The logic of resources and tasks
Giorgi Japaridze, Scott Weinstein · 1998
Despite many attempts, the resource philosophy associated with linear logic and other substructural logics has never really been formalized as a mathematically strict and intuitively convincing resource semantics. The dissertation is devoted to developing this kind of semantics. It introduces an extension of the language of linear logic with a semantics which treats sentences as tasks rather than true/false statements. A resource is understood as an agent capable of accomplishing the task expresses by such a sentence. The corresponding logic can be used as a planning logic, whose advantage over the traditional comprehensive planning logics is that it avoids the representational frame problem and significantly alleviates the inferential frame problem. The logic is shown to be decidable when its language is restricted to the first-order multiplicative-additive (MALL) fragment of the language of linear logic.