| Grigori Mints. Linear lambda-terms and natural deduction. Studia Logica, 1998. To appear. |
....of our proposal we use no new features of natural deduction. The techniques used in this paper to formulate modalities, also apply to Girard s linear logic [20] Conversely there are a number of papers concerning linear logic which could be usefully studied in the context of modal logics, e.g. [3, 29, 28]. We leave this to future work. We also prefer the use of categorical models over traditional Kripke style possible worlds models. Unlike other categorical work we have placed emphasis on modelling the proof theory not just provability. Our resulting model is considerably simpler than other ....
G.E. Mints. Linear lambda-terms and natural deduction. Studia Logica, 60:209--231, 1998.
....for which strong normalization holds and yields unique normal forms. However, non standard presentations bypass commutative conversions and therefore extend the class of strongly normalizing languages (for example allowing Omega as a type constructor) although at the cost of added complexity [Min98]. We will not pursue this thread. A term M of type A is in j long form if it is structured as a sequence consisting solely of constructors (abstractions, pairing and unit) that matches the structure of the type A, applied to atomic terms in those positions where objects of base type are required. ....
Grigori Mints. Linear lambda-terms and natural deduction. Studia Logica, 1998. To appear.
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Grigori Mints. Linear lambda-terms and natural deduction. Studia Logica, 1998. To appear.
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