We present a Revised Projectivity Calculus (denoted RC) that extends the scope of inclusion and exclusion inferences derivable under the Projectivity Calculus (denoted C) developed by Icard (Stud Log 100(4):705–725, 2012 ). After pointing out the inadequacies of C, we introduce four opposition properties (OPs) which have been studied by Chow (in: Aloni et al (eds) Proceedings of the 18th Amsterdam Colloquium, Springer, Berlin, 2012 ; Beziau, Georgiorgakis (eds) New dimensions of the square of opposition, Philosophia Verlag GmbH, München, 2017 ) and are more appropriate for the study of exclusion reasoning. Together with the monotonicity properties (MPs), the OPs will form the basis of RC instead of the additive/multiplicative properties used in C. We also prove some important results of the OPs and their relation with the MPs. We then introduce a set of projectivity signatures together with the associated operations and conditions for valid inferences, and develop RC by inheriting the key features of C. We then show that under RC, we can derive some inferences that are not derivable under C. We finally discuss some properties of RC and point to possible directions of further studies.

中文翻译：

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包含和排除推理的修订投影演算

我们提出了一个修订的投影演算（表示为 RC），它扩展了在 Icard 开发的投影演算（表示为 C）下可推导出的包含和排除推理的范围（Stud Log 100(4):705-725, 2012）。在指出 C 的不足之后，我们介绍了 Chow 研究过的四个对立属性 (OP)（在：Aloni 等人（编着）第 18 届阿姆斯特丹学术讨论会，斯普林格，柏林，2012 年；Beziau，Georgiorgakis（编着）对立平方的新维度，Philosophia Verlag GmbH，慕尼黑，2017 年），更适合于排除推理的研究。与单调性 (MP) 一起，OP 将构成 RC 的基础，而不是 C 中使用的加法/乘法属性。我们还证明了 OP 的一些重要结果及其与 MP 的关系。