Propositional calculus, which is an accomplished system for deductive reasoning, consists of binary operations. However representation of induction or abduction might need a calculation system based on unary operations. In the present paper, we propose a new calculation which consists of only unary operations, for propositional logic. The new calculation system, which is represented by 2 dimensional vectors and 2 × 2 matrices, can emulate truth tables of propositional logic. We call it curried propositional calculus. Moreover, we introduce diagrams which corresponds to logic gates for conventional logical connectives. Consequently, propositional logic which is one of the systems for deductive reasoning is connected to matrix algebra based on unary operations. This result gives a start point to reconstruct a new framework of mathematical logic to study the three types of reasoning, deduction, induction and abduction, comprehensively.
Skip Nav Destination
Article navigation
10 March 2015
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014)
22–28 September 2014
Rhodes, Greece
Research Article|
March 10 2015
Curried propositional calculus and the matrix representation
Moto Kamiura
Moto Kamiura
School of Science and Engineering,
Tokyo Denki University
, Saitama, Japan
[email protected], [email protected]Research Institute of Electrical Communication,
Tohoku University
, Miyagi, Japan
Search for other works by this author on:
Moto Kamiura
,
School of Science and Engineering,
Tokyo Denki University
, Saitama, Japan
[email protected], [email protected]Research Institute of Electrical Communication,
Tohoku University
, Miyagi, Japan
AIP Conf. Proc. 1648, 580008 (2015)
Citation
Moto Kamiura; Curried propositional calculus and the matrix representation. AIP Conf. Proc. 10 March 2015; 1648 (1): 580008. https://doi.org/10.1063/1.4912816
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
5
Views
Citing articles via
Inkjet- and flextrail-printing of silicon polymer-based inks for local passivating contacts
Zohreh Kiaee, Andreas Lösel, et al.
The implementation of reflective assessment using Gibbs’ reflective cycle in assessing students’ writing skill
Lala Nurlatifah, Pupung Purnawarman, et al.
Effect of coupling agent type on the self-cleaning and anti-reflective behaviour of advance nanocoating for PV panels application
Taha Tareq Mohammed, Hadia Kadhim Judran, et al.
Related Content
Illustrating some implications of the conservation laws in relativistic mechanics
Am. J. Phys. (June 2009)
Development of composite mortars based on lime, blastfurnce slag and fly ash
AIP Conf. Proc. (August 2019)
Hermeneutic operative calculus
AIP Conf. Proc. (July 2014)
Constructivistic mathematical logic education
AIP Conf. Proc. (November 2018)