Between Hilbert and Gentzen: four-valued consequence systems and structural reasoning

2021 ◽  
Author(s):  
Yaroslav Shramko
Keyword(s):  
Structural Reasoning

Synthesis of novel pyrazole derivatives using organophosphorus, stibine, and arsine reagents and their antitumor activities

2016 ◽  
Vol 71 (7) ◽  
pp. 765-776 ◽  
Author(s):  
Naglaa F. El-Sayed ◽  
Ewies F. Ewies ◽  
Marwa El-Hussieny ◽  
Leila S. Boulos ◽  
ElSayed M. Shalaby
Keyword(s):  
Cell Line ◽  
Carcinoma Cell ◽  
New Products ◽  
Carcinoma Cell Line ◽  
Breast Carcinoma Cell Line ◽  
Human Breast ◽  
Antitumor Activities ◽  
Hepatocellular Carcinoma Cell Line ◽  
Human Hepatocellular Carcinoma Cell ◽  
Structural Reasoning

AbstractThe reactions of 5-azido-3-methyl-1-phenyl-1H-pyrazole-4-carbaldehyde (azidopyrazole) with several classes of organophosphorus reagents: phosphonium ylides, Wittig-Horner reagents, dialkylphosphonates, trialkylphosphites, tris(dialkylamino)phosphanes, triphenylstibane, triphenylarsane, and Lawesson’s reagent are reported. Structural reasoning for the new products was based on compatible analytical and spectral data. The cytotoxic activity of most of the new products was evaluated against human breast carcinoma cell line (MCF7) and human hepatocellular carcinoma cell line(HepG2). Certain tested compounds showed promising results.

Developing Structural Reasoning with Diagrams

2020 ◽  
Vol 113 (10) ◽  
pp. 812-820
Author(s):  
Hyung Sook Lee ◽  
Jaehoon Yim, ◽  
Jacqueline Coomes
Keyword(s):  
Structural Reasoning

Advance students' strategies by highlighting properties, diverting attention away from procedures and algebraic skills to see the structures in expressions.

scholarly journals A logical analysis of aliasing in imperative higher-order functions

2007 ◽  
Vol 17 (4-5) ◽  
pp. 473-546 ◽  
Author(s):  
MARTIN BERGER ◽  
KOHEI HONDA ◽  
NOBUKO YOSHIDA
Keyword(s):  
Data Structures ◽  
Building Blocks ◽  
Higher Order ◽  
Logical Analysis ◽  
Logical Status ◽  
Open Issue ◽  
Higher Order Functions ◽  
Structural Reasoning

AbstractWe present a compositional programme logic for call-by-value imperative higher-order functions with general forms of aliasing, which can arise from the use of reference names as function parameters, return values, content of references and parts of data structures. The programme logic extends our earlier logic for alias-free imperative higher-order functions with new operators which serve as building blocks for clean structural reasoning about programms and data structures in the presence of aliasing. This has been an open issue since the pioneering work by Cartwright–Oppen and Morris twenty-five years ago. We illustrate usage of the logic for description and reasoning through concrete examples including a higher-order polymorphic Quicksort. The logical status of the new operators is clarified by translating them into (in)equalities of reference names.

EARLY STRUCTURAL REASONING. GENTZEN 1932

2015 ◽  
Vol 8 (4) ◽  
pp. 662-679 ◽  
Author(s):  
ENRICO MORICONI
Keyword(s):  
Inference Rules ◽  
Structural Reasoning ◽  
Opening Section

AbstractThis paper is a study of the opening section of Gentzen’s first publication of 1932, Über die Existenz unabhängiger Axiomensysteme zu unendlichen Satzsystemen, a text which shows the relevance of Hertz’s work of the 1920’s for the young Gentzen. In fact, Gentzen borrowed from Hertz the analysis of the notion of consequence, which was given in terms of the rules of thinning (Verdünnung) and cut (Schnitt) on sequents (there called “sentences”(Sätze)). Moreover, following Hertz again, he also judged it necessary to justify the forms of inference of the system by providing a semantics for them, so that it became possible to make precise the informal notion of consequence, and to show that the inference rules adopted are correct and sufficient.

Looking For and Using Structural Reasoning

2019 ◽  
Vol 112 (4) ◽  
pp. 294-301
Author(s):  
Casey Hawthorne ◽  
Bridget K. Druken
Keyword(s):  
Mathematical Practice ◽  
Solving Equations ◽  
Structural Reasoning

Examples of solving equations and inequalities, analyzing quadratic expressions, and reasoning with functions show three ways to engage students in this mathematical practice.

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