Generic substitutions

Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic properties of the action. In classical logic there is a strong...

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Bibliographic Details
Published in:The Journal of symbolic logic 2005-03, Vol.70 (1), p.61-83
Main Author: Panti, Giovanni
Format: Article
Language:English
Subjects:
03B50
37B05
Algebra
algebraic logic
Equivalence relation
Ergodic theory
Homeomorphism
Lebesgue measures
Logical theorems
Mathematical theorems
Mathematical vectors
spectral spaces
stochastic properties
substitution
Universal algebra
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Summary:Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic properties of the action. In classical logic there is a strong dichotomy: while over finitely many propositional variables everything is trivial, the study of the continuous transformations of the Cantor space is the subject of an extensive literature, and is far from being a completed task. In many-valued logic this dichotomy disappears: already in the finite-variable case many interesting phenomena occur, and the present paper aims at displaying some of these.
ISSN:0022-4812
1943-5886
DOI:10.2178/jsl/1107298510