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On the share of closed IL formulas which are also in GL (CROSBI ID 201625)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Kovač, Vjekoslav ; Čačić, Vedran On the share of closed IL formulas which are also in GL // Archive for mathematical logic, 54 (2015), 7; 741-767. doi: 10.1007/s00153-015-0438-7

Podaci o odgovornosti

Kovač, Vjekoslav ; Čačić, Vedran

engleski

On the share of closed IL formulas which are also in GL

Normal forms for wide classes of closed IL formulas were given in Čačić and Vuković (Math Commun 17:195–204, 2012). Here we quantify asymptotically, in exact numbers, how wide those classes are. As a consequence, we show that the "majority" of closed IL formulas have GL-equivalents, and by that, they have the same normal forms as GL formulas. Our approach is entirely syntactical, except for applying the results of Čačić and Vuković. As a byproduct we devise a convenient way of computing asymptotic behaviors of somewhat general classes of formulas given by their grammar rules. Its applications do not require any knowledge of the recurrence relations, generating functions, or the asymptotic enumeration methods, as all these are incorporated into two fundamental parameters.

interpretability logic ; normal forms ; asymptotic enumeration

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Podaci o izdanju

54 (7)

2015.

741-767

objavljeno

0933-5846

10.1007/s00153-015-0438-7

Povezanost rada

Matematika

Poveznice
Indeksiranost