How exactly does implication work? Philosopher Paul Grice might have had a couple decent ideas.
Logic & Conversation, lecture by Paul Grice - https://msu.edu/~orourk51/800-Phil/Handouts/Readings/Phil%20Lang/Grice-Logic&Conversation-WJL-1989.pdf
“What we say vs what we mean: what is conversational implicature?” by Maria Kasmirli - https://aeon.co/ideas/what-we-say-vs-what-we-mean-what-is-conversational-implicature
Paul Grice, by the Stanford Encyclopedia of Philosophy - https://plato.stanford.edu/entries/grice/#ConvImpl
The Logical Syntax of Language, by Rudolf Carnap - https://altexploit.files.wordpress.com/2017/09/rudolf-carnap-logical-syntax-of-language-international-library-of-philosophy-2001.pdf