LambdaDL: Syntax and Semantics (Preliminary Report)

TL;DR

LambdaDL introduces a type-safe lambda calculus that integrates description logics to enable precise, satisfiable, and conceptualized semantic data access within programming languages.

Contribution

It presents a novel lambda calculus with a modified type system that incorporates description logics for safe semantic data integration.

Findings

Type safety of LambdaDL is formally proven.

Semantic conceptualizations are used as types.

Type-checked query access ensures data correctness.

Abstract

Semantic data fuels many different applications, but is still lacking proper integration into programming languages. Untyped access is error-prone while mapping approaches cannot fully capture the conceptualization of semantic data. In this paper, we present $\lambda_{DL}$,a $\lambda$-calculus with a modified type system to provide type-safe integration of semantic data. This is achieved by the integration of description logics into the $\lambda$-calculus for typing and data access. It is centered around several key design principles. Among these are (1) the usage of semantic conceptualizations as types, (2) subtype inference for these types, and (3) type-checked query access to the data by both ensuring the satisfiability of queries as well as typing query results precisely in $\lambda_{DL}$. The paper motivates the use of a modified type system for semantic data and it provides the theoretic foundation for the integration of description logics as well as the core formal specifications of $\lambda_{DL}$ including a proof of type safety.