Partial proof trees, resource sensitive logics and syntactic constraints

Abstract

We discuss the relationship between a categorial system (PPTS) based on partial proof trees (PPTs) as the building blocks of the system, resource sensitive logics and the nature of syntactic constraints. PPTS incorporates some of the key insights of lexicalized tree adjoining grammar, namely the notion of an extended domain of locality and the consequent factoring of recursion from the domain of dependencies. PPTS therefore inherits the linguistic and computational properties of that system. We discuss the relationship between PPTS, natural deduction, and linear logic proof-nets, and argue that a natural deduction system rather than a proof-net system is more appropriate for the construction of the PPTs. We also show how the use of PPTs allows us to ‘localize’ the management of resources, thereby freeing us from this management as the PPTs are combined.