1. HISTORY

T HIS appendix gives an overview of the Grail system, developed as part of my PhD project, and its use as a tool for the development and proto-typing of grammar fragments for the multimodal Lambek calculus. Grail is an automated theorem prover based on proof nets and algebraic labeling, a combination discussed in Chapter 6. The theorem prover is implemented in SICStus Prolog, the user interface in TclTk. Though the underlying logic, with a minor restriction on the structural rules, is decidable, and the theorem prover can operate automatically, user guidance is often desirable during the proof search. It can increase the performance of the algorithm and, more importantly, help the user visualize the status of the proof attempt thereby showing why a given statement is prov-able or not. The Grail user interface is based on the Prolog debugger. At each proof step the user can take one of the following actions: select allows the user to select an inference step, leap performs automatic proof search until a proof is found, fail marks the current branch of the search tree as unsuccessful and abort abandons the entire proof attempt. In my experience, the interface gives users better insight in the operation of the theorem prover and greatly enhances its facilities for prototyping and debugging of fragments of the multimodal Lambek calculus.