Abstract
We study logics defined in terms of so-called second-order monadic groupoidal quantifiers. These are generalized quantifiers defined by groupoid word-problems or equivalently by context-free languages. We show that, over strings with built-in arithmetic, the extension of monadic second-order logic by all second-order monadic groupoidal quantifiers collapses to its fragment \({{\rm mon-}Q^1_{{\rm Grp}}}{\text{\rm FO}}\). We also show a variant of this collapse which holds without built-in arithmetic. Finally, we relate these results to an open question regarding the expressive power of finite leaf automata with context-free leaf languages.
The first author was partially supported by grant 106300 of the Academy of Finland and the Vilho, Yrjö and Kalle Väisälä Foundation. The second author was partially supported by DFG grant VO 630/6-1.
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Kontinen, J., Vollmer, H. (2008). On Second-Order Monadic Groupoidal Quantifiers. In: Hodges, W., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2008. Lecture Notes in Computer Science(), vol 5110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69937-8_21
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DOI: https://doi.org/10.1007/978-3-540-69937-8_21
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