Substructural Prolog?

Question

Substructural logic is logic without some or all of the structural rules. Is substructural Prolog, substructural logic programming possible? My question is connected with article https://link.springer.com/chapter/10.1007/3-540-40030-3_8 Grammar Induction as Substructural Inductive Logic Programming - if substructural Prolog is possible then one can implement substructural inductive logic programming in it (e.g. http://ilasp.com/ for the answer set version of ILP over Prolog in the non-substructural setting) and apply, e.g. in grammar induction case.

How hard the usual (e.g. SWI) Prolog should be remade to be used as substructural Prolog?

Answer 1

Logic programming with substructural logics has been studied, starting in the second half of the 90's. I am not an expert, but I can probably provide enough references to get you going.

There is Dale Miller's Lolli, a programming language for linear logic programming.

Major research was carried out by Frank Pfenning and his coworkers and students. For example:

• Frank Pfenning: lecture notes on Linear logic programming, part of a course on linear logic (the web site also has some software)

• Iliano Cervesato, Frank Pfenning: A Linear Logical Framework

• Jeff Polakow, Frank Pfenning: Properties of Terms in Continuation-Passing Style in an Ordered Logical Framework

• Frank Pfenning, Robert J. Simmons: Substructural Operational Semantics as Ordered Logic Programming

I am pretty sure someone implemented logic programming for ordered linear logic, poke around the work done by Jeff Polakow and Frank Pfenning. I don't seem to be able to find it right now.