Erratum to: A substructural logic for layered graphs

Abstract

Proposition 6.2 (2) and (3) of 'A substructural logic for layered graphs', by M. Collinson, K. McDonald, and D. Pym, Journal of Logic and Computation (2014) 24 (4): 953-988, are incorrect. We provide explanations of the failures of the intended proofs and specific counterexamples. The paper makes no further use of the claims and there are no consequences for the theory or examples that are presented.

Intuitionistic Layered Graph Logic

“…In particular, we can avoid degenerate cases of layering. (Note that this is a more general definition of scaffold than that taken in [9,10], where the structure was less tightly defined.) Technical considerations also come into play.…”

“…This construction of a countermodel would fail in a labelled tableaux system for LGL (i.e., the layered graph logic with classical additives [9]). This is because it is impossible to construct the internal structure of each subgraph in the model systematically, as the classical semantics for demands strict equality between the graph under interpretation and the decomposition into layers.…”

“…It is easy to see that assignments of resources can be composed and that the algebraic semantics can be easily extended (cf. [9]). …”

“…Layered graphs are an instance of a general algebraic semantics for the logic. Our approach stands in contrast to our previous work in this area [9,10] in that the additive component of the bunched logic [26,18] we employ is intuitionistic, with the consequence that we are able to obtain a tableaux system for the logic together with a completeness theorem for the layered graph semantics. In Section 2, we introduce layered graph semantics and ILGL, the associated intuitionistic layered graph logic.…”