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Everything about Hypersequent
In mathematical logic, the hypersequent framework is an extension of the proof-theoretical framework of sequent calculi used in structural proof theory to provide analytic calculi for logics that are not captured in the sequent framework. A hypersequent is usually taken to be a finite multiset of ordinary sequents, written Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: HypersequentA 5-minute orientation
- Skim a recent paper: Cyclic Hypersequent System for Transitive Closure LogicInfluential work since 2022
- Pick up a classic book: Proof theoryThe most-reprinted book on the subject
- Read the landmark paper: Hypersequent Calculi for Godel Logics -- a SurveyCited 48 times
- Go sideways: Structural proof theoryA closely related topic
- Go sideways: Admissible ruleA closely related topic
📖 Definitions
Noun A multidimensional generalization of a sequent
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Hypersequent Calculi for Godel Logics -- a Survey
Sequent and hypersequent calculi for abelian and łukasiewicz logics
Hypersequent rules with restricted contexts for propositional modal logics
Hypersequent and Display Calculi – a Unified Perspective
LINEAR TIME IN HYPERSEQUENT FRAMEWORK
Hypersequent Calculi for some Intermediate Logics with Bounded Kripke Models
Hypersequent calculi for non-normal modal and deontic logics: countermodels and optimal complexity
Embedding the hypersequent calculus in the display calculus
🆕 Influential since 2022
📚 Books worth reading
- 📕Proof theoryKatalin Bimbo · 2015
Automated Reasoning With Analytic Tableaux and Related MethodsMarta Cialdea Mayer, Fiora Pirri · 2003
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- 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…
- Admissible rule In logic, a rule of inference is admissible in a formal system if the set of theorems of the system does not change when that rule is added to the existing…
- Non-normal modal logic A non-normal modal logic is a variant of modal logic that deviates from the basic principles of normal modal logics. Normal modal logics adhere to the…
- 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…
- 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…
- Substructural logic In logic, a substructural logic is a logic lacking one of the usual structural rules (e.g. of classical and intuitionistic logic), such as weakening, contractio…
- 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}\…
- 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…