PP-2000-14: All proper normal extensions of S5--square have the polynomial size model property

PP-2000-14: Marx, Maarten and Bezhanishvili, Nick (2000) All proper normal extensions of S5--square have the polynomial size model property. [Report]

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Abstract

All proper normal extensions of S5--square have the polynomial size
model property
Maarten Marx, Nick Bezhanishvili

It is shown that all proper normal extensions of the bi-modal system
$S5^2$ have the poly-size model property. In fact, every normal proper
extension $L$ of $S5^2$ is complete with respect to a class of finite
frames $F_L$. To each such class corresponds a natural number $b(L)$
-- the bound of $L$. For every $L$, there exists a polynomial $P(.)$
of degree $b(L)+1$ such that every $L$-satisfiable formula $\phi$ is
satisfiable on an $L$-frame whose universe is bounded by $P(|\phi|)$,
for $|\phi|$ the number of subformulas of $\phi$. It is shown that
this bound is optimal.

Keyword(s): cylindric algebras, products of modal logic

Item Type:	Report
Report Nr:	PP-2000-14
Series Name:	Prepublication (PP) Series
Year:	2000
Date Deposited:	12 Oct 2016 14:36
Last Modified:	12 Oct 2016 14:36
URI:	https://eprints.illc.uva.nl/id/eprint/41

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