一句话：为含否定的高阶逻辑程序提出外延语义，定义分层与局部分层，并证明分层程序不会产生 unknown 真值。
本文研究带否定的高阶逻辑程序的外延语义。作者将 Bezem 为正高阶程序提出的外延语义技术推广到含否定情形，从而给出一种不同于 Charalambidis 等人的外延语义。作为直接结果，论文为所考虑语言定义了分层与局部分层概念，推广经典逻辑程序中的相应概念，并证明对分层及局部分层的高阶逻辑程序，所提语义不会赋予 unknown 真值。最后给出否定性结果：若按 Bezem 的技术把经典逻辑程序的稳定模型语义扩展到高阶情形，一般不能得到外延稳定模型。
We develop an extensional semantics for higher-order logic programs with negation, generalizing the technique that was introduced in [Bezem99,Bezem01] for positive higher-order programs. In this way we provide an alternative extensional semantics for higher-order logic programs with negation to the one proposed in [CharalambidisER14]. As an immediate useful consequence of our developments, we define for the language we consider the notions of stratification and local stratification, which generalize the familiar such notions from classical logic programming. We demonstrate that for stratified and locally stratified higher-order logic programs, the proposed semantics never assigns the unknown truth value. We conclude the paper by providing a negative result: we demonstrate that the well-known stable model semantics of classical logic programming, if extended according to the technique of [Bezem99,Bezem01] to higher-order logic programs, does not in general lead to extensional stable models.Comment: 24 pages. Submitted to Logical Methods in Computer Science
@article{paperbot396,
title = {Extensional Semantics for Higher-Order Logic Programs with Negation},
author = {Panos Rondogiannis and Ioanna Symeonidou},
journal = {Logical Methods in Computer Science},
volume = {Volume 14, Issue 2},
year = {2018},
doi = {10.23638/lmcs-14(2:19)2018}
}