bibliography of many-valued logics and applications

bibliography of many-valued logics and applications

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A list of references for N-valued logics and their applications

References

1

Awodey, S. & Butz, C., 2000,

Topological Completeness

for Higher Order Logic., Journal of Symbolic Logic, 65, 3, 1168–1182.

2

Awodey, S. & Reck, E. R., 2002, Completeness and Categoricity II. Twentieth-Century

Metalogic

to Twenty-first-Century

Semantics

,

History and Philosophy of Logic

, 23, (2): 77–94.

3

Awodey, S., 1996,

Structure

in Mathematics and Logic: A

Categorical

Perspective,

Philosophia Mathematica

, 3: 209–237.

4

Baez, J., 1997, An

Introduction

to

n-Categories

, in

Category Theory

and Computer Science, Lecture Notes in Computer Science

, 1290, Berlin: Springer-Verlag, 1–33.

5

Baez, J. & Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the

Algebra

of Opetopes,
in:

Advances in Mathematics

, 135, 145–206.

6

Baianu, I. C., R. Brown , G. Georgescu and J. F. Glazebrook: 2006, Complex Nonlinear Biodynamics in

Categories

,

Higher Dimensional Algebra

and Łukasiewicz–Moisil Topos:

Transformations

of Neuronal, Genetic and
Neoplastic Networks.,

Axiomathes,

, 16: 82-165.

7

Baianu, I. C.: 1977, A Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non–linear Theory,

Bull. of Math. Biol

.

39

, 249–258.

8

M. Barr and C. Wells.

Toposes, Triples and Theories

. Montreal: McGill University, 2000.

9

Barr, M. & Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag.

10

Birkhoff, G.: 1948,

Lattice Theory

,

Amer. Math. Soc.

, New York.

11

Boicescu, V., A. Filipoiu, G. Georgescu, and S. Rudeanu.: 1991,

Łukasiewicz-Moisil Algebras

,
North-Holland, Amsterdam.

12

Chang, C. C.: 1958, Algebraic analysis of many valued logics.

Trans. Amer. Math. Soc

.,

88

,
467–490.

13

Chang, C. C.: 1959, A new proof of the completeness of the Łukasiewicz axioms,

Transactions

American
Mathematical Society

93

, 74-80.

14

Cignoli, R., Esteva, F., Godo, L. and Torrens, A. : 2000, Basic Fuzzy Logic is the logic of

continuous

t-norms
and their residua,

Soft Computing

4

, 106-112.

15

Cignoli, R.: Moisil algebras,

Notas de Logica Matematica

, Inst. Mat., Univ. Nacional del Sur,
Bahia-Blanca, No. 27.

16

Bourbaki

, N. : 1964.

Eléments de Mathématique, Livre II, Algèbre

,

4

, Hermann, Editor,
Paris.

17

Carnap, R.: 1938,

The Logical Syntax of

Language

, Harcourt, Brace and Co., New York.

18

Ehresmann, C.: 1965,

Catégories et Structures

, Dunod, Paris.

19

Eilenberg, S. and S. MacLane: 1945, The General Theory of

Natural Equivalences

,

Trans. Amer. Math. Soc.

58

, 231–294.

20

Georgescu, G. and D. Popescu: 1968, On

Algebraic Categories

,

Rev. Roum. Math. Pures et Appl.

13

, 337–342.

21

Georgescu, G., and C. Vraciu.: 1970. On the

characterization

of centered Łukasiewicz algebras.

J. Algebra

16

, 486-495.

22

Georgescu, G., and I. Leuştean.: 2000. Towards a probability theory based on Moisil logic,

Soft
Computing

4

, 19-26.

23

Grigolia, R.S.: 1977. Algebraic analysis of Łukasiewicz-Tarski’s

logical systems

, in Wójcicki, R.,
Malinowski, G. (Eds),

Selected Papers on Łukasiewicz Sentential Calculi

, Osolineum, Wroclaw, pp. 81-92.

24

Hilbert, D. and W. Ackerman: 1927,

Grunduge der Theoretischen Logik

, Springer, Berlin.

25

Kan, D.M.: 1958,

Adjoint Functors

,

Trans Amer. Math. Soc.

87

, 294-329.

26

Lambek J. and P. J. Scott: 1986,

Introduction to Higher Order Categorical Logic

, Cambridge University
Press, Cambridge, UK, 1986.

27

Lawvere, F.W.: 1963, Functorial Semantics of Algebraic Theories,

Proc. Natl. Acad. Sci. USA.

50

, 869–872.

28

Löfgren, L.: 1968, An Axiomatic Explanation of

Complete

Self-Reproduction,

Bull. Math. Biophys.

30

, 317–348.

29

Łukasiewicz, J.: 1970,

Selected Works

, (ed.: L. Borkowski), North-Holland Publ. Co., Amsterdam and PWN,
Warsaw.

30

MacLane, S. and I. Moerdijk: 1992,

Sheaves in Geometry and Logic - A first Introduction to Topos Theory

,
Springer Verlag, New York.

31

McCulloch, W. and W. Pitts: 1943, ‘A Logical Calculus of Ideas

Immanent

in Nervous Activity’,

Bull. Math.
Biophys

.

5

, 115–133.

32

McNaughton, R.: 1951, A

theorem

about infinite-valued

sentential logic

,

Journal

Symbolic Logic

16

, 1-13.

33

Moisil, Gr. C.: 1972,

Essai sur les logiques non-chrysippiennes

. Ed. Academiei, Bucharest.

34

Mundici, D.: 1986,

Interpretation

of AF C*-algebras in Łukasiewicz sentential calculus,

J. Functional
Analysis

65

, 15-63.

35

Rose, A.: 1956, Formalisation du calcul propositionnel implicatif à

ℵ

0

valeurs de Łukasiewicz,

C. R. Acad. Sci. Paris

243

,1183-1185.

36

Rose, A. and Rosser, J.B.: 1958, Fragments of many-valued statement calculi,

Transactions American
Mathematical Society

87

, 1-53.

37

Rose, A.: 1962,

Extensions

of Some Theorems of Anderson and Belnap,

J. Symbolic Logic

,

27

,
(4), 423–425.

38

Rose, A.: 1978, ‘Formalisations of Further

ℵ

0

–Valued Łukasiewicz Propositional Calculi’.

J. Symbolic
Logic

,

43

(2): 207-210

39

Rosen, R.: 1958a, A Relational Theory of Biological Systems,

Bull. Math. Biophys.

20

,
245–260.

40

Rosen, R.: 1958b, “The

Representation

of Biological Systems from the Standpoint of the Theory of Categories.”,

Bull. Math. Biophys.

20

, 317-341.

41

Rosen, R.: 1991,

Life Itself

, Columbia University Press, New York.

42

Rosen, R.: 1999,

Essays on Life Itself

, Columbia University Press, New York.

43

Rosenbloom, Paul.: 1950,

The Elements of Mathematical Logic

, Dover, New York.

44

Rosenbloom, Paul.:1962,

ibid.

, Prentice Hall, Englewood Cliffs, N.J.

45

Rosser, J.B. and Turquette, A.R.: 1952,

Many-Valued Logics

. North-Holland Publ. Co., Amsterdam.

Title

bibliography of many-valued logics and applications

Canonical name

BibliographyOfManyvaluedLogicsAndApplications

Date of creation

2013-03-22 18:19:11

Last modified on

2013-03-22 18:19:11

Owner

bci1 (20947)

Last modified by

bci1 (20947)

Numerical id

20

Author

bci1 (20947)

Entry type

Bibliography

Classification

msc 03G30

Classification

msc 03G12

Classification

msc 03G10

Classification

msc 03G20

Classification

msc 03-00

Synonym

many-valued logic

Synonym

nonstandard logics

Synonym

N-valued logic

Related topic

TopicEntryOnTheAlgebraicFoundationsOfMathematics

Related topic

FormalLogicsAndMetaMathematics

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