Live briefing
Everything about Structural proof theory
Subdiscipline of 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, a kind of proof whose semantic properties are exposed. When all the theorems of a logic formalised in a proof calculus have analytic proofs, then the proof calculus can be used to demonstrate such things as consistency, provide decision procedures, and allow mathematical or computational witnesses to be extracted as counterparts to theorems, the kind of task that is more often given to model theory. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Structural proof theoryA 5-minute orientation
- Skim a recent paper: Closed-Loop Valuation Theory: Structural Admissibility, Claimant Boundaries, and Computational Proof through Model CInfluential work since 2022
- Pick up a classic book: How to prove itThe most-reprinted book on the subject
- Read the landmark paper: The Church–Fitch knowability paradox in the light of structural proof theoryCited 22 times
- Go sideways: HypersequentA closely related topic
- Go sideways: Sequent calculusA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
The Church–Fitch knowability paradox in the light of structural proof theory
The λ-Calculus and the Unity of Structural Proof Theory
Glivenko sequent classes in the light of structural proof theory
Structural proof theory for first-order weak Kleene logics
On structural proof theory of the modal logic K+ extended with infinitary derivations
Structural Proof Theory
Structural Proof Theory
Russell’s theory of definite descriptions in the light of structural proof-theory
🆕 Influential since 2022
Closed-Loop Valuation Theory: Structural Admissibility, Claimant Boundaries, and Computational Proof through Model C
Mathematical Logic: Proof Theory, Constructive Mathematics
FORENSIC STRUCTURAL ENGINEERING IN THE MECHANISM OF CRIMINAL LAW EVALUATION OF UNAUTHORIZED CONSTRUCTIONS: ISSUES OF THEORY AND PRACTICE OF PROOF
📚 Books worth reading
How to prove itDaniel J. Velleman · 1994
Concurrent Zero-KnowledgeAlon Rosen · 2006
Proof theory for fuzzy logicsGeorge Metcalfe · 2009
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…
- 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…
- 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…
- Calculus of structures In mathematical logic, the calculus of structures (CoS) is a proof calculus with deep inference for studying the structural proof theory of noncommutative…
- 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…
- 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…
- 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…