Algebraic representation of frame-valued continuous lattices via the open filter monad

2021 ◽  
Author(s):  
Wei Yao ◽  
Yueli Yue
Keyword(s):  
Algebraic Representation ◽  
Continuous Lattices

scholarly journals Focus and contrastive topic in questions and answers, with particular reference to Turkish

2020 ◽  
Vol 46 (1-2) ◽  
pp. 1-71 ◽  
Author(s):  
Beste Kamali ◽  
Manfred Krifka
Keyword(s):  
Algebraic Representation ◽  
Similar Role ◽  
Discourse Coherence ◽  
Dynamic Interpretation ◽  
Contrastive Topic ◽  
Questions And Answers ◽  
Alternative Questions

AbstractMuch recent research has recognized the importance of focus and contrastive topic in assertions for discourse coherence. However, with few exceptions, it has been neglected that focus and contrastive topic also occur in questions, and have a similar role in establishing coherence. We propose a framework of dynamic interpretation based on the notion of Commitment Spaces that show that a uniform interpretation of focus and contrastive topic is possible. The algebraic representation format is rich enough so that a separate introduction of discourse trees is not necessary. The paper discusses these phenomena for Turkish, a language with an explicit focus marker for polar and alternative questions, which distinguishes focus from contrastive topic.

Linear types and approximation

2000 ◽  
Vol 10 (6) ◽  
pp. 719-745 ◽  
Author(s):  
MICHAEL HUTH ◽  
ACHIM JUNG ◽  
KLAUS KEIMEL
Keyword(s):  
Full Subcategory ◽  
Linear Logic ◽  
Domain Theory ◽  
Classical Domain ◽  
Complete Distributivity ◽  
Linear Types ◽  
Continuous Lattices

We study continuous lattices with maps that preserve all suprema rather than only directed ones. We introduce the (full) subcategory of FS-lattices, which turns out to be *-autonomous, and in fact maximal with this property. FS-lattices are studied in the presence of distributivity and algebraicity. The theory is extremely rich with numerous connections to classical Domain Theory, complete distributivity, Topology and models of Linear Logic.

scholarly journals Some operators and dimensions in modular meet-continuous lattices

2018 ◽  
Vol 17 (05) ◽  
pp. 1850094 ◽  
Author(s):  
Mauricio Medina Bárcenas ◽  
José Ríos Montes ◽  
Angel Zaldívar Corichi
Keyword(s):  
Complete Lattice ◽  
Monotone Function ◽  
Continuous Lattice ◽  
Continuous Lattices

Given a complete modular meet-continuous lattice [Formula: see text], an inflator on [Formula: see text] is a monotone function [Formula: see text] such that [Formula: see text] for all [Formula: see text]. If [Formula: see text] is the set of all inflators on [Formula: see text], then [Formula: see text] is a complete lattice. Motivated by preradical theory, we introduce two operators, the totalizer and the equalizer. We obtain some properties of these operators and see how they are related to the structure of the lattice [Formula: see text] and with the concept of dimension.

scholarly journals Investigation of eighth-grade students' understanding of the slope of the linear function

2012 ◽  
Vol 26 (42a) ◽  
pp. 139-162 ◽  
Author(s):  
Osman Birgin
Keyword(s):  
Linear Function ◽  
Analytical Techniques ◽  
Structured Interview ◽  
Linear Functions ◽  
Eighth Grade ◽  
The Black Sea ◽  
Algebraic Representation ◽  
Black Sea Region ◽  
Eighth Grade Students ◽  
Written Questions

This study aimed to investigate eighth-grade students' difficulties and misconceptions and their performance of translation between the different representation modes related to the slope of linear functions. The participants were 115 Turkish eighth-grade students in a city in the eastern part of the Black Sea region of Turkey. Data was collected with an instrument consisting of seven written questions and a semi-structured interview protocol conducted with six students. Students' responses to questions were categorized and scored. Quantitative data was analyzed using the SPSS 17.0 statistical packet program with cross tables and one-way ANOVA. Qualitative data obtained from interviews was analyzed using descriptive analytical techniques. It was found that students' performance in articulating the slope of the linear function using its algebraic representation form was higher than their performance in using transformation between graphical and algebraic representation forms. It was also determined that some of them had difficulties and misunderstood linear function equations, graphs, and slopes and could not comprehend the connection between slope and the x- and y-intercepts.

scholarly journals MultiAspect Graphs: Algebraic Representation and Algorithms

Algorithms ◽  
2016 ◽  
Vol 10 (1) ◽  
pp. 1 ◽  
Author(s):  
Klaus Wehmuth ◽  
Éric Fleury ◽  
Artur Ziviani
Keyword(s):  
Algebraic Representation

scholarly journals LOOPS, SURFACES AND GRASSMANN REPRESENTATION IN TWO- AND THREE-DIMENSIONAL ISING MODELS

1999 ◽  
Vol 14 (29) ◽  
pp. 4549-4574 ◽  
Author(s):  
C. R. GATTRINGER ◽  
S. JAIMUNGAL ◽  
G. W. SEMENOFF
Keyword(s):  
Three Dimensional ◽  
Ising Models ◽  
Algebraic Representation ◽  
Simple Derivation ◽  
Counting Problems ◽  
Intrinsic Geometry ◽  
Geometry Factor ◽  
Loop Expansion ◽  
Loop Surface

We construct an algebraic representation of the geometrical objects (loop and surface variables) dual to the spins in 2 and 3D Ising models. This algebraic calculus is simpler than dealing with the geometrical objects, in particular when analyzing geometry factors and counting problems. For the 2D case we give the corrected loop expansion of the free energy and the radius of convergence for this series. For the 3D case we give a simple derivation of the geometry factor which prevents overcounting of surfaces in the intrinsic geometry representation of the partition function, and find a classification of the surfaces to be summed over. For 2 and 3D we derive a compact formula for 2n-point functions in loop (surface) representation.

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