2000/06/05 by Andrea Asperti, Asperti, Andrea, Luca Roversi +1
Computer Science · #F.1.1 #F.4.1 #FOS: Computer and information sciences #I.2.3 #Logic in Computer Science (cs.LO) #cs.LO
paper · pdf · doi:10.48550/arxiv.cs/0006010
arxiv created 2000/06/05 · arxiv updated 2009/11/30
This paper is a structured introduction to Light Affine Logic, and to its intuitionistic fragment. Light Affine Logic has a polynomially costing cut elimination (P-Time correctness), and encodes all P-Time Turing machines (P-Time completeness). P-Time correctness is proved by introducing the Proof nets for Intuitionistic Light Affine Logic. P-Time completeness is demonstrated in full details thanks to a very compact program notation. On one side, the proof of P-Time correctness describes how the complexity of cut elimination is controlled, thanks to a suitable cut elimination strategy that exploits structural properties of the Proof nets. This allows to have a good catch on the meaning of the ``paragraph'' modality, which is a peculiarity of light logics. On the other side, the proof of P-Time completeness, together with a lot of programming examples, gives a flavor of the non trivial task of programming with resource limitations, using Intuitionistic Light Affine Logic derivations as programs.