2008/05/14 by Genta Ito, Ito, Genta
Computer Science · #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.0805.2063
openalex publication_date 2008/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a construction of a certain infinite complete partial order (CPO) that differs from the standard construction used in Scott's denotational semantics. In addition, we construct several other infinite CPO's. For some of those, we apply the usual Fixed Point Theorem (FPT) to yield a fixed point for every continuous function μ:2→ 2 (where 2 denotes the set \0,1\), while for the other CPO's we cannot invoke that theorem to yield such fixed points. Every element of each of these CPO's is a binary string in the monotypic form and we show that invalidation of the applicability of the FPT to the CPO that Scott's constructed yields the concept of replication.