Lattice Logic Properly Displayed
Logic
2016-12-31 v1 Logic in Computer Science
Abstract
We introduce a proper display calculus for (non-distributive) Lattice Logic which is sound, complete, conservative, and enjoys cut-elimination and sub-formula property. Properness (i.e. closure under uniform substitution of all parametric parts in rules) is the main interest and added value of the present proposal, and allows for the smoothest Belnap-style proof of cut-elimination. Our proposal builds on an algebraic and order-theoretic analysis of the semantic environment of lattice logic, and applies the guidelines of the multi-type methodology in the design of display calculi.
Cite
@article{arxiv.1612.05930,
title = {Lattice Logic Properly Displayed},
author = {Giuseppe Greco and Alessandra Palmigiano},
journal= {arXiv preprint arXiv:1612.05930},
year = {2016}
}