Handle: Engineering Artificial Musical Creativity at the “Trickery” Level - Computational Creativity Research: Towards Creative Machines - page 284

type NP and semantic value mary . The word 'loves' is a bit more complex. It has
syntactic type

( / ) \

NP , which means that the word 'loves' combines with an
NP on the left to give a phrase with type

S NP

; it then combines with an NP
on the right to give a phrase of type S , which is of course a complete sentence. The
word 'loves' has a lambda function as its semantic value; this function indicates the
operations we just described. The following is a parse tree for “John loves Mary”,
which results in an analysis that gives us loves

( S / NP )

( john , mary ) as the meaning of the

whole sentence at the bottom of the parse.

John
NP

loves

Mary
NP

: john ( S / NP ) \ NP : λ xy . loves ( x , y )

S / NP : λ y . loves ( john , y ) : mary

S : loves ( john , mary )

We observe that the CCG formalism can be adapted to music in order to enable us
to handle semantically rich theories of music that can go beyond shallow syntactic
forms to the deep meaning of musical pieces. While Steedman [23] presents a CCG
grammar for music, the grammar lacks any formal semantics; this is understandable,
given that the motivation behind Steedman's project was not to give a cognitive
account of music. Our semantics, specified using the Cognitive Event Calculus, has
intensional operators and fluents, both of which would eventually be necessary for
modeling all aspects of music and cognition, from composition and generation to
performance and listening.
Fig. 14.3 shows a part of the signature of our preliminary music calculus. We
have self-explanatory sorts for representing different aspects of the musical universe.
Note has its usual standard interpretation. A Score is a sequence of notes formed
using the function symbol add .A MusicParticle is a note played at a particular
moment and can be considered the simplest MusicPhrase . Simpler MusicPhrase s
combine in myriad ways to form complex MusicPhrase s; this is represented using
combine . The rendition of a Score using a Recommendation in a performance
results in a MusicPhrase . The music phrases have meanings Meaning which form
a subset of the lambda expressions; the meanings combine using reduce . The phrases
have abstract types Type ; the types combine using apply . Allowed combinations of
music phrases are represented using allowed . Recommendations by the conductor