Skip to Main content Skip to Navigation
New interface
Conference papers

Projective unification through duality

Abstract : Unification problems can be formulated and investigated in an algebraic setting, by identifying substitutions to modal algebra homomorphisms. This opens the door to applications of the notorious duality between modal algebras and descriptive frames. Through substantial use of this correspondence, we give a necessary and sufficient condition for modal formulas to be projective. Applying this result to a number of different logics, we then obtain concise and lightweight proofs of their projective-or non-projective-character. In particular, we prove that the projective extensions of K5 are exactly the extensions of K45. This resolves the open question of whether K5 is projective.
Document type :
Conference papers
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03762785
Contributor : Philippe Balbiani Connect in order to contact the contributor
Submitted on : Monday, August 29, 2022 - 8:05:09 AM
Last modification on : Tuesday, August 30, 2022 - 3:54:48 AM

File

aiml22.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03762785, version 1

Citation

Philippe Balbiani, Quentin Gougeon. Projective unification through duality. Advances in Modal Logic (AiML 2022), Aug 2022, Rennes, France. ⟨hal-03762785⟩

Share

Metrics

Record views

41

Files downloads

7