Intensional Logic for a Montague Grammar
Intensional Logic for a Montague Grammar

Summary/Abstract: In the paper Kułacka (2011) I introduced the syntax of a Montague grammar, following Richard Montague’s paper on The Proper Treatment of Quantification (1973, reprinted in 2002), and I also provided some historical background of the grammar and its significance. In the aforementioned paper, I discussed the ungrammatical sequences that are generated by the grammar. This paper will continue with the topic; I will explain the part of Montague’s paper on the syntax and semantics of an artificial language of Intensional Logic, which is used as intermediary between the objects and relations between them in a possible world, and expressions of the fragment of English, as introduced in Kułacka (2011). According to Montague, the procedure should be as follows: the expressions of natural language are translated into the expressions of a language of Intensional Logic and these have interpretations in the world. It is worth mentioning that the term ‘a Montague grammar’ stands for a language with its syntax and semantics, which is equivalent to a fragment of English. The presentation is based on the following works: Dowty et al. (1981), Gamut (1991), Montague (2002), Morrill (1994). However, we need to start with Lambda Calculus, which is used in calculating (composing) the logical expressions of Intensional Logic.

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