As far as I can see, there is no way to do this without using a database. The “algorithm” itself would be a combination of the database structure and the queries made for it.
For example, a relational database in which there is a table of English words, each of two columns: a word and one or more parts of speech, is the most basic base for processing a language. A more complex table of verbs with two columns, a word and "temporal characteristics" will also be more complex.
As an example, the word "be" always describes a state. Therefore, a program that sees the word be (or its conjugation: is, is, was, etc.) can immediately recognize the sentence as a description of the state state. Obviously, the word “fulfill” will immediately mean achievement, and “achievement” will always mean achievement. But do not forget that of the four categories that you indicated, only “state” and “event” are mutually exclusive (with the exception of the present participle, for example, in the sentence “Event occurs”). In addition, the state can also be an achievement or an achievement (“I am an Olympic champion”), and therefore an event can occur (“I finished tomorrow”.).
Achievements and achievements are also subjective terms and depend on the feelings of both the speaker and the reader. Words such as “achievement,” “achieved,” and “succeeding,” are deliberate expressions of a sense of achievement, and therefore can always be classified as such. However, this is a priori information and therefore requires the implementation of a relational database.
Finally, some “temporal characteristics” of some words change depending on the other words in the sentence . For example, in the sentence "I smell good." "Smell" is a verb of state. In the sentence "I smell bacon," this is a verb of action. These verbs are action verbs followed by a noun (transitive), state verbs that are followed by an adjective (nominal predicate) and action verbs, followed by none (intransitive). Therefore, the analyzer will have to check the words that follow it in the sentence, one as a noun or adjective, and this recognizes the role of the verb in the sentence. This is a joint effort between the database, knowing the parts of the speech of each word, and an algorithm that allows you to parse the sentence correctly (and just knowing that it generally needs to parse it).
This is just a brief overview of lessographic calculations and just my knowledge on this subject. It is much more and obviously tedious to populate the database with words and their parts of speech, definitions, roles, etc. There may exist databases pre-filled with information that a lexicographic computer scientist will have to implement such a system (but I do not claim to know where to find them).
Hope I helped and good luck!