scholarly journals Modal logics with hard diamond-free fragments

2020 ◽  
Vol 30 (1) ◽  
pp. 3-25
Author(s):  
Antonis Achilleos
Keyword(s):  
General Setting ◽  
Modal Logics ◽  
Propositional Variable ◽  
High Complexity

Abstract We investigate the complexity of modal satisfiability for a family of multi-modal logics with interdependencies among the modalities. In particular, we examine four characteristic multi-modal logics with dependencies and demonstrate that, even if we restrict the formulae to be diamond-free and to have only one propositional variable, these logics still have a high complexity. This result identifies and isolates two sources of complexity: the presence of axiom $D$ for some of the modalities and certain modal interdependencies. We then further investigate and characterize the complexity of the diamond-free, 1-variable fragments of multi-modal logics in a general setting.

scholarly journals Fusions of Description Logics and Abstract Description Systems

2002 ◽  
Vol 16 ◽  
pp. 1-58 ◽  
Author(s):  
F. Baader ◽  
C. Lutz ◽  
H. Sturm ◽  
F. Wolter
Keyword(s):  
Large Class ◽  
Description Logics ◽  
General Setting ◽  
Modal Logics ◽  
Common Generalization ◽  
Abstract Description ◽  
Normal Modal Logics ◽  
Combining Logics

Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion. Though description logics are closely related to modal logics, they are not necessarily normal. In addition, ABox reasoning in description logics is not covered by the results from modal logics. In this paper, we extend the decidability transfer results from normal modal logics to a large class of description logics. To cover different description logics in a uniform way, we introduce abstract description systems, which can be seen as a common generalization of description and modal logics, and show the transfer results in this general setting.

scholarly journals Density of truth in modal logics

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Zofia Kostrzycka
Keyword(s):  
Binary Tree ◽  
Modal Logics ◽  
Propositional Variable ◽  
Modal Formula ◽  
International Audience

International audience The aim of this paper is counting the probability that a random modal formula is a tautology. We examine $\{ \to,\Box \}$ fragment of two modal logics $\mathbf{S5}$ and $\mathbf{S4}$ over the language with one propositional variable. Any modal formula written in such a language may be interpreted as a unary binary tree. As it is known, there are finitely many different formulas written in one variable in the logic $\mathbf{S5}$ and this is the key to count the proportion of tautologies of $\mathbf{S5}$ among all formulas. Although the logic $\mathbf{S4}$ does not have this property, there exist its normal extensions having finitely many non-equivalent formulas.

ALGEBRA OF PREDICATES AND RELATED GEOMETRIC MODELS CREATION IN REGARDS OF UNIFIED STATE EXAM IN INFORMATICS (RUSSIAN EGE)

2019 ◽  
pp. 40-47
Author(s):  
E. A. Mironchik
Keyword(s):  
Geometric Model ◽  
Main Idea ◽  
Formal Logic ◽  
High Complexity ◽  
Geometric Models ◽  
Complexity Problem ◽  
Logical Expression ◽  
State Examination

The article discusses the method of solving the task 18 on the Unified State Examination in Informatics (Russian EGE). The main idea of the method is to write the conditions of the problem utilizing the language of formal logic, using elementary predicates. According to the laws of logic the resulting complex logical expression would be transformed into an expression, according to which a geometric model is supposed to be constructed which allows to obtain an answer. The described algorithm does allow high complexity problem to be converted into a simple one.

Challenges and Benefits of Product-Like SRAM in Technology Development

2011 ◽  
Author(s):  
Felix Beaudoin ◽  
Stephen Lucarini ◽  
Fred Towler ◽  
Stephen Wu ◽  
Zhigang Song ◽  
...  
Keyword(s):  
Technology Development ◽  
Random Access ◽  
Random Access Memory ◽  
Static Random Access Memory ◽  
Development Phase ◽  
High Complexity ◽  
Access Memory ◽  
Integration Schemes ◽  
Front End

Abstract For SRAMs with high logic complexity, hard defects, design debug, and soft defects have to be tackled all at once early on in the technology development while innovative integration schemes in front-end of the line are being validated. This paper presents a case study of a high-complexity static random access memory (SRAM) used during a 32nm technology development phase. The case study addresses several novel and unrelated fail mechanisms on a product-like SRAM. Corrective actions were put in place for several process levels in the back-end of the line, the middle of the line, and the front-end of the line. These process changes were successfully verified by demonstrating a significant reduction of the Vmax and Vmin nest array block fallout, thus allowing the broader development team to continue improving random defectivity.

Modal logics with Belnapian truth values

2010 ◽  
Vol 20 (3) ◽  
pp. 279-304 ◽  
Author(s):  
Serge P Odintsov ◽  
Heinrich Wansing
Keyword(s):  
Modal Logics ◽  
Truth Values

scholarly journals Directed unions of local monoidal transforms and GCD domains

2019 ◽  
Vol 19 (04) ◽  
pp. 2050061
Author(s):  
Lorenzo Guerrieri
Keyword(s):  
Prime Ideal ◽  
Local Ring ◽  
Maximal Ideal ◽  
General Setting ◽  
Regular Local Ring ◽  
Dimension Formula

Let [Formula: see text] be a regular local ring of dimension [Formula: see text]. A local monoidal transform of [Formula: see text] is a ring of the form [Formula: see text], where [Formula: see text] is a regular parameter, [Formula: see text] is a regular prime ideal of [Formula: see text] and [Formula: see text] is a maximal ideal of [Formula: see text] lying over [Formula: see text] In this paper, we study some features of the rings [Formula: see text] obtained as infinite directed union of iterated local monoidal transforms of [Formula: see text]. In order to study when these rings are GCD domains, we also provide results in the more general setting of directed unions of GCD domains.

scholarly journals Meta-Deflectors Made of Dielectric Nanohole Arrays with Anti-Damage Potential

Photonics ◽  
2021 ◽  
Vol 8 (4) ◽  
pp. 107
Author(s):  
Haichao Yu ◽  
Feng Tang ◽  
Jingjun Wu ◽  
Zao Yi ◽  
Xin Ye ◽  
...  
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Laser Cutting ◽  
High Complexity ◽  
Damage Potential ◽  
Optical Components ◽  
Nanohole Arrays ◽  
Intense Light ◽  
Polarization Of Light ◽  
Air Hole

In intense-light systems, the traditional discrete optical components lead to high complexity and high cost. Metasurfaces, which have received increasing attention due to the ability to locally manipulate the amplitude, phase, and polarization of light, are promising for addressing this issue. In the study, a metasurface-based reflective deflector is investigated which is composed of silicon nanohole arrays that confine the strongest electric field in the air zone. Subsequently, the in-air electric field does not interact with the silicon material directly, attenuating the optothermal effect that causes laser damage. The highest reflectance of nanoholes can be above 99% while the strongest electric fields are tuned into the air zone. One presentative deflector is designed based on these nanoholes with in-air-hole field confinement and anti-damage potential. The 1st order of the meta-deflector has the highest reflectance of 55.74%, and the reflectance sum of all the orders of the meta-deflector is 92.38%. The optothermal simulations show that the meta-deflector can theoretically handle a maximum laser density of 0.24 W/µm2. The study provides an approach to improving the anti-damage property of the reflective phase-control metasurfaces for intense-light systems, which can be exploited in many applications, such as laser scalpels, laser cutting devices, etc.

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