolution based on the mathematics of ordered sets.
A 2Categorical Presentation of Term Graph Rewriting
 CATEGORY THEORY AND COMPUTER SCIENCE, VOLUME 1290 OF LNCS
, 1997
"... It is wellknown that a term rewriting system can be faithfully described by a cartesian 2category, where horizontal arrows represent terms, and cells represent rewriting sequences. In this paper we propose a similar, original 2categorical presentation for term graph rewriting. Building on a re ..."
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Cited by 34 (17 self)
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It is wellknown that a term rewriting system can be faithfully described by a cartesian 2category, where horizontal arrows represent terms, and cells represent rewriting sequences. In this paper we propose a similar, original 2categorical presentation for term graph rewriting. Building on a result presented in [8], which shows that term graphs over a given signature are in onetoone correspondence with arrows of a gsmonoidal category freely generated from the signature, we associate with a term graph rewriting system a gsmonoidal 2category, and show that cells faithfully represent its rewriting sequences. We exploit the categorical framework to relate term graph rewriting and term rewriting, since gsmonoidal (2)categories can be regarded as "weak" cartesian (2)categories, where certain (2)naturality axioms have been dropped.
Algebraic GraphBased Approach to Management of MultiBase Systems,II: Mathematical Aspects of Schema Integration
 TR9502, FRAME INFORM SYSTEMS
, 1995
"... ..."
View merging in the presence of incompleteness and inconsistency
 Requir. Eng
, 2006
"... View merging, also called view integration, is a key problem in conceptual modeling. Large models are often constructed and accessed by manipulating individual views, but it is important to be able to consolidate a set of views to gain a unified perspective, to understand interactions between views, ..."
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Cited by 33 (10 self)
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View merging, also called view integration, is a key problem in conceptual modeling. Large models are often constructed and accessed by manipulating individual views, but it is important to be able to consolidate a set of views to gain a unified perspective, to understand interactions between views, or to perform various types of analysis. View merging is complicated by incompleteness and inconsistency: Stakeholders often have varying degrees of confidence about their statements. Their views capture different but overlapping aspects of a problem, and may have discrepancies over the terminology being used, the concepts being modeled, or how these concepts should be structured. Once views are merged, it is important to be able to trace the elements of the merged view back to their sources and to the merge assumptions related to them. In this paper, we present a framework for merging incomplete and inconsistent graphbased views. We introduce a formalism, called annotated graphs, with a builtin annotation scheme for modeling incompleteness and inconsistency. We show how structurepreserving maps can be employed to express the relationships between disparate views modeled as annotated graphs, and provide a general algorithm for merging views with arbitrary interconnections. We provide a systematic way to generate and represent the traceability information required for tracing the merged view elements back to their sources, and to the merge assumptions giving rise to the elements.
Combining effects: sum and tensor
"... We seek a unified account of modularity for computational effects. We begin by reformulating Moggi’s monadic paradigm for modelling computational effects using the notion of enriched Lawvere theory, together with its relationship with strong monads; this emphasises the importance of the operations ..."
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Cited by 29 (4 self)
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We seek a unified account of modularity for computational effects. We begin by reformulating Moggi’s monadic paradigm for modelling computational effects using the notion of enriched Lawvere theory, together with its relationship with strong monads; this emphasises the importance of the operations that produce the effects. Effects qua theories are then combined by appropriate bifunctors on the category of theories. We give a theory for the sum of computational effects, which in particular yields Moggi’s exceptions monad transformer and an interactive input/output monad transformer. We further give a theory of the commutative combination of effects, their tensor, which yields Moggi’s sideeffects monad transformer. Finally we give a theory of operation transformers, for redefining operations when adding new effects; we derive explicit forms for the operation transformers associated to the above monad transformers.
Formalising Ontologies and Their Relations
 In Proceedings of DEXA’99
, 1999
"... . Ontologies allow the abstract conceptualisation of domains, but a given domain can be conceptualised through many different ontologies, which can be problematic when ontologies are used to support knowledge sharing. We present a formal account of ontologies that is intended to support knowledg ..."
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Cited by 28 (1 self)
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. Ontologies allow the abstract conceptualisation of domains, but a given domain can be conceptualised through many different ontologies, which can be problematic when ontologies are used to support knowledge sharing. We present a formal account of ontologies that is intended to support knowledge sharing through precise characterisations of relationships such as compatibility and refinement. We take an algebraic approach, in which ontologies are presented as logical theories. This allows us to characterise relations between ontologies as relations between their classes of models. A major result is cocompleteness of specifications, which supports merging of ontologies across shared subontologies. 1 Introduction Over the last decade ontologies  best characterised as explicit specifications of a conceptualisation of a domain [17]  have become increasingly important in the design and development of knowledge based systems, and for knowledge representations generally. They...
Computational Comonads and Intensional Semantics
, 1991
"... We explore some foundational issues in the development of a theory of intensional semantics. A programming language may be given a variety of semantics, differing in the level of abstraction; one generally chooses the semantics at an abstraction level appropriate for reasoning about a particular kin ..."
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Cited by 27 (1 self)
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We explore some foundational issues in the development of a theory of intensional semantics. A programming language may be given a variety of semantics, differing in the level of abstraction; one generally chooses the semantics at an abstraction level appropriate for reasoning about a particular kind of program property. Extensional semantics are typically appropriate for proving properties such as partial correctness, but an intensional semantics at a lower abstraction level is required in order to reason about computation strategy and thereby support reasoning about intensional aspects of behavior such as order of evaluation and efficiency. It is obviously desirable to be able to establish sensible relationships between two semantics for the same language, and we seek a general categorytheoretic framework that permits this. Beginning with an "extensional" category, whose morphisms we can think of as functions of some kind, we model a notion of computation as a comonad with certain e...
Analysis of inconsistency in graphbased viewpoints
 In ASE
, 2003
"... Eliciting the requirements for a proposed system typically involves different stakeholders with different expertise, responsibilities, and perspectives. Viewpointsbased approaches have been proposed as a way to manage incomplete and inconsistent models gathered from multiple sources. In this paper, ..."
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Cited by 27 (11 self)
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Eliciting the requirements for a proposed system typically involves different stakeholders with different expertise, responsibilities, and perspectives. Viewpointsbased approaches have been proposed as a way to manage incomplete and inconsistent models gathered from multiple sources. In this paper, we propose a categorytheoretic framework for the analysis of fuzzy viewpoints. Informally, a fuzzy viewpoint is a graph in which the elements of a lattice are used to specify the amount of knowledge available about the details of nodes and edges. By defining an appropriate notion of morphism between fuzzy viewpoints, we construct categories of fuzzy viewpoints and prove that these categories are (finitely) cocomplete. We then show how colimits can be employed to merge the viewpoints and detect the inconsistencies that arise independent of any particular choice of viewpoint semantics. We illustrate an application of the framework through a casestudy showing how fuzzy viewpoints can serve as a requirements elicitation tool in reactive systems. 1
Fibring NonTruthFunctional Logics: Completeness Preservation
 Journal of Logic, Language and Information
, 2000
"... Fibring has been shown to be useful for combining logics endowed with truthfunctional semantics. One wonders if bring can be extended in order to cope with logics endowed with nontruthfunctional semantics as, for example, paraconsistent logics. The rst main contribution of the paper is a po ..."
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Cited by 26 (20 self)
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Fibring has been shown to be useful for combining logics endowed with truthfunctional semantics. One wonders if bring can be extended in order to cope with logics endowed with nontruthfunctional semantics as, for example, paraconsistent logics. The rst main contribution of the paper is a positive answer to this question. Furthermore, it is shown that this extended notion of bring preserves completeness under certain reasonable conditions. This completeness transfer result, the second main contribution of the paper, generalizes the one established by Zanardo et al. and is obtained using a new technique exploiting the properties of the metalogic where the (possibly nontruthfunctional) valuations are de ned. The modal paraconsistent logic of da Costa and Carnielli is obtained by bring and its completeness is so established.