21,655 research outputs found
Behavioral institutions and refinements in generalized hidden logics
We investigate behavioral institutions and refinements in the context of the object oriented paradigm. The novelty of our approach is the application of generalized abstract algebraic logic theory of hidden heterogeneous deductive systems (called hidden k-logics) to the algebraic specification of object oriented programs. This is achieved through the Leibniz congruence relation and its combinatorial properties. We reformulate the notion of hidden k-logic as well as the behavioral logic of a hidden k-logic as institutions. We define refinements as hidden signature morphisms having the extra property of preserving logical consequence. A stricter class of refinements, the ones that preserve behavioral consequence, is studied. We establish sufficient conditions for an ordinary signature morphism to be a behavioral refinement. © J.UCS.FCT via UIM
The foundational legacy of ASL
Abstract. We recall the kernel algebraic specification language ASL and outline its main features in the context of the state of research on algebraic specification at the time it was conceived in the early 1980s. We discuss the most significant new ideas in ASL and the influence they had on subsequent developments in the field and on our own work in particular.
Linear groups in Galois fields. A case study of tacit circulation of explicit knowledge
This preprint is the extended version of a paper that will be published in
the proceedings of the Oberwolfach conference "Explicit vs tacit knowledge in
mathematics" (January 2012). It presents a case study on some algebraic
researches at the turn of the twentieth century that involved mainly French and
American authors. By investigating the collective dimensions of these works,
this paper sheds light on the tension between the tacit and the explicit in the
ways some groups of texts hold together, thereby constituting some shared
algebraic cultures. Although prominent algebraists such as Dickson made
extensive references to papers published in France, and despite the roles
played by algebra and arithmetic in the development of the American
mathematical community, our knowledge of the circulations of knowledge between
France and the United States at the beginning of the 20th century is still very
limited. It is my aim to tackle such issues through the case study of a
specific collective approach to finite group theory at the turn of the 20th
century. This specific approach can be understood as a shared algebraic culture
based on the long run circulation of some specific procedures of decompositions
of the analytic forms of substitutions. In this context, the general linear
group was introduced as the maximal group in which an elementary abelian group
(i.e., the multiplicative group of a Galois field) is a normal subgroup
Algebraic cobordism theory attached to algebraic equivalence
Based on the algebraic cobordism theory of Levine and Morel, we develop a
theory of algebraic cobordism modulo algebraic equivalence.
We prove that this theory can reproduce Chow groups modulo algebraic
equivalence and the semi-topological -groups. We also show that with
finite coefficients, this theory agrees with the algebraic cobordism theory.
We compute our cobordism theory for some low dimensional varieties. The
results on infinite generation of some Griffiths groups by Clemens and on
smash-nilpotence by Voevodsky and Voisin are also lifted and reinterpreted in
terms of this cobordism theory.Comment: 30 pages. A version of this article was accepted to appear in J.
K-theor
Service-oriented logic programming
We develop formal foundations for notions and mechanisms needed to support
service-oriented computing. Our work builds on recent theoretical advancements
in the algebraic structures that capture the way services are orchestrated and
in the processes that formalize the discovery and binding of services to given
client applications by means of logical representations of required and
provided services. We show how the denotational and the operational semantics
specific to conventional logic programming can be generalized using the theory
of institutions to address both static and dynamic aspects of service-oriented
computing. Our results rely upon a strong analogy between the discovery of a
service that can be bound to an application and the search for a clause that
can be used for computing an answer to a query; they explore the manner in
which requests for external services can be described as service queries, and
explain how the computation of their answers can be performed through
service-oriented derivatives of unification and resolution, which characterize
the binding of services and the reconfiguration of applications
Some analogs of Zariski's Theorem on nodal line arrangements
For line arrangements in P^2 with nice combinatorics (in particular, for
those which are nodal away the line at infinity), we prove that the
combinatorics contains the same information as the fundamental group together
with the meridianal basis of the abelianization. We consider higher dimensional
analogs of the above situation. For these analogs, we give purely combinatorial
complete descriptions of the following topological invariants (over an
arbitrary field): the twisted homology of the complement, with arbitrary rank
one coefficients; the homology of the associated Milnor fiber and Alexander
cover, including monodromy actions; the coinvariants of the first higher
non-trivial homotopy group of the Alexander cover, with the induced monodromy
action.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-28.abs.htm
An Institutional Framework for Heterogeneous Formal Development in UML
We present a framework for formal software development with UML. In contrast
to previous approaches that equip UML with a formal semantics, we follow an
institution based heterogeneous approach. This can express suitable formal
semantics of the different UML diagram types directly, without the need to map
everything to one specific formalism (let it be first-order logic or graph
grammars). We show how different aspects of the formal development process can
be coherently formalised, ranging from requirements over design and Hoare-style
conditions on code to the implementation itself. The framework can be used to
verify consistency of different UML diagrams both horizontally (e.g.,
consistency among various requirements) as well as vertically (e.g.,
correctness of design or implementation w.r.t. the requirements)
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