Abstract
Para>One can hardly understand the fine structure of finitely presented (especially of finitely generated free and projective) MV-algebras without a working knowledge of the basic properties of rational polyhedra and their regular triangulations. The simplexes of these triangulations provide the volume elements of the integrals that evaluate the average truth-value of formulas and compute the invariant Rényi conditional introduced later in this book. Rational polyhedra are the genuine algebraic varieties of the formulas
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Cignoli, R. L. O., D’Ottaviano, I. M. L., Mundici, D. (2000). Algebraic foundations of many-valued reasoning, Vol. 7 of Trends in Logic. Dordrecht: Kluwer.
Stallings, J. R. (1967). Lectures on polyhedral topology. Mumbay: Tata Institute of Fundamental Research.
Ewald, G. (1996). Combinatorial convexity and algebraic geometry. Graduate Texts in Mathematics (Vol. 168). Heidelberg: Springer.
Alexander J. W., (1930). The combinatorial theory of complexes. Annals of Mathematics, 31, 292–320.
Mundici, D. (1988). Free products in the category of abelian \({\ell }\)-groups with strong unit. Journal of Algebra, 113, 89–109.
Busaniche, M., Mundici, D. (2007). Geometry of Robinson consistency in Łukasiewicz logic. Annals of Pure and Applied Logic, 147, 1–22.
Galatos, N., Ono, H. (2006). Algebraization, parametrized local deduction theorem and interpolation for substructural logics over FL. Studia Logica, 83, 279–308.
Wroński, A. (1985). On a form of equational interpolation property. In Foundations of Logic and Linguistic, Dorn, G. Weingartner, P. (Eds.). Salzburg, June 19, 1984, pp 23–29. New York: Plenum.
Bacisch, P. D. (1975). Amalgamation properties and interpolation theorems for equational theories, Algebra Universalis, 5, 45–55.
Bacisch, P. D. (1972). Injectivity in model theory, \({\it Colloquium}\,\,{\it Mathematicum},\) 25, 165–176.
Czelakowski, J. P., Pigozzi, D. (1999). Amalgamation and interpolation in abstract algebraic logic. In X. Caicedo et al., (Eds.) Models, algebras, and proofs, Bogotá, 1995, Lecture Notes in Pure and Applied Mathematics (Vol. 203, pp. 187–265). New York: Marcel Dekker.
Kihara, H., Ono, H. (2010). Interpolation properties, Beth definability properties and amalgamation properties for substructural logics, Journal of Logic and Computation 20(4), 823–875.
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Mundici, D. (2011). Rational Polyhedra, Interpolation, Amalgamation. In: Advanced Łukasiewicz calculus and MV-algebras. Trends in Logic, vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0840-2_2
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