In the next section, we identify a restricted pattern of use of linear logic in the glue analyses we are aware of, including those in [Crouch and van Genabith 1997, Dalrymple et al 1996,Dalrymple et al 1995] . And we show why that fragment is computationally feasible. In other words, while the glue approach could be used to express computationally intractable analyses, actual analyses have adhered to a pattern of use of linear logic that is tractable.
The rest of the paper shows how this pattern of use can be exploited to efficiently capture all possible deductions. We present a conservative extension of linear logic that allows a reformulation of the semantic contributions to better exploit this pattern, almost turning them into Horn clauses. We present a deduction algorithm for this formulation that yields a compact description of the possible deductions. And finally, we show how that description of deductions can be turned into a compact underspecified description of the possible meanings.