sequent calculus
Formal derivation framework
Sequent calculus is a formal system in mathematical logic for analyzing proofs.
Unlike natural deduction, which mimics ordinary reasoning, sequent calculus represents logical arguments as sequences of formulas on either side of a turnstile symbol, showing what follows from what.
The format makes proof structure explicit and is particularly useful for proving properties about logic itself—like whether a system is consistent or whether proofs can be simplified.
Rotating single-passage barrier
- axiomSelf-evident starting principle
- contractionReduction in size
- weakeningBecoming less strong
- exchangeMutual giving and receiving
context · premise · conclusion
Adjusting to a standard
- decidabilityAlgorithmic resolution capability
- consistencyReliable adherence to standards
- completenessState of being whole
- derivationSource or origin tracing
admissibility · focusing · polarization · metatheory · interpolation
turnstile
Rotating single-passage barrier
- axiomSelf-evident starting principle
- contractionReduction in size
- weakeningBecoming less strong
exchange · context · premise · conclusion
normalization
Adjusting to a standard
- decidabilityAlgorithmic resolution capability
- consistencyReliable adherence to standards
- completenessState of being whole
derivation · admissibility · focusing · polarization · metatheory · interpolation
classical
Of ancient Greece/Rome
- logicpremise, premises, conclusion, conclusions, inference
- Formal Methodsspecifications, invariants, preconditions, soundness, completeness
- Constructive Logicintuitionism, Heyting algebra, constructivism, double negation, natural deduction
- formal systemsformal logic, axioms, postulates, derivation, proofs
- linear logictensor, par, with, plus, of course
- Proof Theoryproof, theorem, axiom, lemma, corollary