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In this paper, using the representation theorem of Moisil (see ) 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
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
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
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. ...
In this subsection we will recall some basic definitions and results on the representation of tense Lukasiewicz-Moisil algebras (see  ). Definition 2.4. ... In this subsection we will recall some basic definitions and results on the representation of tense Boolean algebras (see  ,  ). Definition 2.1. ...doi:10.21136/mb.2015.144400 fatcat:do3eihcy7fdbhhog6weznbaske
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
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
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  ). ...doi:10.18778/0138-06188.8.131.52.05 fatcat:rjyeimyebvazvltunfzgcpv3zm
<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
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. ...
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  for monadic nvalued Lukasiewicz-Moisil algebras. ...doi:10.21136/mb.2012.142998 fatcat:prn7xvbw5jeqtkztpawbkh4vtu
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
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
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
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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