Everything about Linear logic
System of resource-aware logic
Linear logic is a substructural logic proposed by French logician 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. Although the logic has also been studied for its own sake, more broadly, 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. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Linear logicA 5-minute orientation
- Skim a recent paper: Novel logic mining incorporating log linear approachInfluential work since 2022
- Pick up a classic book: Mathematical proofsThe most-reprinted book on the subject
- Read the landmark paper: Linear logicCited 2,843 times
- Go sideways: Natural deductionA closely related topic
- Go sideways: Intuitionistic logicA closely related topic
📖 Definitions
Noun A logic in which two structural rules are missing from its sequent calculus: those for weakening and contraction; which has some extra logical connectives, so that it has both "additive" and "multiplicative" versions of the typical binary connectives and truth constants; and which has a pair of modal, "exponential" operators for resource management, to help make up for the loss of the two structural rules.
🏆 Landmark papers (most cited)
Linear logic
Logic Programming with Focusing Proofs in Linear Logic
Computational interpretations of linear logic
Quantales and (noncommutative) linear logic
Light Linear Logic
Linear-Input Logic
A new deconstructive logic: linear logic
Kripke models for linear logic
🆕 Influential since 2022
Novel logic mining incorporating log linear approach
Programmable Logic Controllers Past Linear Temporal Logic for Monitoring Applications in Industrial Control Systems
The Linear City: illustrating the logic of spatial equilibrium
Neurosymbolic Motion and Task Planning for Linear Temporal Logic Tasks
Analyzing Students’ Performance Using Fuzzy Logic and Hierarchical Linear Regression
📚 Books worth reading
Mathematical proofsGary Chartrand, Albert D. Polimeni · 2002
Logic-Based Methods for OptimizationJohn Hooker · 2000
Analog VLSIShih-Chii Liu · 2002
Equations with involutive operatorsN. K. Karapeti͡ant͡s, Nikolai Karapetiants · 2001
Invariant sets for WindowsTimothy N. Dragunov, Svetlana A. Boykova · 1999
A Beginner's Guide to Graph TheoryW.D. Wallis · 2000
From Linear Operators to Computational BiologyMartin Davis · 2012
A mathematical structure for emergent computationVictor Korotkich, V. Korotkikh · 1999
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Natural deduction In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to…
- Intuitionistic logic Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical…
- Proof-theoretic semantics Proof-theoretic semantics is a branch of proof theory and an approach to the semantics of logic in which the meaning of propositions and logical connectives…
- Propositional logic Propositional logic is a branch of classical logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic, or…
- Sequent calculus In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a…
- Structural proof theory In mathematical logic, structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof…
- Focused proof In mathematical logic, focused proofs are a family of analytic proofs that arise through goal-directed proof-search, and are a topic of study in structural…
- Sequent In mathematical logic, a sequent is a very general kind of conditional assertion. A 1 , … , A m ⊢ B 1 , … , B n . {\displaystyle A_{1},\,\dots ,A_{m}\…