On the Existence of a Modal-Logical Basis for Monadic Second-Order Logic

Hella, Lauri; Tulenheimo, Tero

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1093/logcom/exs001

Title :

On the Existence of a Modal-Logical Basis for Monadic Second-Order Logic

Author(s) :

Hella, Lauri [Auteur]
University of Tampere [Finland]
Tulenheimo, Tero [Auteur]
Savoirs, Textes, Langage (STL) - UMR 8163 [STL]

Journal title :

Journal of logic and computation

Pages :

1-24

Publisher :

Oxford University Press (OUP)

Publication date :

2012-03-13

ISSN :

0955-792X

HAL domain(s) :

Sciences de l'Homme et Société/Philosophie
Mathématiques [math]/Logique [math.LO]

English abstract : [en]

Kamp (PhD Thesis, University of California, LA) proved that the tense logic of the connectives Until and Since is expressively complete over the class DCLO of Dedekind complete linear orders in the sense that this logic ...
Show more >Kamp (PhD Thesis, University of California, LA) proved that the tense logic of the connectives Until and Since is expressively complete over the class DCLO of Dedekind complete linear orders in the sense that this logic can express exactly the same conditions over DCLO as first-order logic. In the present article a modification of the question of expressive completeness is considered--the question of whether there exists a basis consisting of a finite number of modal-logical connectives for monadic second-order logic. The notion of k-dimensional basis that Gabbay (1981, Aspects of Philosophical Logic, 91-117) defined relative to FO is generalized to arbitrary abstract logics, and it is shown that a finite 2-dimensional basis exists for MSO on the class FLO of all finite linear structures. Beauquier and Rabinovich (2002, J. Logic. Comput., 12, 243-253) have proven that there is no finite 1-dimensional basis for MSO on FLO. Thus, the result yielding a 2-dimensional basis cannot be improved.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Savoirs, Textes, Langage (STL) - UMR 8163

Source :

Harvested from HAL

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