Semantic bounds for everyday language

Semiotica 188 (1/4):363-372 (2012)
Abstract
We consider the notion of everyday language. We claim that everyday language is semantically bounded by the 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 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).
Keywords everyday language  natural language  semantics  second–order logic  finite models  computational complexity
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