Montague-Gallin’s Intensional Logic, Structured Meanings and Scott’s Domains
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In this paper we present an extension of Montague-Gallin’s Intensional Logic, called Hyperintensional Logic (HL), which includes both the notion of structured meaning and the notion of Scott’s domain. On the one hand, structured meanings solve the problem of the failure of substitutivity of logically equivalent sentences in propositional attitude contexts. On the other hand, Scott’s domains solve in a general and natural way the set-theoretical problem of the reiteration of hyperintensional functors,which are functors denoting functions taking structured meanings (or intensional structures) as arguments. HL has many advantages on a similar, but in many respects different system already suggested by the author1. First, the logical connectives and the quantifiers are easier to define; secondly, we need to define only one system of inverse limits instead of two; finally, it is a natural conservative extension of a well known formal system. In what follows an acquaintance with Montague-Gallin’s Intensional Logic (see , ), Structured Meanings Semantics (see , ) and Domain Theory (see , , , ) is presupposed.
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