限制性推理规则与次协调
Restricted Rules of Inference and Paraconsistency
摘要：
在本文中，我们研究了逻辑的两个同伴，即，左变量包含同伴和限制规则同伴，它们的性质和相互关系，特别是与次协调。证明了两个伴点重合的一个充分条件。本文给出了两个新的逻辑系统--直觉次协调弱Kleene逻辑（IPWK）和次协调预粗糙逻辑（PPRL）--作为左变量包含逻辑的例子。IPWK是直觉命题逻辑（IPC）的左变量包含同伴，也是IPC的限制规则同伴，PPRL是Pre-Rough逻辑（PRL）的左变量包含同伴，但与PRL的限制规则同伴不同.这相当于引入了一个污染的真假值，旨在表示一种不确定性状态。
英文摘要：
In this paper, we study two companions to a logic, viz., the left variable inclusion companion and the restricted rules companion, their nature and interrelations, especially in connection with paraconsistency. A sufficient condition for the two companions to coincide has also been proved. Two new logical systems - Intuitionistic Paraconsistent Weak Kleene logic (IPWK) and Paraconsistent Pre-Rough logic (PPRL) - are presented here as examples of logics of left variable inclusion. IPWK is the left variable inclusion companion of Intuitionistic Propositional logic (IPC) and is also the restricted rules companion of it. PPRL, on the other hand, is the left variable inclusion companion of Pre-Rough logic (PRL) but differs from the restricted rules companion of it. We have discussed algebraic semantics for these logics in terms of Płonka sums. This amounts to introducing a contaminating truth value, intended to denote a state of indeterminacy.
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