Open AccessNote on Deduction Theorems in Contraction-Free Logics
Author(s) -
Karel Chvalovský,
Petr Cintula
Publication year - 2018
Publication title -
epic series in computing
Language(s) - English
Resource type - Conference proceedings
ISSN - 2398-7340
DOI - 10.29007/c66c
Subject(s) - contraction (grammar) , natural deduction , mathematics , hierarchy , discrete mathematics , computer science , t norm fuzzy logics , algebra over a field , pure mathematics , artificial intelligence , linguistics , philosophy , membership function , fuzzy set , economics , market economy , fuzzy logic
In this short paper we present a finer analysis of the variants of Local Deduction Theorem in contraction-free logics. We define some natural generalisations called Implicational Deduction Theorems and study their basic properties. The hierarchy of classes of logics defined by these theorems is presented.