2016/05/06 by Fritz Müller, Müller, Fritz
Computer Science · #Artificial Intelligence in Games #F.3.2 #F.4.1 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #cs.LO
paper · pdf · doi:10.48550/arxiv.1605.01886
35 pages, 4 figures
arxiv created 2016/05/06 · openalex publication_date 2016/05/06 · arxiv updated 2016/05/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Normann proved that the domains of the game model of PCF (the domains of sequential functionals) need not be dcpos. Sazonov has defined natural domains for a theory of such incomplete domains. This paper further develops that theory. It defines lub-rules that infer natural lubs from existing natural lubs, and lub-rule classes that describe axiom systems like that of natural domains. There is a canonical proper subcategory of the natural domains, the closed directed lub partial orders (cdlubpo), that corresponds to the complete lub-rule class of all valid lub-rules. Cdlubpos can be completed to restricted dcpos, which are dcpos that retain the data of the incomplete cdlubpo as a subset.