Decidability/complexity of Entailment
The entailment relation in full CLL is undecidable. Fragments of CLL are often considered, for which the decision problem is more subtle:
- Multiplicative linear logic (MLL): only the multiplicative connectives. MLL entailment is NP-complete.
- Multiplicative-additive linear logic (MALL): only multiplicatives and additives (i.e., exponential-free). MALL entailment is PSPACE-complete.
- Multiplicative-exponential linear logic (MELL): only multiplicatives and exponentials. The decidability of MELL entailment is currently open.
Read more about this topic: Linear Logic
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