1,720,983 research outputs found
An expansion of Basic Logic with fixed points
No full textWe introduce an expansion of Basic Logic (BL) with new connectives which express fixed points of continuous formulas, i.e. formulas of BL whose connectives are among (Formula presented.). The algebraic semantics of this logic is studied together with some of its subclasses corresponding to extensions of the above-mentioned expansion. The axiomatic extensions are proved to be standard complete
Geometrical dualities for Łukasiewicz logic
Full text linkThis is the transcript of a featured talk given on the 15th of September 2011 at the XIX Congeresso dell'Unione Matematica Italiana held in Bologna, Italy. It is based on a joint work with Vincenzo Marra of the University of Milan that was published in Vincenzo Marra and Luca Spada. The dual adjunction between MV-algebras and Tychonoff spaces, Studia Logica 100(1-2):253-278, 2012. Special issue of Studia Logica in memoriam Leo Esakia (L. Beklemishev, G. Bezhanishvili, D. Mundici and Y. Venema Editors).
The article develops a general dual adjunction between MV-algebras (the algebraic equivalents of Łukasiewicz logic) and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. Such a dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. Further the duality theorem for finitely presented objects is obtained from the general adjunction by a further specialisation. The treatment is aimed at emphasising the generality of the framework considered here in the prototypical case of MV-algebras
Continuous Approximations of MV-Algebra with Product and Product Residuation: A Cathegory-Theoretic Equivalence
No full textMV-algebras, infinite dimensional polyhedra, and natural dualities
No full textWe connect the dual adjunction between MV-algebras and Tychonoff spaces with the general theory of natural dualities, and provide a number of applications. In doing so, we simplify the aforementioned construction by observing that there is no need of using presentations of MV-algebras in order to obtain the adjunction. We also provide a description of the dual maps that is intrinsically geometric, and thus avoids the syntactic notion of definable map. Finally, we apply these results to better explain the relation between semisimple tensor products and coproducts of MV-algebras, and we extend beyond the finitely generated case the characterisations of strongly semisimple and polyhedral MV-algebras
Advances in the theory of LP algebras
No full textRecently an expansion of LP1/2 logic with fixed points has been considered. In the present work we study the algebraic semantics of this logic, namely μLP algebras, from algebraic, model theoretic and computational standpoints.
We provide a characterisation of free μLP algebras as a family of particular functions from [0,1]n to [0,1].
We show that the first-order theory of linearly ordered μLP algebras enjoys quantifier elimination, being, more precisely, the model completion of the theory of linearly ordered LP1/2 algebras. Furthermore, we give a functional representation of any LP1/2 algebra in the style of Di Nola Theorem for MV-algebras and finally we prove that the equational theory of μLP algebras is in PSPACE
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