Abstract
Linear logic, introduced by Jean-Yves Girard [Girard 1987], has aroused considerable interest among logicians and theoretical computer scientists. Among other things, linear logic is said to be a resource-conscious logic and a logic of actions. According to Girard [Girard 1995], it should be viewed as an extension of classical logic, rather than as an alternative logic.
All three authors acknowledge the financial support of the NSERC (Natural Sciences and Engineering Research Council) of Canada.
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Notes
All three authors acknowledge the financial support of the NSERC (Natural Sciences and Engineering Research Council) of Canada.
From [Girard 1995]: “The most traditional, and also the less interesting semantics of linear logic associates values to formulas, in the spirit of classical model theory. Therefore it only modelizes provability, and not proofs.”
We thank Vaughan Pratt for informing us about the electronic forum on linear logic, and for a compendium of messages about the relational model.
The abbreviations used in the table are the following: add. for additive, mult, for multiplicative, exp. for exponential, conj. for conjunctive and disj. for disjunctive.
Note that the additive operators of linear logic correspond to the absolute or Boolean operators of relation algebra and the multiplicative operators to the relative or Peircean operators [Tarski 1941].
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© 1997 Springer-Verlag Wien
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Desharnais, J., Hodgson, B., Mullins, J. (1997). Linear Logic. In: Brink, C., Kahl, W., Schmidt, G. (eds) Relational Methods in Computer Science. Advances in Computing Sciences. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6510-2_7
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DOI: https://doi.org/10.1007/978-3-7091-6510-2_7
Publisher Name: Springer, Vienna
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