5,129 research outputs found
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.
Formalization of Universal Algebra in Agda
In this work we present a novel formalization of universal algebra in Agda. We show that heterogeneous signatures can be elegantly modelled in type-theory using sets indexed by arities to represent operations. We prove elementary results of heterogeneous algebras, including the proof that the term algebra is initial and the proofs of the three isomorphism theorems. We further formalize equational theory and prove soundness and completeness. At the end, we define (derived) signature morphisms, from which we get the contravariant functor between algebras; moreover, we also proved that, under some restrictions, the translation of a theory induces a contra-variant functor between models.Fil: Gunther, Emmanuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Gadea, Alejandro Emilio. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pagano, Miguel Maria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin
The nonmultiplicativity of the signature modulo 8 of a fibre bundle is an Arf–Kervaire invariant
It was proved by Chern, Hirzebruch and Serre that the signature of a fibre
bundle is multiplicative if the fundamental group of the base acts trivially on
the cohomology ring of the fibre with real coefficients, in which case the
signature of the total space equals the product of the signatures of base and
fibre. Hambleton, Korzeniewski and Ranicki proved that in any case the
signature is multiplicative modulo 4. In this paper we present two results
concerning the multiplicativity modulo 8: firstly we identify the obstruction
to multiplicativity modulo 8 with the Arf-Kervaire invariant of a Pontryagin
squaring operation. Furthermore, we prove that if the fibre is even-dimensional
and the action of the fundamental group of the base is trivial on the middle
cohomology of the fibre with coefficients, then this
Arf-Kervaire invariant takes value 0 and hence the signature is multiplicative
modulo 8.Comment: 42 pages, 2 figures, final version to appear in AGT. Improved
exposition, corrected typos and errors, but no changes in results with
respect to version
From configuration to dynamics -- Emergence of Lorentz signature in classical field theory
The Lorentzian metric structure used in any field theory allows one to
implement the relativistic notion of causality and to define a notion of time
dimension. This article investigates the possibility that at the microscopic
level the metric is Riemannian, i.e. locally Euclidean, and that the Lorentzian
structure, that we usually consider as fundamental, is in fact an effective
property that emerges in some regions of a 4-dimensional space with a positive
definite metric. In such a model, there is no dynamics nor signature flip
across some hypersurface; instead, all the fields develop a Lorentzian dynamics
in these regions because they propagate in an effective metric. It is shown
that one can construct a decent classical field theory for scalars, vectors and
(Dirac) spinors in flat spacetime. It is then shown that gravity can be
included but that the theory for the effective Lorentzian metric is not general
relativity but of the covariant Galileon type. The constraints arising from
stability, the equivalence principle and the constancy of fundamental constants
are detailed and a phenomenological picture of the emergence of the Lorentzian
metric is also given. The construction, while restricted to classical fields in
this article, offers a new view on the notion of time.Comment: 19 pages, 2 figures; published versio
Geometric Langlands Twists of N = 4 Gauge Theory from Derived Algebraic Geometry
We develop techniques for describing the derived moduli spaces of solutions
to the equations of motion in twists of supersymmetric gauge theories as
derived algebraic stacks. We introduce a holomorphic twist of N=4
supersymmetric gauge theory and compute the derived moduli space. We then
compute the moduli spaces for the Kapustin-Witten topological twists as its
further twists. The resulting spaces for the A- and B-twist are closely related
to the de Rham stack of the moduli space of algebraic bundles and the de Rham
moduli space of flat bundles, respectively. In particular, we find the
unexpected result that the moduli spaces following a topological twist need not
be entirely topological, but can continue to capture subtle algebraic
structures of interest for the geometric Langlands program.Comment: 55 pages; minor correction
Deverbal semantics and the Montagovian generative lexicon
We propose a lexical account of action nominals, in particular of deverbal
nominalisations, whose meaning is related to the event expressed by their base
verb. The literature about nominalisations often assumes that the semantics of
the base verb completely defines the structure of action nominals. We argue
that the information in the base verb is not sufficient to completely determine
the semantics of action nominals. We exhibit some data from different
languages, especially from Romance language, which show that nominalisations
focus on some aspects of the verb semantics. The selected aspects, however,
seem to be idiosyncratic and do not automatically result from the internal
structure of the verb nor from its interaction with the morphological suffix.
We therefore propose a partially lexicalist approach view of deverbal nouns. It
is made precise and computable by using the Montagovian Generative Lexicon, a
type theoretical framework introduced by Bassac, Mery and Retor\'e in this
journal in 2010. This extension of Montague semantics with a richer type system
easily incorporates lexical phenomena like the semantics of action nominals in
particular deverbals, including their polysemy and (in)felicitous
copredications.Comment: A revised version will appear in the Journal of Logic, Language and
Informatio
A Survey of Languages for Specifying Dynamics: A Knowledge Engineering Perspective
A number of formal specification languages for knowledge-based systems has been developed. Characteristics for knowledge-based systems are a complex knowledge base and an inference engine which uses this knowledge to solve a given problem. Specification languages for knowledge-based systems have to cover both aspects. They have to provide the means to specify a complex and large amount of knowledge and they have to provide the means to specify the dynamic reasoning behavior of a knowledge-based system. We focus on the second aspect. For this purpose, we survey existing approaches for specifying dynamic behavior in related areas of research. In fact, we have taken approaches for the specification of information systems (Language for Conceptual Modeling and TROLL), approaches for the specification of database updates and logic programming (Transaction Logic and Dynamic Database Logic) and the generic specification framework of abstract state machine
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