Adding Real Coefficients to Łukasiewicz Logic: An Application to Neural Networks

2013 ◽  
pp. 77-85 ◽  
Author(s):  
Antonio Di Nola ◽  
Brunella Gerla ◽  
Ioana Leustean
Keyword(s):  
Neural Networks ◽  
Łukasiewicz Logic ◽  
Lukasiewicz Logic

scholarly journals Dynamic Łukasiewicz logic and its application to immune system

2021 ◽  
Author(s):  
Antonio Di Nola ◽  
Revaz Grigolia ◽  
Nunu Mitskevich ◽  
Gaetano Vitale
Keyword(s):  
Immune System ◽  
Scalar Multiplication ◽  
Kripke Semantics ◽  
Łukasiewicz Logic ◽  
Lukasiewicz Logic ◽  
Regular Algebras

AbstractIt is introduced an immune dynamic n-valued Łukasiewicz logic $$ID{\L }_n$$ I D Ł n on the base of n-valued Łukasiewicz logic $${\L }_n$$ Ł n and corresponding to it immune dynamic $$MV_n$$ M V n -algebra ($$IDL_n$$ I D L n -algebra), $$1< n < \omega $$ 1 < n < ω , which are algebraic counterparts of the logic, that in turn represent two-sorted algebras $$(\mathcal {M}, \mathcal {R}, \Diamond )$$ ( M , R , ◊ ) that combine the varieties of $$MV_n$$ M V n -algebras $$\mathcal {M} = (M, \oplus , \odot , \sim , 0,1)$$ M = ( M , ⊕ , ⊙ , ∼ , 0 , 1 ) and regular algebras $$\mathcal {R} = (R,\cup , ;, ^*)$$ R = ( R , ∪ , ; , ∗ ) into a single finitely axiomatized variety resembling R-module with “scalar” multiplication $$\Diamond $$ ◊ . Kripke semantics is developed for immune dynamic Łukasiewicz logic $$ID{\L }_n$$ I D Ł n with application in immune system.

Dynamic Łukasiewicz Logic and Dynamic MV-algebras

2020 ◽  
Vol 124 ◽  
pp. 103-110
Author(s):  
Antonio Di Nola ◽  
Revaz Grigolia ◽  
Gaetano Vitale
Keyword(s):  
Łukasiewicz Logic ◽  
Lukasiewicz Logic ◽  
Mv Algebras

New phase transitions for formulas in Łukasiewicz logic

2020 ◽  
Vol 14 (6) ◽  
Author(s):  
Mohamed El Halaby ◽  
Areeg Abdalla
Keyword(s):  
Phase Transitions ◽  
Łukasiewicz Logic ◽  
Lukasiewicz Logic ◽  
New Phase

On the infinite-valued Łukasiewicz logic that preserves degrees of truth

2006 ◽  
Vol 45 (7) ◽  
pp. 839-868 ◽  
Author(s):  
Josep Maria Font ◽  
Àngel J. Gil ◽  
Antoni Torrens ◽  
Ventura Verdú
Keyword(s):  
Łukasiewicz Logic ◽  
Lukasiewicz Logic

Łukasiewicz Logic: From Proof Systems To Logic Programming

2005 ◽  
Vol 13 (5) ◽  
pp. 561-585 ◽  
Author(s):  
George Metcalfe ◽  
Nicola Olivetti ◽  
Dov Gabbay
Keyword(s):  
Logic Programming ◽  
Łukasiewicz Logic ◽  
Proof Systems ◽  
Lukasiewicz Logic

Admissible Rules of Lukasiewicz Logic

2010 ◽  
Vol 20 (2) ◽  
pp. 425-447 ◽  
Author(s):  
E. Jerabek
Keyword(s):  
Łukasiewicz Logic ◽  
Admissible Rules ◽  
Lukasiewicz Logic
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