I hope my possibly partial answer won't get me jumped, but I have found it incredibly helpful in many situations like yours to locate the term with the appropriate semantics on Wikipedia in a language I speak, which can often times disambiguate it better than a dictionary and provide examples for its use within the article. It worked well for me in many cases where I was unsure which of the many translation for an English term to use.
So, if you want the more formal term of logical implication, or any very specific concept, I navigate to the appropriate page in any of the other languages I speak (I speak five languages and some terms I only know in one of them) and then simply choose the language in which I really want to understand the term and its use, plus surrounding context.
The page https://en.wikipedia.org/wiki/Material_conditional brought me to the Japanese term 論理包含. That's the noun for the concept, though, as a regular dictionary can then verify for you, but you are a lot closer. You can then see the various ways in which the concept is conveyed and look for which verbs are used to express the transitive relationship. Thus, further down the article you will find:
P ⇒ Q（P implies Q、P は Q を包含する）
This way, you can disambiguate the term and find the precise concept in a language you are more comfortable with first. If you just type "implies" in a dictionary then it will look up all other ways in which it is used, not just the one semantic you are trying to describe. There are other, similar terms, such as "indicative conditional" and specifying the precise meaning you want to convey in such an exact manner goes beyond most dictionaries. I am still learning Japanese, but because I am a PhD student I need a lot of technical terms like the one above for which a simple dictionary usually yields the wrong term or I do not know which one to use. I had just read the Japanese article about Boolean logic so I just had to contribute this answer when I saw this question about "implication".
I think this might also be a helpful answer because you asked for an answer without kanji. The nice thing is that virtually all Japanese Wikipedia pages have the kanji and its reading in hiragana in the first sentence with the term, so this might be a good way to satisfy your request:
論理包含（ろんりほうがん、含意（がんい）、内含、英: implication、IMP）は ...
If you are saying that something "means" or is equivalent with something then the simple 意味【いみ】as the other replies have explained much better looks like a more fitting choice. But if it's really important to be precise about it and say something like an animal being a shiba implies that it is a dog (but not the other way around, as would be a logical equivalence) then this might be of interest to you and others looking for ways to express actual implication. I might have misinterpreted your question, but it sounded a little like you were unsatisfied with the term "A means B" because you wanted to express something more akin to formal implication of this sort, so I hope this does not confuse and adds a meaningful addition to the other answers.
If you are looking for something with more informal nuance of "hint at" it seems the verb "ほのめかす" conveys that. Then there is also 示唆【しさ】する which is more formal to the level of something that would be used to express implication in an article. In the concrete context you provide the former does not fit, but you would probably use it in a context where you want to say that something is not expressly stated but should be read as "reading between the lines". It depends on what kind of "implies" you mean and although your example narrows down which ones you mean, we all sometimes forget all the different contexts in which we use the same word in English but actually convey a subtly different context.
If you want to draw more attention to something "denoting/exemplifying/showing" something else I think the verb 示【しめ】す can be used. This way you can express something like "His title showed/implied his knowledge in the field." as opposed to simply "means" to convey that something has an implication beyond its immediate meaning/definition as you seemed to try to do.