## Logic of subtyping (2005)

Venue: | Theoretical Computer Science |

Citations: | 3 - 2 self |

### BibTeX

@ARTICLE{Naumov05logicof,

author = {Pavel Naumov},

title = {Logic of subtyping},

journal = {Theoretical Computer Science},

year = {2005},

volume = {2005}

}

### OpenURL

### Abstract

We introduce new modal logical calculi that describe subtyping properties of Cartesian product and disjoint union type constructors as well as mutually-recursive types defined using those type constructors. Basic Logic of Subtyping S extends classical propositional logic by two new binary modalities ⊗ and ⊕. An interpretation of S is a function that maps standard connectives into set-theoretical operations (intersection, union, and complement) and modalities into Cartesian product and disjoint union type constructors. This allows S to capture many subtyping properties of the above type constructors. We also consider logics Sρ and S ω ρ that incorporate into S mutually-recursive types over arbitrary and well-founded universes correspondingly. The main results are completeness of the above three logics with respect to appropriate type universes. In addition, we prove Cut elimination theorem for S and establish decidability of S and S ω ρ.