Dynamic Algebras and the Nature of Induction
Name
MIT-LCS-TM-159.pdf
Size
4.53 MB
Format
Adobe PDF
Checksum (MD5)
3606304d3d48ba0020447dceb017f5ed
Author(s)
Pratt, Vaughan R.
Date Issued
March 1980
Series/Report no.
MIT-LCS-TM-159
Abstract
Dynamic algebras constitute the variety (equationally defined class) of models of the Segerberg axioms for propositional dynamic logic. We obtrain the following results (to within inseparability). (i) In any dynamic algebra * is reflexive transitive closure. (ii) Every free dynamic algebra can be factored into finite dynamic algebras. (iii) Every finite dynamic algebra is isomorphic to a Kripke structure. (ii) and (iii) imply Parikh's completeness theorem for the Segerberg axioms. We also present an approach to treating the inductive aspect of recursion within dynamic algebras.
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