PEIRCE’S CALCULI FOR CLASSICAL PROPOSITIONAL LOGIC

2018 ◽  
Vol 13 (3) ◽  
pp. 509-540 ◽  
Author(s):  
MINGHUI MA ◽  
AHTI-VEIKKO PIETARINEN
Keyword(s):  
Propositional Logic ◽  
Natural Deduction ◽  
Sequent Calculus ◽  
Theoretic Analysis ◽  
Classical Propositional Logic ◽  
Deduction System ◽  
Natural Deduction System ◽  
Logical Algebra ◽  
Graphical System ◽  
Logical Calculi

AbstractThis article investigates Charles Peirce’s development of logical calculi for classical propositional logic in 1880–1896. Peirce’s 1880 work on the algebra of logic resulted in a successful calculus for Boolean algebra. This calculus, denoted byPC, is here presented as a sequent calculus and not as a natural deduction system. It is shown that Peirce’s aim was to presentPCas a sequent calculus. The law of distributivity, which Peirce states in 1880, is proved using Peirce’s Rule, which is a residuation, inPC. The transitional systems of the algebra of the copula that Peirce develops since 1880 paved the way to the 1896 graphical system of the alpha graphs. It is shown how the rules of the alpha system reinterpret Boolean algebras, answering Peirce’s statement that logical graphs supply a new system of fundamental assumptions to logical algebra. A proof-theoretic analysis is given for the connection betweenPCand the alpha system.

scholarly journals Multidimensional Model of Product Quality Formation

2021 ◽  
Vol 346 ◽  
pp. 01006
Author(s):  
Julius Tchigirinsky ◽  
Nadezhda Gribanova ◽  
Alina Gontar ◽  
Nataly Chigirinskaya
Keyword(s):  
Computational Complexity ◽  
Coordinate Space ◽  
Multidimensional Model ◽  
Information Structures ◽  
Design Task ◽  
Functional Capabilities ◽  
Logical Algebra ◽  
Modern Information ◽  
Multidimensional Optimization

Based on the analysis of the functional capabilities of modern information systems, the paper substantiates the applicability of multidimensional combined information structures for computer-assistant planning in machinery production. A multidimensional optimization model has been developed for elementary technological surface-treatment routing in the case of using complex quality indicators determined by the operational properties of products. The dimensions of its coordinate space are determined by the number of technical constraints that govern the quality of the product. The paper provides an example of an algorithm that uses logical algebra operations to reduce the coordinate space of the model and to reduce the computational complexity of the design task.

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