Modeling Silence: A Penta-Valued Paraconsistent Logic
摘要
Silence is a diverse and intangible concept that we learn to interpret within the context where it appears. Here we show that there are various knowledge areas that have studied such phenomenon. We argue that “silence” is a manifestation of intentional communication. The seventh thesis of the Tractatus of Wittgenstein focuses on linguistic silence: “Whereof one cannot speak, thereof one must be silent”. We claim that some well known many-valued logics can be used to interpret the notion of “silence”. So, we introduce a new penta-valued paraconsistent logic that we name MS. This logic is both genuine and paracomplete, introducing a new value, denoted as s, which aims to model the concept of “silence”. MS is a conservative extension of FDEe, a logic originally proposed by Priest. By removing the “implication” connective from MS, we obtain FDEe. Conversely, if the ineffability value is removed from the MS, it leads to the well-known tetra-valued logic introduced by Avron. We will discuss several key properties of this new logic, highlighting its unique characteristics, and how it differs from or extends existing logical systems.