I relied on the Logic of English (LoE) phonograms to give myself a better understanding of English pronunciation since the spelling gives me a hard time (even as native speaker), but I noticed that the phonograms do not match any accent/dialect I am aware of. LoE appears to be using a variant of the American Heritage Dictionary (AHD) pronunciation key, but represents /u/ and /ʊ/ with <ö> and <ü>.
LoE seems to be intended for speakers of General American (GenAm), not Received Pronunciation (RP), yet it distinguishes /ɑ/ (<ä>) and /ɒ/ (<ŏ>) but not /ɔ/ (represented in AHD as <ô>). As far as I know, the father-bother merger (/ɑ/=/ɒ/) and cot-caught merger (/ɒ/=/ɔ/) never led to that outcome.
LoE matches neither RP nor GenAm. RP distinguishes /ɔ/ but LoE does not, while LoE distinguishes /ɒ/ but GenAm does not. What does it match?