# Questions tagged [linear-logic]

Linear logic is a substructural logic proposed by Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter. Ideas from linear logic have been influential in fields such as programming languages, game semantics, and quantum physics, as well as linguistics, particularly because of its emphasis on resource-boundedness, duality, and interaction.

49 questions
Filter by
Sorted by
Tagged with
1 vote
37 views

• 67
311 views

### Is currying valid in Linear logic and Relevance logic?

In Classical and Intuitionistic logic we have what I will call the "currying equivalence": $P \rightarrow (Q \rightarrow P) \equiv (P \land Q) \rightarrow P$ But linear and relevance logics do not ...
• 1,413
84 views

### Transforming intuitionistic propositional validities into validities of linear logic

A tableaux method for linear logic is briefly discussed in https://www.academia.edu/6591354/TABLEAU_METHODS_FOR_SUBSTRUCTURAL_LOGICS?auto=download D'Agostino writes (p.418-9): ''It is ...
• 1,413
1k views

### Why is it called linear logic?

Why is it called "Linear" Logic? What's linear about it?
• 233
142 views

### Resource request: linear logic

Is there any correct book/textbook/pdf to understand what is linear logic ? I do research in (standard) logic/model theory, so I'm totally ok with a text which assumes mathematical maturity.
109 views

### Can I derive $\vdash \Gamma$ from $\vdash \Gamma, A, A^\bot$?

The Wikipedia article on linear logic mentions the following as an initial sequent: $$\over \vdash A, A^\bot$$ As far as I can understand from informal descriptions of linear-logic semantics, this ...
• 133
125 views

### Basic equivalences in linear logic

How do we obtain the equivalence $A \otimes 0 \equiv 0$ and its dual in linear logic? Are they a consequence of cut-elimination? I found them listed as basic equivalences in the following resource: ...
• 31
1k views