Looking for papers and articles on modal substructural logics
I know of work adding temporal modalities to linear logic to produce what has been called temporal linear logic (in contrast to LTL = linear-time temporal logic). This is quite interesting: a formula (without a modality) is interpreted as resources being available now. The next time modality $\bigcirc-$ is interpreted as resources being available in the next time step. The box modality $\Box-$ means that the resources can be consumed at any point in the future,
determined by the holder of the resources, whereas $\lozenge-$ means that the resources can be consumed at any point in time determined by the system. Notice the duality between the holder of the resource and the system.


Banbara, M., Kang, K.-S., Hirai, T., Tamura, N.: Logic programming in a fragment of intuitionistic temporal linear logic. In: Codognet, P. (ed.) ICLP 2001. LNCS, vol. 2237, pp. 315–330. Springer, Heidelberg (2001)
Hirai, T.: Propositional temporal linear logic and its application to concurrent systems. EICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (Special Section on Concurrent Systems Technology) E83- A(11), 2219–2227 (2000)
Hirai, T.: Temporal Linear Logic and Its Application. PhD thesis, The Graduate School of Science and Technology, Kobe University, Japan (September 2000).
Kamide, N.: Temporalizing Linear Logic Bulletin of the Section of Logic Volume 36:3/4 (2007), pp. 173–182


There are a few papers adding all sorts of modalities to linear and affine logic:


Kamide, N.: Linear and affine logics with temporal, spatial and epistemic logics. Theoretical Computer Science 252, 165–207 (2006).
Kamide, N: Combining Soft Linear Logic and Spatio-Temporal Operators. J Logic Computation (2004) 14 (5): 625-650.


The work on temporal linear logic has been applied in agent-oriented programming and coordination, making essential use of the interpretation of the modalities described above:


Kungas, P.: Temporal linear logic for symbolic agent negotiation. In: Zhang, C., W. Guesgen, H., Yeap, W.-K. (eds.) PRICAI 2004. LNCS, vol. 3157, pp. 23–32. Springer, Heidelberg (2004)
Pham, D.Q., Harland, J., Winikoff, M.: Modelling agent’s choices in temporal linear logic. In: Baldoni, M., Son, T.C., van Riemsdijk, M.B., Winikoff, M. (eds.) DALT 2007. LNCS, vol. 4897, pp. 140–157. Springer, Heidelberg (2008)
Clarke, D. Coordination: Reo, Nets and Logic. 
FMCO proceedings, LNCS, vol.  5382. (2008)