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Locus solum: From the rules of logic to the logic of rules. (English) Zbl 0999.68545
Fribourg, Laurent (ed.), Computer science logic. 15th international workshop, CSL 2001, 10th annual conference of the EACSL, Paris, France, September 10-13, 2001. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 2142, 38 (2001).
Summary: Logic is no longer about a preexisting external reality, but about its own protocols, its own geometry. Typically the negation is not about saying “NOT”, but about the mirror, the duality “I” vs. “the world” ...
The new approach encompasses the old one, typically if “I” win, “the world” loses, i.e., wins “NOT”. When logical artifacts are identified with their own rules of production, LOCATIVE phenomena arise. In particular, one realises that usual logic (including linear logic) is SPIRITUAL, i.e., up to isomorphism. But there is a deeper locative level, with indeed a more regular structure. Typically the usual (additive) conjunction has the value of categorical product in usual logic, and enjoys commutativity, associativity, etc. up to isomorphism.
In ludics, what corresponds is a plain intersection \(G \cap H\), which is really associative, commutative, etc. (no isomorphisms); it contains the usual conjunction as a delocalised case \(\varphi(G) \cap \psi(H)\). Incidentally this shows that the categorical view of logic – if very useful – is wrong... Nature abhors an isomorphism!
LUDICS is a monist approach to logic – without this nonsense distinction syntax/semantics/meta – just plain logical artifacts, period.
For the entire collection see [Zbl 0971.00033].

MSC:
68Q01 General topics in the theory of computing
68Q60 Specification and verification (program logics, model checking, etc.)
03B70 Logic in computer science
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