93 research outputs found
Formal Concept Analysis and Resolution in Algebraic Domains
We relate two formerly independent areas: Formal concept analysis and logic
of domains. We will establish a correspondene between contextual attribute
logic on formal contexts resp. concept lattices and a clausal logic on coherent
algebraic cpos. We show how to identify the notion of formal concept in the
domain theoretic setting. In particular, we show that a special instance of the
resolution rule from the domain logic coincides with the concept closure
operator from formal concept analysis. The results shed light on the use of
contexts and domains for knowledge representation and reasoning purposes.Comment: 14 pages. We have rewritten the old version according to the
suggestions of some referees. The results are the same. The presentation is
completely differen
Bifinite Chu Spaces
This paper studies colimits of sequences of finite Chu spaces and their
ramifications. Besides generic Chu spaces, we consider extensional and
biextensional variants. In the corresponding categories we first characterize
the monics and then the existence (or the lack thereof) of the desired
colimits. In each case, we provide a characterization of the finite objects in
terms of monomorphisms/injections. Bifinite Chu spaces are then expressed with
respect to the monics of generic Chu spaces, and universal, homogeneous Chu
spaces are shown to exist in this category. Unanticipated results driving this
development include the fact that while for generic Chu spaces monics consist
of an injective first and a surjective second component, in the extensional and
biextensional cases the surjectivity requirement can be dropped. Furthermore,
the desired colimits are only guaranteed to exist in the extensional case.
Finally, not all finite Chu spaces (considered set-theoretically) are finite
objects in their categories. This study opens up opportunities for further
investigations into recursively defined Chu spaces, as well as constructive
models of linear logic
Logical Relations for Monadic Types
Logical relations and their generalizations are a fundamental tool in proving
properties of lambda-calculi, e.g., yielding sound principles for observational
equivalence. We propose a natural notion of logical relations able to deal with
the monadic types of Moggi's computational lambda-calculus. The treatment is
categorical, and is based on notions of subsconing, mono factorization systems,
and monad morphisms. Our approach has a number of interesting applications,
including cases for lambda-calculi with non-determinism (where being in logical
relation means being bisimilar), dynamic name creation, and probabilistic
systems.Comment: 83 page
A Formal Model for Trust in Dynamic Networks
We propose a formal model of trust informed by the Global Computing scenario and focusing on the aspects of trust formation, evolution, and propagation. The model is based on a novel notion of trust structures which, building on concepts from trust management and domain theory, feature at the same time a trust and an information partial order
Formal Concept Analysis and Resolution on Algebraic Domains - Preliminary Report
We relate two formerly independent areas: Formal concept analysis and logic of domains. We will establish a correspondence between contextual attribute logic on formal contexts resp. concept lattices and a clausal logic on coherent algebraic cpos. We show how to identify the notion of formal concept in the domain theoretic setting. In particular, we show that a special instance of the resolution rule from the domain logic coincides with the concept closure operator from formal concept analysis. The results shed light on the use of contexts and domains for knowledge representation and reasoning purposes
A Categorical View on Algebraic Lattices in Formal Concept Analysis
Formal concept analysis has grown from a new branch of the mathematical field
of lattice theory to a widely recognized tool in Computer Science and
elsewhere. In order to fully benefit from this theory, we believe that it can
be enriched with notions such as approximation by computation or
representability. The latter are commonly studied in denotational semantics and
domain theory and captured most prominently by the notion of algebraicity, e.g.
of lattices. In this paper, we explore the notion of algebraicity in formal
concept analysis from a category-theoretical perspective. To this end, we build
on the the notion of approximable concept with a suitable category and show
that the latter is equivalent to the category of algebraic lattices. At the
same time, the paper provides a relatively comprehensive account of the
representation theory of algebraic lattices in the framework of Stone duality,
relating well-known structures such as Scott information systems with further
formalisms from logic, topology, domains and lattice theory.Comment: 36 page
The evolution of the footwall to the Ronda subcontinental mantle peridotites: insights from the Nieves Unit (western Betic Cordillera)
Strongly heterogeneous deformation and extreme metamorphic gradients characterize the dominantly carbonate Nieves Unit in the footwall to the Ronda mantle extrusion wedge in the western Betic Cordillera. A well-developed foliation and mineral lineation, together with isoclinal intrafolial folds, occur in silicate-bearing, calcite or dolomite marbles within a c. 1.5 km thick metamorphic aureole underlying the peridotites. For the inferred maximum pressure of 300 MPa, petrological investigations allow us to define temperature ranges for the main zones of the metamorphic aureole: >510 °C (probably c. 700 °C) for the forsterite zone; 510–430 °C for the diopside zone; 430–360 °C for the tremolite zone; 360–330 °C for the phlogopite zone. Field structural analysis integrated with petrological, microstructural and electron backscatter diffraction textural data document large finite strains consistent with general shear within the metamorphic aureole, associated with NW-directed thrusting of the peridotites. On the other hand, post-kinematic silicate growth suggests that heat diffusion from the high-temperature peridotites continued after the final emplacement of the Ronda mantle extrusion wedge, leading to final zoning of the metamorphic aureole and to local partial annealing of calcite marble textures, particularly in the highest-temperature zone of the thermally softened footwall carbonates. Following substantial cooling, renewed crustal shortening affected the whole Nieves Unit, resulting in widespread development of NE–SW-trending meso-scale folds
EPR of Compound I: An Illustrated Revision of the Theoretical Model
Compound I has been postulated to be the reactive species in many heme catalysts, which performs different chemistry and shows different properties in different enzymes. The aim of this review is to present a comprehensive model which has been successfully used to interpret the EPR spectra of various Compound I species. The theoretical approach established by seminal articles will be revisited and its ability to explain experimental results will be illustrated by simulating selected spectra from the literature. Compound I stores two oxidizing equivalents, one in the paramagnetic iron(IV)-oxo moiety, and another one as a free radical on the porphyrin ligand or an amino acid in the protein. To describe the interactions of the two paramagnetic species with each other and with their local environment, the spin Hamiltonian of the system is built step by step. The Fe(IV) center is described using a two-hole model. The effect of the crystal-field and spin–orbit coupling on the energy levels is calculated with this simple approach, which allows to obtain spin Hamiltonian parameters like zero-field splitting and effective g-values for the iron. The magnetic interaction between the Fe(IV) center and the free radical is considered and allowed to vary in sign (ferromagnetic to antiferromagnetic) and magnitude to interpret the EPR of Compound I species in different systems. Since orbital overlap is crucial for exchange interaction, special emphasis is made in obtaining the orientation of Fe semi-occupied orbitals by extending the counter-rotation concept, which relates the directions of magnetic, electronic, and molecular axes
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