
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.
[SHS.PHIL] Humanities and Social Sciences/Philosophy, word model, monadic second-order logic, k-dimensional modal logic, [MATH.MATH-LO] Mathematics [math]/Logic [math.LO], Expressive completeness, regular language
[SHS.PHIL] Humanities and Social Sciences/Philosophy, word model, monadic second-order logic, k-dimensional modal logic, [MATH.MATH-LO] Mathematics [math]/Logic [math.LO], Expressive completeness, regular language
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 0 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
