## 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.

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(Show Context)
Citation Context ...ve constructors (Mendler [1991] and Coquand and Paulin [1990]) may be considered as quasi-quantifiers. Kopylov and Nogin [2001] established that modal logic of squash operator is, in fact, Lax Logic [=-=Fairtlough and Mendler, 1997-=-]. If instead of types one considers languages then logical connectives corresponding to product and star operations are described by Interval Temporal Logic (Moszkowski and Manna [1984]). 1.2 Logic o... |

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(Show Context)
Citation Context ...structors is not limited to product, disjoint union, and function, one can raise a question about logical principles describing behavior of other type constructors. For example, list, partial object [=-=Smith, 1995-=-] and squash [Constable et al., 1986] types can be viewed as modalities while inductive and co-inductive constructors (Mendler [1991] and Coquand and Paulin [1990]) may be considered as quasi-quantifi... |

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