February  2006, 15(1): 237-258. doi: 10.3934/dcds.2006.15.237

Dynamical properties of logical substitutions


Department of Mathematics and Computer Science, University of Udine, via delle Scienze 208, 33100 Udine, Italy

Received  November 2004 Revised  June 2005 Published  February 2006

Many kinds of algebraic structures have associated dual topological spaces, among others commutative rings with $1$ (this being the paradigmatic example), various kinds of lattices, boolean algebras, C *-algebras, .... These associations are functorial, and hence algebraic endomorphisms of the structures give rise to continuous selfmappings of the dual spaces, which can enjoy various dynamical properties; one then asks about the algebraic counterparts of these properties. We address this question from the point of view of algebraic logic. The datum of a set of truth-values and a "conjunction'' connective on them determines a propositional logic and an equational class of algebras. The algebras in the class have dual spaces, and the duals of endomorphisms of free algebras provide dynamical models for Frege deductions in the corresponding logic.
Citation: Giovanni Panti. Dynamical properties of logical substitutions. Discrete & Continuous Dynamical Systems, 2006, 15 (1) : 237-258. doi: 10.3934/dcds.2006.15.237

Doston Jumaniyozov, Ivan Kaygorodov, Abror Khudoyberdiyev. The algebraic classification of nilpotent commutative algebras. Electronic Research Archive, 2021, 29 (6) : 3909-3993. doi: 10.3934/era.2021068


G. Mashevitzky, B. Plotkin and E. Plotkin. Automorphisms of categories of free algebras of varieties. Electronic Research Announcements, 2002, 8: 1-10.


Vladimir Müller, Aljoša Peperko. Lower spectral radius and spectral mapping theorem for suprema preserving mappings. Discrete & Continuous Dynamical Systems, 2018, 38 (8) : 4117-4132. doi: 10.3934/dcds.2018179


Vu Hoang Linh, Volker Mehrmann. Spectral analysis for linear differential-algebraic equations. Conference Publications, 2011, 2011 (Special) : 991-1000. doi: 10.3934/proc.2011.2011.991


Grégory Berhuy. Algebraic space-time codes based on division algebras with a unitary involution. Advances in Mathematics of Communications, 2014, 8 (2) : 167-189. doi: 10.3934/amc.2014.8.167


Adrian Petruşel, Radu Precup, Marcel-Adrian Şerban. On the approximation of fixed points for non-self mappings on metric spaces. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 733-747. doi: 10.3934/dcdsb.2019264


Ilwoo Cho, Palle Jorgense. Free probability on $ C^{*}$-algebras induced by hecke algebras over primes. Discrete & Continuous Dynamical Systems - S, 2019, 12 (8) : 2221-2252. doi: 10.3934/dcdss.2019143


Thomas Honold, Ivan Landjev. The dual construction for arcs in projective Hjelmslev spaces. Advances in Mathematics of Communications, 2011, 5 (1) : 11-21. doi: 10.3934/amc.2011.5.11


Ferenc Weisz. Dual spaces of mixed-norm martingale Hardy spaces. Communications on Pure & Applied Analysis, 2021, 20 (2) : 681-695. doi: 10.3934/cpaa.2020285


Keonhee Lee, Ngoc-Thach Nguyen, Yinong Yang. Topological stability and spectral decomposition for homeomorphisms on noncompact spaces. Discrete & Continuous Dynamical Systems, 2018, 38 (5) : 2487-2503. doi: 10.3934/dcds.2018103


Jędrzej Śniatycki. Integral curves of derivations on locally semi-algebraic differential spaces. Conference Publications, 2003, 2003 (Special) : 827-833. doi: 10.3934/proc.2003.2003.827


Adina Juratoni, Flavius Pater, Olivia Bundău. Operator representations of logmodular algebras which admit $\gamma-$spectral $\rho-$dilations. Electronic Research Announcements, 2012, 19: 49-57. doi: 10.3934/era.2012.19.49


B. S. Lee, Arif Rafiq. Strong convergence of an implicit iteration process for a finite family of Lipschitz $\phi -$uniformly pseudocontractive mappings in Banach spaces. Numerical Algebra, Control & Optimization, 2014, 4 (4) : 287-293. doi: 10.3934/naco.2014.4.287


Laurent Amour, Jérémy Faupin. Inverse spectral results in Sobolev spaces for the AKNS operator with partial informations on the potentials. Inverse Problems & Imaging, 2013, 7 (4) : 1115-1122. doi: 10.3934/ipi.2013.7.1115


Matthew S. Keegan, Berta Sandberg, Tony F. Chan. A multiphase logic framework for multichannel image segmentation. Inverse Problems & Imaging, 2012, 6 (1) : 95-110. doi: 10.3934/ipi.2012.6.95


Byung-Soo Lee. A convergence theorem of common fixed points of a countably infinite family of asymptotically quasi-$f_i$-expansive mappings in convex metric spaces. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 557-565. doi: 10.3934/naco.2013.3.557


Adeolu Taiwo, Lateef Olakunle Jolaoso, Oluwatosin Temitope Mewomo. Viscosity approximation method for solving the multiple-set split equality common fixed-point problems for quasi-pseudocontractive mappings in Hilbert spaces. Journal of Industrial & Management Optimization, 2021, 17 (5) : 2733-2759. doi: 10.3934/jimo.2020092


Jinsen Guo, Yongwu Zhou, Baixun Li. The optimal pricing and service strategies of a dual-channel retailer under free riding. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021056


Matthias Täufer, Martin Tautenhahn. Scale-free and quantitative unique continuation for infinite dimensional spectral subspaces of Schrödinger operators. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1719-1730. doi: 10.3934/cpaa.2017083


Pierre Gervais. A spectral study of the linearized Boltzmann operator in $ L^2 $-spaces with polynomial and Gaussian weights. Kinetic & Related Models, 2021, 14 (4) : 725-747. doi: 10.3934/krm.2021022

2020 Impact Factor: 1.392


  • PDF downloads (70)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]