A Compact [0,1]-valued First-order Lukasiewicz Logic with Identity on Hilbert Space

D. Mundici

doi:10.1093/logcom/exp017

A Compact [0,1]-valued First-order Lukasiewicz Logic with Identity on Hilbert Space

Journal of Logic and Computation ◽

10.1093/logcom/exp017 ◽

2009 ◽

Vol 21 (3) ◽

pp. 509-525 ◽

Cited By ~ 3

Author(s):

D. Mundici

Keyword(s):

Hilbert Space ◽

Łukasiewicz Logic ◽

First Order ◽

Lukasiewicz Logic

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Herbrand's Theorem, Skolemization and Proof Systems for First-Order Lukasiewicz Logic

Journal of Logic and Computation ◽

10.1093/logcom/exn059 ◽

2008 ◽

Vol 20 (1) ◽

pp. 35-54 ◽

Cited By ~ 10

Author(s):

M. Baaz ◽

G. Metcalfe

Keyword(s):

Łukasiewicz Logic ◽

First Order ◽

Proof Systems ◽

Lukasiewicz Logic ◽

Herbrand’S Theorem ◽

Herbrand's Theorem

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Proof Theory for First Order Łukasiewicz Logic

Lecture Notes in Computer Science - Automated Reasoning with Analytic Tableaux and Related Methods ◽

10.1007/978-3-540-73099-6_5 ◽

2007 ◽

pp. 28-42 ◽

Cited By ~ 1

Author(s):

Matthias Baaz ◽

George Metcalfe

Keyword(s):

Proof Theory ◽

Łukasiewicz Logic ◽

First Order ◽

Lukasiewicz Logic

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A First-Order Łukasiewicz Logic with [0, 1]-Identity

Advanced Łukasiewicz calculus and MV-algebras ◽

10.1007/978-94-007-0840-2_19 ◽

2011 ◽

pp. 215-225

Author(s):

D. Mundici

Keyword(s):

Łukasiewicz Logic ◽

First Order ◽

Lukasiewicz Logic

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Compactness in first order Lukasiewicz logic

Logic Journal of IGPL ◽

10.1093/jigpal/jzr034 ◽

2011 ◽

Vol 20 (1) ◽

pp. 254-265 ◽

Cited By ~ 2

Author(s):

N. R. Tavana ◽

M. Pourmahdian ◽

F. Didehvar

Keyword(s):

Łukasiewicz Logic ◽

First Order ◽

Lukasiewicz Logic

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Infinite-Valued First-Order Łukasiewicz Logic: Hypersequent Calculi Without Structural Rules and Proof Search for Sentences in the Prenex Form

Siberian Advances in Mathematics ◽

10.3103/s1055134418020013 ◽

2018 ◽

Vol 28 (2) ◽

pp. 79-100

Author(s):

A. S. Gerasimov

Keyword(s):

Łukasiewicz Logic ◽

Structural Rules ◽

First Order ◽

Proof Search ◽

Lukasiewicz Logic ◽

Hypersequent Calculi

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Dynamic Łukasiewicz logic and its application to immune system

Soft Computing ◽

10.1007/s00500-021-05955-3 ◽

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.

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