# Questions tagged [linear-logic]

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21 questions
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### Lambek calculus, linear logic, and linear algebra

In his 1958 paper, The Mathematics of Sentence Structure, Joachim Lambek introduced the Lambek calculus. In modern terms, it could be understood as a syntax for biclosed monoidal categories, and he ...
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### Proof of ¬(¬1 ⊗ ¬1) in tensorial logic

I believe I once had a proof of this proposition, but it's been lost to the mists of time and old hard drives, so who knows if it was correct, and try as I might I can't seem to reproduce it. Is it ...
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### Dioperads vs polycategories

As defined by Gan, a dioperad consists of sets of operations $P(n,m)$ with "$n$ inputs and $m$ outputs", which can be composed by joining one output of one operation to one input of another, giving ...
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### Differential categories vs McBride's notion of derivative

Has anyone done an analysis to see if Blute, Cockett, and Seely's differential categories suffice to provide a notion of 1-hole context in the symmetric monoidal setting?
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### Can a relationship be constructed between the Coherence space and Phase space semantics of linear logic?

I'm not very familiar with linear logic, so please bear with me, i.e., please "read between the lines" to my underlying question if I don't formulate it rigorously correctly. To help model some of my ...
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### Embedding of classical into intuitionistic linear logic

Following on from this recent question, there is another construction that is well-known, but I don’t know a good primary source for: the Kolmogorov-style double-negation embedding of classical into ...
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### Conservativity of multiplicative linear logic over intuitionistic multiplicative linear logic

It is well known that multiplicative linear logic (MLL) is conservative over intuitionistic multiplicative linear logic (IMLL). In other words, if an IMLL formula is provable in MLL then it is already ...
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### Is it possible to implement η-reduction in interaction nets?

There are several ways to encode λ-terms in interaction nets; for instance, using the original optimal algorithm by Lamping, or compiling λ-calculus into interaction combinators. However, all the ...
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### Looking for papers and articles on the Tarskian Möglichkeit

Some background: Łukasiewicz many-valued logics were intended as modal logics, and Łukasiewicz gave an extensional definition of the modal operator: $\Diamond A =_{def} \neg A \to A$ (which he ...
Multiplicative intuitionistic linear logic (MILL) has only multiplicative conjunction $\otimes$ and linear implication $\multimap$ as connectives. It has models in symmetric monoidal closed ...