Questions tagged [linear-logic]

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12 votes
1 answer
737 views

Is Girard's LU just an embedding of classical and intuitionistic logic into linear logic?

This question is about Girard's system LU, presented in his paper On the unity of logic. Girard starts by giving a "modal" sequent calculus with two zones of both hypotheses and consequents, $\Gamma;\...
Mike Shulman's user avatar
11 votes
2 answers
2k views

Can linear logic be used to resolve unexpected hanging/surprise examination paradox?

In the Unexpected Hanging Paradox, the prisoner tries to narrow down their date of execution using seemingly sound logical reasoning. They instead arrive at a contradiction. When the paradox is ...
wlad's user avatar
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6 votes
1 answer
379 views

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 ...
Robin Houston's user avatar
5 votes
1 answer
557 views

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 ...
Robin Houston's user avatar
1 vote
1 answer
88 views

Injecting premises into two implicational premises connected by a tensor (multiplicative conjunction) in linear logic

I have another question regarding linear logic: I want to get to the proof E, using the premises in (1-4). Is this at all possible? 1: $A$ 2: $C$ 3: $(A\multimap B)\otimes(C\multimap D)$ 4: $B\...
Zerkezhi's user avatar