Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1093/logcom/exs001 | J. Log. Comput. |
Keywords | Field | DocType |
arbitrary abstract logic,1-dimensional basis,finite number,monadic second-order logic,2-dimensional basis,tense logic,k-dimensional basis,dedekind complete linear order,modal-logical basis,first-order logic,finite linear structure,regular language | Discrete mathematics,Multimodal logic,Substructural logic,Zeroth-order logic,Algorithm,Many-valued logic,Predicate logic,Mathematics,Intermediate logic,Monadic predicate calculus,Dynamic logic (modal logic) | Journal |
Volume | Issue | ISSN |
23 | 1 | 0955-792X |
Citations | PageRank | References |
0 | 0.34 | 11 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lauri Hella | 1 | 331 | 35.67 |
| Tero Tulenheimo | 2 | 16 | 5.19 |