scholarly journals On Presupposition Projection with Trivalent Connectives

2019 ◽  
Vol 29 ◽  
pp. 582
Author(s):  
Yoad Winter
Keyword(s):  
Natural Generalization ◽  
Projection Algorithm ◽  
Presupposition Projection ◽  
Definition Of ◽  
As Effects

A basic puzzle about presuppositions concerns their projection from propositional constructions. This problem has regained much attention in the last decade since many of its prominent accounts, including variants of the trivalent Strong Kleene connectives, suffer from the so-called *proviso problem*.This paper argues that basic insights of the Strong Kleene system can be used without invoking the proviso problem. It is shown that the notion of *determinant value* that underlies the definition of the Strong Kleene connectives leads to a natural generalization of the filtering conditions proposed in Karttunen's article ``Presuppositions of compound sentences'' (LI, 1973). Incorporating this generalized  condition into an incremental projection algorithm avoids the proviso problem as well as the derivation of conditional presuppositions. It is argued that the same effects that were previously modelled using conditional presuppositions may be viewed as effects of presupposition suspension and contextual inference on presupposition projection.

A note on recursive functions

1996 ◽  
Vol 6 (2) ◽  
pp. 127-139 ◽  
Author(s):  
Nicoletta Sabadini ◽  
Sebastiano Vigna ◽  
Robert F. C. Walters
Keyword(s):  
Programming Language ◽  
Concurrent Programming ◽  
Natural Generalization ◽  
Computational Power ◽  
Recursive Functions ◽  
Definition Of ◽  
Computable Functions

In this paper, we propose a new and elegant definition of the class of recursive functions, which is analogous to Kleene's definition but differs in the primitives taken, thus demonstrating the computational power of the concurrent programming language introduced in Walters (1991), Walters (1992) and Khalil and Walters (1993).The definition can be immediately rephrased for any distributive graph in a countably extensive category with products, thus allowing a wide, natural generalization of computable functions.

scholarly journals Cosserat Elastoplastic Finite Elements for Masonry Structures

2014 ◽  
Vol 624 ◽  
pp. 131-138 ◽  
Author(s):  
Michele Godio ◽  
Ioannis Stefanou ◽  
Karam Sab ◽  
Jean Sulem
Keyword(s):  
Finite Elements ◽  
Projection Algorithm ◽  
Elastic Plates ◽  
Discrete Elements ◽  
Backward Euler ◽  
Out Of Plane ◽  
Evolution Laws ◽  
Definition Of ◽  
Closest Point Projection ◽  
Point Projection

A Finite Elements formulation previously developed for Cosserat elastic plates, has been extended herein to the elastoplastic framework. Material non-linearities are taken into account through the implementation of a backward-Euler closest-point-projection algorithm, for which the definition of non-smooth yield loci and non-associated plastic potentials and evolution laws is made possible. An existing homogenized elastic constitutive model and a set of yield criteria for the out-of-plane behaviour of block-masonry are implemented in the code and their validity is discussed based on the comparison with Discrete Elements simulations. The comparison is carried out in both the static and the dynamic regime.

ON ONE-MEMBRANE P SYSTEMS OPERATING IN SEQUENTIAL MODE

2005 ◽  
Vol 16 (05) ◽  
pp. 867-881 ◽  
Author(s):  
ZHE DANG ◽  
OSCAR H. IBARRA
Keyword(s):  
Natural Generalization ◽  
P Systems ◽  
P System ◽  
Catalytic Systems ◽  
Semilinear Sets ◽  
System A ◽  
Vector Addition ◽  
Parallel Version ◽  
Proper Subclass ◽  
Definition Of

In the standard definition of a P system, a computation step consists of a parallel application of a "maximal" set of nondeterministically chosen rules. Referring to this system as a parallel P system, we consider in this paper a sequential P system, in which each step consists of an application of a single nondeterministically chosen rule. We show the following:1. For 1-membrane purely catalytic systems (pure CS's), the sequential version is strictly weaker than the parallel version in that the former defines (i.e., generates) exactly the semilinear sets, whereas the latter is known to define nonrecursive sets.2. For 1-membrane communicating P systems (CPS's), the sequential version can only define a proper subclass of the semilinear sets, whereas the parallel version is known to define nonrecursive sets.3. Adding a new type of rule of the form: ab → axbyccomedcometo the CPS (a natural generalization of the rule ab → axbyccomein the original model), where x, y ∈ {here, out}, to the sequential 1-membrane CPS makes it equivalent to a vector addition system.4. Sequential 1-membrane symport/antiport systems (SA's) are equivalent to vector addition systems, contrasting the known result that the parallel versions can define nonrecursive sets.5. Sequential 1-membrane SA's whose rules have radius 1, (1,1), (1,2) (i.e., of the form (a, out), (a, in), (a, out; b, in), (a, out; bc, in)) generate exactly the semilinear sets. However, if the rules have radius 1, (1,1), (2,1) (i.e., of the form (ab, out; c, in)), the SA's can only generate a proper subclass of the semilinear sets.

Landau Damping and Entropy

1967 ◽  
Vol 22 (11) ◽  
pp. 1682-1689
Author(s):  
F. Winterberg
Keyword(s):  
Velocity Fluctuation ◽  
Natural Generalization ◽  
Landau Damping ◽  
Mean Square ◽  
Velocity Fluctuations ◽  
Equilibrium Configurations ◽  
The Mean ◽  
Definition Of ◽  
Non Equilibrium

It is shown that the well-known LANDAU-damping entropy paradox can be resolved by considering a macroscopic entropy as defined by CLAUSIUS instead of the microscopic entropy defined by BOLTZMΛNN. Although both entropy definitions are identical for equilibrium configurations, the same in general is not true for non-equilibrium configurations. To extend the entropy definition of CLAUSIUS to non-equilibrium configurations requires a generalization of the concept of temperature to nonequilibrium configurations. A natural generalization of the concept of temperature to non-equilibrium configurations is to put the temperature proportional to the mean square velocity fluctuation. In this way a macroscopic entropy can be defined which is then proportional to the logarithm of the mean square velocity fluctuation. In the case of LANDAU damping it can be shown that two states having the same statistical permutability and thus the same microscopic entropy may have different mean square velocity fluctuations. One should therefore consider, besides the microscopic disorder defined by BOLTZMANN, which is proportional to the logarithm of the permutability, a macroscopic disorder which is proportional to the logarithm of the mean square velocity fluctuation.In the case of LANDAU damping the microscopic entropy does not change with time; the macroscopic entropy, however, increases steadily with time.

scholarly journals Relative-perfectness of discrete gradient vector fields and multi-parameter persistent homology

2021 ◽  
Author(s):  
Claudia Landi ◽  
Sara Scaramuccia
Keyword(s):  
Morse Theory ◽  
Vector Fields ◽  
Persistent Homology ◽  
Natural Generalization ◽  
Heterogeneous Data ◽  
Gradient Vector ◽  
Discrete Gradient ◽  
The One ◽  
Definition Of ◽  
Geometric Content

AbstractThe combination of persistent homology and discrete Morse theory has proven very effective in visualizing and analyzing big and heterogeneous data. Indeed, topology provides computable and coarse summaries of data independently from specific coordinate systems and does so robustly to noise. Moreover, the geometric content of a discrete gradient vector field is very useful for visualization purposes. The specific case of multivariate data still demands for further investigations, on the one hand, for computational reasons, it is important to reduce the necessary amount of data to be processed. On the other hand, for analysis reasons, the multivariate case requires the detection and interpretation of the possible interdepedance among data components. To this end, in this paper we introduce and study a notion of perfectness for discrete gradient vector fields with respect to multi-parameter persistent homology, called relative-perfectness. As a natural generalization of usual perfectness in Morse theory for homology, relative-perfectness entails having the least number of critical cells relevant for multi-parameter persistence. As a first contribution, we support our definition of relative-perfectness by generalizing Morse inequalities to the filtration structure where homology groups involved are relative with respect to subsequent sublevel sets. In order to allow for an interpretation of critical cells in 2-parameter persistence, our second contribution consists of two inequalities bounding Betti tables of persistence modules from above and below, via the number of critical cells. Our last result is the proof that existing algorithms based on local homotopy expansions allow for efficient computability over simplicial complexes up to dimension 2.

scholarly journals A class of hypergraphs that generalizes chordal graphs

2010 ◽  
Vol 106 (1) ◽  
pp. 50 ◽  
Author(s):  
Eric Emtander
Keyword(s):  
Simplicial Complexes ◽  
Natural Generalization ◽  
Chordal Graphs ◽  
Graph Algebras ◽  
Higher Dimensional ◽  
Dimensional Version ◽  
Definition Of ◽  
Flag Complexes ◽  
Circuit Graph

In this paper we introduce a class of hypergraphs that we call chordal. We also extend the definition of triangulated hypergraphs, given by H. T. Hà and A. Van Tuyl, so that a triangulated hypergraph, according to our definition, is a natural generalization of a chordal (rigid circuit) graph. R. Fröberg has showed that the chordal graphs corresponds to graph algebras, $R/I(\mathcal{G})$, with linear resolutions. We extend Fröberg's method and show that the hypergraph algebras of generalized chordal hypergraphs, a class of hypergraphs that includes the chordal hypergraphs, have linear resolutions. The definitions we give, yield a natural higher dimensional version of the well known flag property of simplicial complexes. We obtain what we call $d$-flag complexes.

scholarly journals The Complexity of Computing the Cylindrical and the $t$-Circle Crossing Number of a Graph

10.37236/7193 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Frank Duque ◽  
Hernán González-Aguilar ◽  
César Hernández-Vélez ◽  
Jesús Leaños ◽  
Carolina Medina
Keyword(s):  
Analogous Result ◽  
Natural Generalization ◽  
Crossing Number ◽  
Number Problem ◽  
Minimum Number ◽  
Np Complete ◽  
Concentric Circles ◽  
Definition Of ◽  
Open Question

A plane drawing of a graph is cylindrical if there exist two concentric circles that contain all the vertices of the graph, and no edge intersects (other than at its endpoints) any of these circles. The cylindrical crossing number of a graph \(G\) is the minimum number of crossings in a cylindrical drawing of \(G\). In his influential survey on the variants of the definition of the crossing number of a graph, Schaefer lists the complexity of computing the cylindrical crossing number of a graph as an open question. In this paper, we prove that the problem of deciding whether a given graph admits a cylindrical embedding is NP-complete, and as a consequence we show that the \(t\)-cylindrical crossing number problem is also NP-complete. Moreover, we show an analogous result for the natural generalization of the cylindrical crossing number,  namely the \(t\)-crossing number.

Imprecise Functional Dependencies

2009 ◽  
pp. 190-198
Author(s):  
Vincenzo Deufemia ◽  
Giuseppe Polese ◽  
Mario Vacca
Keyword(s):  
Functional Dependence ◽  
Natural Generalization ◽  
Multimedia Databases ◽  
Functional Dependency ◽  
Fundamental Concept ◽  
Functional Dependencies ◽  
Strongly Connected ◽  
Definition Of

Functional dependencies represent a fundamental concept in the design of a database since they are capable of capturing some semantics of the data strongly connected with the occurrence of redundancy in a database. The development of applications working on fuzzy and multimedia databases has required the extension of the functional dependency notion to these new types of data. Unfortunately, the concept of imprecise functional dependence or fuzzy functional dependence (IFD, for short) has not had a cogent and largely accepted definition yet. In fact, in attempt to capture different aspects of this notion of many proposals of IFD definition exist in literature, all having semantics and objectives somewhat unclear, especially with respect to the concern of redundancy (Bosc, et al., 1994, Cubero & Vila, 1994, Raju & Majumdar, 1988, Tyagi, et al., 2005, Wang, et al., 2000). Moreover, the debate on the definition of the concept of fuzzy functional dependency seems to be still in progress, as shown by the following question: “But the question remains: are these extended notions of functional dependency a natural generalization?” (Tyagi et al., 2005).

Instantaneous polarization attributes and directional filtering

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 872-881 ◽  
Author(s):  
Igor B. Morozov ◽  
Scott B. Smithson
Keyword(s):  
Effective Means ◽  
Polarization Vector ◽  
Seismic Signal ◽  
Natural Generalization ◽  
Number Of Components ◽  
Instantaneous Phase ◽  
Directional Filtering ◽  
Multicomponent Seismic ◽  
Definition Of ◽  
Phase Amplitude

We introduce a systematic definition of instantaneous attributes for an arbitrary multicomponent seismic signal. The definition is a natural generalization of known complex trace attributes of a one‐component signal. Instantaneous amplitude and all polarization parameters are defined as invariants of “instantaneous phase rotation.” The principal feature of our approach is the unique definition of the instantaneous phase for a signal with any number of components. Plots of subtle polarization parameters of multicomponent seismic data are easily obtained using conventional seismic plotting routines. We illustrate our approach on a synthetic example and apply it to real 3‐component, wide‐angle crustal data. Plots of polarization attributes provide evidence for shear‐wave splitting in an [Formula: see text] arrival. Having determined the instantaneous polarization vector, we design a new type of time‐domain spatial directional filter. The filter enhances linearly polarized events with specified instantaneous polarization. The filter can work with any number of components in the data, has no user‐specified parameters, and is controlled only by the signal. We conclude that rigorously defined instantaneous phase, amplitude, and polarization attributes provide new effective means for the visualization, analysis, and processing of multicomponent signal.

scholarly journals Chirality, a new key for the definition of the connection and curvature of a Lie-Kac superalgebra

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jean Thierry-Mieg
Keyword(s):  
Scalar Field ◽  
Lie Algebra ◽  
Bianchi Identity ◽  
Parallel Transport ◽  
Lie Superalgebra ◽  
Natural Generalization ◽  
Yang Mills ◽  
Complex Functions ◽  
Definition Of ◽  
Mills Field

Abstract A natural generalization of a Lie algebra connection, or Yang-Mills field, to the case of a Lie-Kac superalgebra, for example SU(m/n), just in terms of ordinary complex functions and differentials, is proposed. Using the chirality χ which defines the supertrace of the superalgebra: STr(…) = Tr(χ…), we construct a covariant differential: D = χ(d + A) + Φ, where A is the standard even Lie-subalgebra connection 1-form and Φ a scalar field valued in the odd module. Despite the fact that Φ is a scalar, Φ anticommutes with (χA) because χ anticommutes with the odd generators hidden in Φ. Hence the curvature F = DD is a superalgebra-valued linear map which respects the Bianchi identity and correctly defines a chiral parallel transport compatible with a generic Lie superalgebra structure.

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