The Grail theorem prover: Type theory for syntax and semantics

As the name suggests, type-logical grammars are a grammar formalism based on logic and type theory. From the prespective of grammar design, type-logical grammars develop the syntactic and semantic aspects of linguistic phenomena hand-in-hand, letting the desired semantics of an expression inform the syntactic type and vice versa. Prototypical examples of the successful application of type-logical grammars to the syntax-semantics interface include coordination, quantifier scope and extraction.This chapter describes the Grail theorem prover, a series of tools for designing and testing grammars in various modern type-logical grammars which functions as a tool . All tools described in this chapter are freely available

Modelling Combinatorial Auctions in Linear Logic

We show that linear logic can serve as an expressive framework in which to model a rich variety of combinatorial auction mechanisms. Due to its resource-sensitive nature, linear logic can easily represent bids in combinatorial auctions in which goods may be sold in multiple units, and we show how it naturally generalises several bidding languages familiar from the literature. Moreover, the winner determination problem, i.e., the problem of computing an allocation of goods to bidders producing a certain amount of revenue for the auctioneer, can be modelled as the problem of finding a proof for a particular linear logic sequent

LT revisited : explanation-based learning and the logic of Principia mathematica

This paper describes an explanation-based learning (EBL) system based on a version of Newell, Shaw and Simon's LOGIC-THEORIST (LT). Results of applying this system to propositional calculus problems from Principia Mathematica are compared with results of applying several other versions of the same performance element to these problems. The primary goal of this study is to characterize and analyze differences between not learning, rote learning (LT's original learning method), and EBL. Another aim is to provide base-line characterizations of the performance of a simple problem solver in the context of the Principa problems, in the hope that these problems can be used as a benchmark for testing improved learning methods, just as problems like chess and the eight puzzle have been used as benchmarks in research on search methods