> MAPPING SYNTAX TO LOGIC > > "RelEx + RelEx2Logic” maps syntactic structures into logical > structures. It takes in structures that care about left vs. right, > and outputs symmetric structures that don’t care about left vs. right. > The output of this semantic mapping framework, given a sentence, can > be viewed as a set of type judgments, i.e. a set of assignations of > terms to types. (Categorially, assigning term t to type T > corresponds to an arrow “t \circ ! : Gamma ---> T” where ! is an arrow > pointing to the unit of the category and Gamma is the set of type > definitions of the typed lambda calculus in question, and \circ is > function composition) .
One philosophically nice observation here is: Frege's "principle of compositionality" here corresponds to the observation that there is a morphism from the asymmetric monoidal category corresponding to link grammar, into the symmetric locally cartesian closed category corresponding to lambda calculus w/ dependent types... This principle basically says that you can get the meaning of the whole by combining the meaning of the parts, in language... The case of "Every man who has a donkey, beats it" illustrates that in order to get compositionality for weird sentences like this, you basically want to have dependent types in your lambda calculus at the logic end of your mapping... -- Ben -- You received this message because you are subscribed to the Google Groups "opencog" group. To unsubscribe from this group and stop receiving emails from it, send an email to opencog+unsubscr...@googlegroups.com. To post to this group, send email to opencog@googlegroups.com. Visit this group at https://groups.google.com/group/opencog. To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CACYTDBeG7g9VCWqr_wDp_WsW3bNoNseazL%3D0pXRqSyBqjoMgjA%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
