Galois connections in categorial type logic

C. Areces, R. Bernardi, and M. Moortgat. Galois connections in categorial type logic. Electronic Notes in Theoretical Computer Science, 53:3–20, 2001. Extended version of FGMOL'01 paper of the same title.

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Abstract

The introduction of unary connectives has proved to be an important addition to the categorial vocabulary. The connectives considered so far are order-preserving; in this paper instead, we consider the addition of order-reversing, Galois connected operators. In §2 we do the basic model-theoretic and proof-theoretic groundwork. In §3 we use the expressive power of the Galois connected operators to restrict the scopal possibilities of generalized quantifier expressions, and to describe a typology of polarity items.

BibTeX

@Article{Areces2001b,
  author =       "C. Areces and R. Bernardi and M. Moortgat",
  journal =      "Electronic Notes in Theoretical Computer Science",
  title =        "Galois connections in categorial type logic",
  year =         "2001",
  abstract =     "The introduction of unary connectives has proved to be
                 an important addition to the categorial vocabulary. The
                 connectives considered so far are order-preserving; in
                 this paper instead, we consider the addition of
                 order-reversing, Galois connected operators. In §2 we
                 do the basic model-theoretic and proof-theoretic
                 groundwork. In §3 we use the expressive power of the
                 Galois connected operators to restrict the scopal
                 possibilities of generalized quantifier expressions,
                 and to describe a typology of polarity items.",
  note =         "Extended version of FGMOL'01 paper of the same
                 title.",
  pages =        "3--20",
  volume =       "53",
}