Antonio Di Nola
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Antonio Di Nola has a total of 46 co-authors. Here are the top co-authors by number of shared publications:
Revaz Grigolia
Iv. Javakhisvili Tbilisi State University
12 shared publicationsEsko Turunen
Tampere University of Technology
11 shared publications- Revaz Grigolia
Department o mathematics, Faculty of exact and Natural sciences, Tbilisi State University Tbilisi, Georgia
8 shared publications - Gaetano Vitale
Department of Mathematics, University of Salerno, Fisciano, Italy
7 shared publications Giacomo Lenzi
Department of MathematicsUniversity of SalernoVia Giovanni Paolo II 13284084FiscianoITALY
7 shared publications- Lawrence P. Belluce
British Columbia University
7 shared publications
Latest Publications
- Open Access
- 22 September 2025
- Published by Springer Nature in Algebra universalis
- Vol. 86 (4) , 1-20
The prime spectrum of $\ell $-groups and MV-algebrasAs a main result, we characterize prime spectra of abelian lattice ordered groups. Further we introduce some categories based on spectral spaces, lattices and Priestley spaces. Then we have a characterization of the variety generated by the Chang MV-algebra and we study this variety. Next we generalize the results to every variety generated by a Komori chain.
- 22 September 2025
- Published by Springer Nature in Algebra universalis
- Vol. 86 (4) , 1-20
Open AccessThe prime spectrum of $\ell $-groups and MV-algebrasAs a main result, we characterize prime spectra of abelian lattice ordered groups. Further we introduce some categories based on spectral spaces, lattices and Priestley spaces. Then we have a characterization of the variety generated by the Chang MV-algebra and we study this variety. Next we generalize the results to every variety generated by a Komori chain.
- Open Access
- 8 May 2024
- Published by Springer Nature in Archive for Mathematical Logic
- Vol. 63 (7-8) , 893-919
Spectral MV-algebras and equispectrality
In this paper we study the set of MV-algebras with given prime spectrum and we introduce the class of spectral MV-algebras. An MV-algebra is spectral if it is generated by the union of all its prime ideals (or proper ideals, or principal ideals, or maximal ideals). Among spectral MV-algebras, special attention is devoted to bipartite MV-algebras. An MV-algebra is bipartite if it admits an homomorphism onto the MV-algebra of two elements. We prove that both bipartite MV-algebras and spectral MV-algebras can be finitely axiomatized in first order logic. We also prove that there is only, up to isomorphism, a set of MV-algebras with given prime spectrum. A further part of the paper is devoted to some relations between bipartite MV-algebras and their states. Recall that a state on an MV-algebra is a generalization of a probability measure on a Boolean algebra. Particular states are the states with Bayes’ property. We show that an MV-algebra admits a state with the Bayes’ property if and only if it is bipartite.
- 8 May 2024
- Published by Springer Nature in Archive for Mathematical Logic
- Vol. 63 (7-8) , 893-919
Open AccessSpectral MV-algebras and equispectrality
In this paper we study the set of MV-algebras with given prime spectrum and we introduce the class of spectral MV-algebras. An MV-algebra is spectral if it is generated by the union of all its prime ideals (or proper ideals, or principal ideals, or maximal ideals). Among spectral MV-algebras, special attention is devoted to bipartite MV-algebras. An MV-algebra is bipartite if it admits an homomorphism onto the MV-algebra of two elements. We prove that both bipartite MV-algebras and spectral MV-algebras can be finitely axiomatized in first order logic. We also prove that there is only, up to isomorphism, a set of MV-algebras with given prime spectrum. A further part of the paper is devoted to some relations between bipartite MV-algebras and their states. Recall that a state on an MV-algebra is a generalization of a probability measure on a Boolean algebra. Particular states are the states with Bayes’ property. We show that an MV-algebra admits a state with the Bayes’ property if and only if it is bipartite.
- Open Access
- 1 January 2024
- Published by KMAN Publication Incorporation
- Vol. 5 (1) , 3-9
Two-generated free Sωn -algebras
Two-generated free MV -algebras are described in the variety of Sωn -algebras
- 1 January 2024
- Published by KMAN Publication Incorporation
- Vol. 5 (1) , 3-9
Open AccessTwo-generated free Sωn -algebras
Two-generated free MV -algebras are described in the variety of Sωn -algebras
- Open Access
- 2 July 2022
- Published by Springer Nature in Soft Computing
- Vol. 26 (19) , 9823-9830
Epistemic Łukasiewicz logic of partial knowledge
We offer a new logic, called Epistemic Łukasiewicz logic of partial knowledge that is represented as multimodal epistemic Łukasiewicz logic $$K\text{\L} _\text {P}(n)$$ with n knowledge operators $$\Box _i$$ $$(1 \le i \le n)$$ interpreted in a non-archimedean monadic MV-algebra. We choose knowledge operators, which can be estimated by some grading (different kinds of knowledge): absolute knowledge or partial knowledge. We consider a very special type of partial knowledge. Actually, we take infinitesimal elements (the radical) of perfect MV-algebras as a range of this estimation. The choice of infinitesimal elements seems suitable for actual situations like a measure of partial information.- 2 July 2022
- Published by Springer Nature in Soft Computing
- Vol. 26 (19) , 9823-9830
Open AccessEpistemic Łukasiewicz logic of partial knowledge
We offer a new logic, called Epistemic Łukasiewicz logic of partial knowledge that is represented as multimodal epistemic Łukasiewicz logic $$K\text{\L} _\text {P}(n)$$ with n knowledge operators $$\Box _i$$ $$(1 \le i \le n)$$ interpreted in a non-archimedean monadic MV-algebra. We choose knowledge operators, which can be estimated by some grading (different kinds of knowledge): absolute knowledge or partial knowledge. We consider a very special type of partial knowledge. Actually, we take infinitesimal elements (the radical) of perfect MV-algebras as a range of this estimation. The choice of infinitesimal elements seems suitable for actual situations like a measure of partial information. - Open Access
- 1 February 2022
- Published by Walter de Gruyter GmbH in Mathematica Slovaca
- Vol. 72 (1) , 1-10
Expanding Lattice Ordered Abelian Groups to Riesz Spaces
First we give a necessary and sufficient condition for an abelian lattice ordered group to admit an expansion to a Riesz space (or vector lattice). Then we construct a totally ordered abelian group with two non-isomorphic Riesz space structures, thus improving a previous paper where the example was a non-totally ordered lattice ordered abelian group. This answers a question raised by Conrad in 1975. We give also a partial solution to another problem considered in the same paper. Finally, we apply our results to MV-algebras and Riesz MV-algebras.
- 1 February 2022
- Published by Walter de Gruyter GmbH in Mathematica Slovaca
- Vol. 72 (1) , 1-10
Open AccessExpanding Lattice Ordered Abelian Groups to Riesz Spaces
First we give a necessary and sufficient condition for an abelian lattice ordered group to admit an expansion to a Riesz space (or vector lattice). Then we construct a totally ordered abelian group with two non-isomorphic Riesz space structures, thus improving a previous paper where the example was a non-totally ordered lattice ordered abelian group. This answers a question raised by Conrad in 1975. We give also a partial solution to another problem considered in the same paper. Finally, we apply our results to MV-algebras and Riesz MV-algebras.
- Open Access
- 23 June 2021
- Published by Springer Nature in Soft Computing
- Vol. 25 (15) , 9773-9780
Dynamic Łukasiewicz logic and its application to immune system
It is introduced an immune dynamicn-valued Łukasiewicz logic $$ID{\L }_n$$ on the base ofn-valued Łukasiewicz logic $${\L }_n$$ and corresponding to it immune dynamic $$MV_n$$ -algebra ( $$IDL_n$$ -algebra), $$1< n < \omega $$ , which are algebraic counterparts of the logic, that in turn represent two-sorted algebras $$(\mathcal {M}, \mathcal {R}, \Diamond )$$ that combine the varieties of $$MV_n$$ -algebras $$\mathcal {M} = (M, \oplus , \odot , \sim , 0,1)$$ and regular algebras $$\mathcal {R} = (R,\cup , ;, ^*)$$ into a single finitely axiomatized variety resemblingR-module with “scalar” multiplication $$\Diamond $$ . Kripke semantics is developed for immune dynamic Łukasiewicz logic $$ID{\L }_n$$ with application in immune system.- 23 June 2021
- Published by Springer Nature in Soft Computing
- Vol. 25 (15) , 9773-9780
Open AccessDynamic Łukasiewicz logic and its application to immune system
It is introduced an immune dynamicn-valued Łukasiewicz logic $$ID{\L }_n$$ on the base ofn-valued Łukasiewicz logic $${\L }_n$$ and corresponding to it immune dynamic $$MV_n$$ -algebra ( $$IDL_n$$ -algebra), $$1< n < \omega $$ , which are algebraic counterparts of the logic, that in turn represent two-sorted algebras $$(\mathcal {M}, \mathcal {R}, \Diamond )$$ that combine the varieties of $$MV_n$$ -algebras $$\mathcal {M} = (M, \oplus , \odot , \sim , 0,1)$$ and regular algebras $$\mathcal {R} = (R,\cup , ;, ^*)$$ into a single finitely axiomatized variety resemblingR-module with “scalar” multiplication $$\Diamond $$ . Kripke semantics is developed for immune dynamic Łukasiewicz logic $$ID{\L }_n$$ with application in immune system. - 6 July 2020
- Published by Springer Nature in Algebra universalis
- Vol. 81 (3) , 1-43
The spectrum problem for Abelian $\ell $-groups and MV-algebras- 6 July 2020
- Published by Springer Nature in Algebra universalis
- Vol. 81 (3) , 1-43
The spectrum problem for Abelian $\ell $-groups and MV-algebras- 29 June 2020
- Published by Elsevier in International Journal of Approximate Reasoning
- Vol. 124, 103-110
Dynamic Łukasiewicz Logic and Dynamic MV-algebras
- 29 June 2020
- Published by Elsevier in International Journal of Approximate Reasoning
- Vol. 124, 103-110
Dynamic Łukasiewicz Logic and Dynamic MV-algebras
- Open Access
Heyting Algebra and Gödel Algebra vs. various Topological Systems and Esakia Space: a Category Theoretic Study
In this paper intuitionistic topological system and its properties have been introduced. Categorical interrelationships among Heyting algebra, G\"odel algebra, Esakia space and proposed intuitionistic topological systems have also been studied in details.
Open AccessHeyting Algebra and Gödel Algebra vs. various Topological Systems and Esakia Space: a Category Theoretic Study
In this paper intuitionistic topological system and its properties have been introduced. Categorical interrelationships among Heyting algebra, G\"odel algebra, Esakia space and proposed intuitionistic topological systems have also been studied in details.
- Open Access
- 1 May 2020
- Published by CMV Verlag in Journal of Algebraic Hyperstructures and Logical Algebras
- Vol. 1 (2) , 1-7
On the free S^{ω}_{1} -algebras
One and two-generated free MV -algebras are algebraically described in the variety generated by perfectMV -algebras.
- 1 May 2020
- Published by CMV Verlag in Journal of Algebraic Hyperstructures and Logical Algebras
- Vol. 1 (2) , 1-7
Open AccessOn the free S^{ω}_{1} -algebras
One and two-generated free MV -algebras are algebraically described in the variety generated by perfectMV -algebras.