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Some remarks on the representation theorem of moisil

Alexandru Filipoiu
1981 Discrete Mathematics  
In this paper, using the representation theorem of Moisil (see [2]) the autho: introduces and examines the conc'ept of representability of Lukasiewic :! algebras.  ...  The results and notations used are from Cl]. [Z]. Let 0 be the order type of a chain J with a first element 0 and a last element 1. Definition 1.  ...  Moisirl in 1968, who pointed out the special role opt' .?L, in the category of 0.v.L.a: in the following representation theorem: Theorem 1 (Moisil [2)). For every 0.~. L. a,.  ... 
doi:10.1016/0012-365x(81)90163-1 fatcat:oajdb63zpveexby3f5blyxz6fm

Tense θ-valued Moisil propositional logic

Carmen Chiriţă
2010 International Journal of Computers Communications & Control  
The proof of this theorem is based on the representation theorem of tense θ-valued Łukasiewicz-Moisil algebras, developed in a previous paper.  ...  The main result is a completeness theorem for tense θ-valued Moisil propositional logic.  ...  Chiriţă We remark that the logical structure of TM θ (k-theorems and k-deduction) combines the logical stuctures of two logical systems: the θ-valued Moisil logic and tense classical logic.  ... 
doi:10.15837/ijccc.2010.5.2220 fatcat:olj533ncwvfc5mx7xui2mvwi7q

On the representation of L-M algebra by intuitionistic fuzzy subsets

Zedam Lemnaouar, Amroune Abdelaziz
2006 ARIMA  
These notions lead us to show that the set IF(X) of all intuitionistic fuzzy subsets on a universe X can be equipped with a structure of involutive theta-valued Lukasiewicz-Moisil algebra.  ...  International audience In this paper we introduce the notions of intuitionistic weak alpha-cut and untuitionistic strong alpha-cut of intuitionistic fuzzy subsets of a universe X.  ...  The authors are also grateful to the editor and referees for their useful remarks and suggestions concerning this paper.  ... 
doi:10.46298/arima.1845 fatcat:idrtcrkh35g2rauh7chqhx6c44

Page 8190 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
In this paper, we focus on the representation of one class 03 MATHEMATICAL LOGIC AND FOUNDATIONS 8190 of lattice implication algebras, namely, the complete and quasi- atomic lattice implication algebras  ...  A structure called a Moisil model of order n (Mmn for short) is also introduced which defines the semantics of M,,, and a natural completeness theorem is established.  ... 

A representation theorem for tense $n\times m$-valued Łukasiewicz-Moisil algebras

Aldo Victorio Figallo, Gustavo Pelaitay
2015 Mathematica Bohemica  
In this subsection we will recall some basic definitions and results on the representation of tense Lukasiewicz-Moisil algebras (see [10] ). Definition 2.4.  ...  In this subsection we will recall some basic definitions and results on the representation of tense Boolean algebras (see [4] , [18] ). Definition 2.1.  ... 
doi:10.21136/mb.2015.144400 fatcat:do3eihcy7fdbhhog6weznbaske

Monadic n×m-valued Lukasiewicz-Moisil algebras [article]

Aldo V. Figallo, Claudia Sanza
2014 arXiv   pre-print
Finally, some functional representation theorems for these algebras are given and the relationship between them is pointed out.  ...  Here we initiate an investigation into the class mLMn×m of monadic n×m-valued Lukasiewicz-Moisil algebras (or mLMn×m-algebras), namely n×m-valued Lukasiewicz-Moisil algebras endowed with a unary operation  ...  Remark 4. 1 1 Taking into account (iii) in Remark 2.2, the principal congruences of monadic n-valued Lukasiewicz-Moisil algebras can be characterized as in Theorem 4.2 by means of the + operation defined  ... 
arXiv:1202.5806v2 fatcat:xusfia2uuzc4baemvbjd3csini

Mutually exclusive nuances of truth in Moisil logic [article]

Denisa Diaconescu, Ioana Leustean
2014 arXiv   pre-print
Moisil logic, having as algebraic counterpart Ł ukasiewicz-Moisil algebras, provide an alternative way to reason about vague information based on the following principle: a many-valued event is characterized  ...  However, using the original definition of Ł ukasiewicz-Moisil algebra, the principle does not apply for subalgebras.  ...  At algebraic level it gives an efficient method for obtaining important results, lifting properties of Boolean algebras to the level of Lukasiewicz-Moisil algebras (see Moisil's representation theorem,  ... 
arXiv:1412.3008v1 fatcat:djn7bazrsjes5ju7fxifmdu424

Tense Polyadic N × M-Valued Łukasiewicz–Moisil Algebras

Aldo V. Figallo, Gustavo Pelaitay
2015 Bulletin of the Section of Logic  
Our main result is a representation theorem for tense polyadic n × m-valued Lukasiewicz-Moisil algebras. * The support of CONICET is gratefully acknowledged by Gustavo Pelaitay.  ...  Here we initiate an investigation into the class tpLMn×m of tense polyadic n × m-valued Lukasiewicz-Moisil algebras.  ...  One of the main results in the theory of polyadic Boolean algebras is Halmos representation theorem (see [22] ).  ... 
doi:10.18778/0138-0680.44.3.4.05 fatcat:rjyeimyebvazvltunfzgcpv3zm

Grigore C. Moisil (1906 - 1973) and his School in Algebraic Logic

George Georgescu, Afrodita Iorgulescu, Sergiu Rudeanu
2006 International Journal of Computers Communications & Control  
<p>We present in the paper a very concise but updated survey emphasizing the research done by Gr. C. Moisil and his school in algebraic logic.</p>  ...  This yields in particular the representation theorem of Moisil. The construction of the functors C and T was given by Moisil himself.  ...  1 j=1 ((r j x) − ∨ r j y) ≤ y. þ (Representation theorem of Moisil) Every LM n algebra can be embedded in a direct product of copies of the canonical LM n algebra L n .  ... 
doi:10.15837/ijccc.2006.1.2276 fatcat:yazxh23wfnadxkywz6mfl6tx6e

Page 1490 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
The paper presents an analysis of rather methodological aspects of Cantor’s well-known theorem on the uncountability of the set of real numbers. A.  ...  (RS-AOS-C; Moscow) The time-sharing principle and an analysis of a class of quasifinite plausible arguments (on the example of G. Cantor’s theorem on uncountability). (Russian) Dokl. Akad.  ... 

Monadic $\boldsymbol n\boldsymbol \times \boldsymbol m$-valued Łukasiewicz-Moisil algebras

A. V. Figallo, C. Sanza
2012 Mathematica Bohemica  
In the particular case of monadic n-valued Lukasiewicz-Moisil algebras, Theorem 5.3 and (iii) in Remark 2.2 allow us to determine the semimodal, involutive and closed subsets of the space associated with  ...  Functional representation theorems for mLM n×m -algebras In the present section, we will generalize the results obtained in [9] for monadic nvalued Lukasiewicz-Moisil algebras.  ... 
doi:10.21136/mb.2012.142998 fatcat:prn7xvbw5jeqtkztpawbkh4vtu

Representation theorems for θ-valued Lukasiewicz algebras

Alexandru Filipoiu
1981 Discrete Mathematics  
Acknowledgements The author wishes to express his gratitude to Professor S. Rudeanui for stimulating him to investigate the problems discussed in this paper and also for valuable remarks.  ...  The subalgebras of the algebras of the form .M(9) wi?, be called O-valued Moisil fields.  ...  Using the notions intyoduced before we obtain the following reprlzsentatlon theorem: Theorem 1. Any &vaiued Lukasiewicz algebra i's isomorphic with a certain 8 -valued Moisil field.  ... 
doi:10.1016/0012-365x(81)90254-5 fatcat:g77pddpifvcm7jqwgs2gjjyuyy

Mutually Exclusive Nuances of Truth in Moisil Logic

Denisa Diaconescu, Ioana Leustean
2015 Scientific Annals of Computer Science  
Moisil logic, having as algebraic counterpart Lukasiewicz-Moisil algebras, provides an alternative way to reason about vague information based on the following principle: a many-valued event is characterized  ...  However, using the original definition of Lukasiewicz-Moisil algebra, the principle does not apply for subalgebras.  ...  As consequence, the theory of Lukasiewicz-Moisil algebras offers various and powerful tools for analyzing uncertainty, its distinguished feature being the determination principle.  ... 
doi:10.7561/sacs.2015.1.69 fatcat:lyi5vs7b2vbfxpy5inhqbjym7i

Free algebras in varieties of BL-algebras generated by a BL n-chain

Manuela Busaniche, Roberto Cignoli
2006 Journal of the Australian Mathematical Society  
Such descriptions are known for some subvarieties of BL-algebras. The best known example is the representation of classical propositions by Boolean functions.  ...  In the proof of this result a central role is played by the Moisil algebra reducts of algebras in MV n .  ...  Since A € V n MV, n-valued Moisil algebras Boolean elements of Freely* (~'~1^0 depend on some operators that can be denned on each MV n -algebra.  ... 
doi:10.1017/s1446788700014117 fatcat:h2fqpmpfinalbimbii35kgnat4

Page 1416 of Mathematical Reviews Vol. 51, Issue 5 [page]

1976 Mathematical Reviews  
part of the paper is the following representation theorem, originally due to Moisi [op. cit., p. 322].  ...  The well-known result of Halmos on the representation of monadic Boolean algebras by Boolean-valued functions is generalized.  ... 
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