A categorial grammar of Spanish auxiliary chains

Spanish auxiliary sequences as in Juan puede haber tenido que estar empezando a trabajar hasta tarde 'Juan may have had to be starting to work until late', traditionally termed auxiliary chains, have two properties that are not naturally captured in phrase-structure approaches to syntax: (i) they follow no a priori fixed order; auxiliary permutations have different meanings, none of which is any more basic than any other (cf. Juan puede estar trabajando 'Juan may be working' and Juan está pudiendo trabajar 'Juan is currently able to work'); and (ii) the syntactic and semantic relations established within a chain go beyond strict monotonicity or cumulative influence; rather, they present different kinds of syntactic relations in distinct local domains. We show that an alternative to syntax grounded in a modification of the categorial grammar introduced in Ajdukiewicz (1935) that closely follows Montague (1973), Dowty (1978, 1979, 2003), and Schmerling (1983a, b, 2019) provides effective tools for subsuming Spanish auxiliary chains in an explicit and explanatory grammar