Semantical bounds for everyday language
Marcin Mostowski, Jakub Szymanik

Abstract:
We consider the notion of "everyday language". We claim that everyday
language is semantically bounded by properties expressible in the
existential fragment of second-order logic. Two arguments for this
thesis are formulated. Firstly, we show that so-called Barwise's test
of negation normality (Barwise 1979) works properly only when assuming
our main thesis. Secondly, we discuss the argument from practical
computability for finite universes. Everyday language sentences are
directly or indirectly verifiable. We show that in both cases they are
bounded by second-order existential properties. Moreover, there are
known examples of everyday language sentences which are the most
difficult in this class ($NPTIME$-complete, see Mostowski &
Wojtyniak, 2004).

Keywords: everyday language, natural language, semantics,
  second-order logic, finite models