Towards a Simply Typed CALculus for Semantic Knowledge Bases

16 pagesPublished: May 15, 2012

Abstract

This paper demonstrates how a constructive version of the description logic ALC can serve as a semantic type system for an extension of the simply typed $\lambda$-calculus to express computations in knowledge bases. This cALculus embodies a functional core language which provides static type checking of semantic information for programming with data whose structure is organised under a relational data model. The cALculus arises from a natural interpretation of the tableau rules for constructive ALC following the Curry-Howard-Isomorphism.

Keyphrases: Constructive Description Logic, Curry-Howard isomorphism, Modal Type Theory, simply typed lambda calculus

In: Berndt Müller (editor). LAM'10. 3rd International Workshop on Logics, Agents, and Mobility, vol 7, pages 52--67