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Conference Papers Year : 2021

Covariant Subtyping Applied to Semantic Predicate Calculi

William Babonnaud

Abstract

Manipulating type hierarchies in formal semantic frameworks is often performed through a subtyping relation which obeys the contravariant rule for the left argument of a function type, due to the traditional representation of predicates as functions. This approach has however serious drawbacks when handling modifiers for first-order predicates. The present paper adopts an opposite view on subtyping by introducing a predicate calculus with a covariant behaviour, endowed with a categorical semantics in which subtyping coercions behave as generalisations of injective functions, and predicates are assimilated to powerobjects. This calculus is type safe in the sense that it prevents unwanted term applications, and is shown to provide a solution for the difficulties faced by a contravariant subtyping.
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Dates and versions

hal-03542057 , version 1 (07-02-2022)

Identifiers

  • HAL Id : hal-03542057 , version 1

Cite

William Babonnaud. Covariant Subtyping Applied to Semantic Predicate Calculi. LACL 2021 - Logical Aspects of Computational Linguistics, Dec 2021, Montpellier (online), France. ⟨hal-03542057⟩
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