Everything about Sequent calculus
Style of formal logical argumentation
In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology instead of an unconditional tautology. Each conditional tautology is inferred from other conditional tautologies on earlier lines in a formal argument according to rules and procedures of inference, giving a better approximation to the natural style of deduction used by mathematicians than David Hilbert's earlier style of formal logic, in which every line was an unconditional tautology. More subtle distinctions may exist; for example, propositions may implicitly depend upon non-logical axioms. In that case, sequents signify conditional theorems of a first-order theory rather than conditional tautologies. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Sequent calculusA 5-minute orientation
- Skim a recent paper: Cascade laser optimization for 3 H 4 → 3 H 5 and 3 F 4 → 3 H 6 sequent transitions in Tm 3+ -doped materialsInfluential work since 2022
- Pick up a classic book: Guide to parallel programming on Sequent computer systemsThe most-reprinted book on the subject
- Read the landmark paper: Precipitation of heavy metals from wastewater using simulated flue gas: Sequent additions of fly ash, lime and carbon dioxideCited 385 times
- Go sideways: SequentA closely related topic
- Go sideways: Natural deductionA closely related topic
đź“– Definitions
Adjective That comes after in time or order; subsequent.
Adjective That follows on as a result, conclusion etc.; consequent to, on, upon.
Adjective Recurring in succession or as a series; successive, consecutive.
Noun Something that follows in a given sequence.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Precipitation of heavy metals from wastewater using simulated flue gas: Sequent additions of fly ash, lime and carbon dioxide
Contraction-free sequent calculi for intuitionistic logic
SeQuent Please World Wide Registry
Classical hydraulic jump: sequent depths
Automatic registration of UAV-borne sequent images and LiDAR data
Deep sequent systems for modal logic
Phase semantics and sequent calculus for pure noncommutative classical linear propositional logic
Sequent calculi for induction and infinite descent
🆕 Influential since 2022
Cascade laser optimization for 3 H 4 → 3 H 5 and 3 F 4 → 3 H 6 sequent transitions in Tm 3+ -doped materials
A robust and efficient algorithm for graph coloring problem based on Malatya centrality and sequent independent sets
Synthesis and Photophysical Properties of Carbazole-Functionalized Diazaphosphepines via Sequent P–N Chemistry
A Proof Tree Builder for Sequent Calculus and Hoare Logic
SeCaV: A Sequent Calculus Verifier in Isabelle/HOL
đź“š Books worth reading
Guide to parallel programming on Sequent computer systemsAnita Osterhaug · 1987
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- 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…
- 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…
- 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…
- Deduction theorem In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly…
- Suppes–Lemmon notation Suppes–Lemmon notation is a natural deductive logic notation system developed by E.J. Lemmon. Derived from Suppes' method, it represents natural deduction…
- Proof theory Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitati…
- Hilbert system In logic, more specifically proof theory, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style system, Hilbert-style proof system, Hilbert-style…