We study definability of second-order generalized quantifiers. We show that the question whether a second-order generalized quantifier Q1 is definable in terms of another quantifier Q2, the base logic being monadic second-order logic, reduces to the question if a quantifier Q1* is definable in FO(Q2*,<,+,×) for certain first-order quantifiers Q1* and Q2*. We use our characterization to show new definability and non-definability results for second-order generalized quantifiers. We also show that the monadic second-order majority quantifier Most1 is not definable in second-order logic. © 2014 Elsevier Inc.
A characterization of definability of second-order generalized quantifiers with applications to non-definability / Kontinen, Juha; Szymanik, Jakub. - In: JOURNAL OF COMPUTER AND SYSTEM SCIENCES. - ISSN 0022-0000. - 80:6(2014), pp. 1152-1162. [10.1016/j.jcss.2014.04.007]
A characterization of definability of second-order generalized quantifiers with applications to non-definability
Szymanik, Jakub
2014-01-01
Abstract
We study definability of second-order generalized quantifiers. We show that the question whether a second-order generalized quantifier Q1 is definable in terms of another quantifier Q2, the base logic being monadic second-order logic, reduces to the question if a quantifier Q1* is definable in FO(Q2*,<,+,×) for certain first-order quantifiers Q1* and Q2*. We use our characterization to show new definability and non-definability results for second-order generalized quantifiers. We also show that the monadic second-order majority quantifier Most1 is not definable in second-order logic. © 2014 Elsevier Inc.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
