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Everything about Substructural logic
Branch of non-classical logic
In logic, a substructural logic is a logic lacking one of the usual structural rules, such as weakening, contraction, exchange or associativity. Two of the more significant substructural logics are relevance logic and linear logic. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Substructural logicA 5-minute orientation
- Skim a recent paper: Editorial Introduction: Substructural Logics and MetainferencesInfluential work since 2022
- Pick up a classic book: Mathematical structures for computer scienceThe most-reprinted book on the subject
- Read the landmark paper: Substructural fuzzy logicsCited 134 times
- Go sideways: HypersequentA closely related topic
- Go sideways: Structural proof theoryA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Substructural fuzzy logics
Substructural logics on display
Constructive Logic with Strong Negation as a Substructural Logic
Structural Completeness in Substructural Logics
Constructive Logic with Strong Negation is a Substructural Logic. I
Constructive Logic with Strong Negation is a Substructural Logic. II
Substructural epistemic logics
Gaggles, Gentzen and Galois: how to display your favourite substructural logic
🆕 Influential since 2022
Editorial Introduction: Substructural Logics and Metainferences
A SUBSTRUCTURAL GENTZEN CALCULUS FOR ORTHOMODULAR QUANTUM LOGIC
Projectivity and unification in substructural logics of generalized rotations
COLLECTION FRAMES FOR DISTRIBUTIVE SUBSTRUCTURAL LOGICS
On the Adequacy of a Substructural Logic for Mathematics and Science
📚 Books worth reading
Mathematical structures for computer scienceJudith L. Gersting · 1982
The pyramid principleBarbara Minto · 1978
Discrete and combinatorial mathematicsRalph P. Grimaldi · 1985
Substructural LogicsF. Paoli · 2002- 📕Introduction to Substructural LogicsGreg Restall · 2002
Quantifiers, propositions, and identityRobert Goldblatt · 2011
An Introduction to Substructural LogicsGreg Restall · 2000
Residuated latticesNikolaos Galatos · 2007
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Hypersequent In mathematical logic, the hypersequent framework is an extension of the proof-theoretical framework of sequent calculi used in structural proof theory…
- 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…
- Linear 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…
- 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…
- 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}\…
- Structural rule In the logical discipline of proof theory, a structural rule is an inference rule of a sequent calculus that does not refer to any logical connective but…
- Cut-elimination theorem The cut-elimination theorem (or Gentzen's Hauptsatz) is the central result establishing the significance of the sequent calculus. It was originally proved…
- 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…