Prof. Lee and user6726 have given excellent answers above. Though I think the OP's use of semantic criterion isn't completely wrong: The problem is, as Prof. Lee has pointed out above, that he assumes there must be a set of necessary and sufficient conditions that allow us to deduce what a 'verb' is like, and such conditions don't exist.
But semantic criteria are helpful in identifying prototypical verbs in a language. When we start analysing a language, after all, we have no idea what morphosyntactic criteria there are for us to identify word classes with. Words with similar functional, morphological and syntactic behaviour as these prototypical verbs would then be classified as 'verbs'.
Givón (2001) gave this set of criteria for identifying prototype verbs:
- High temporal instability
- Great temporal compactness
- Events involving concrete participant nouns
- Often great complexity in meaning
- Either agentive or about mental activity
So once we've identified a set of prototype verbs in a language - e.g. 'kill', 'stab', 'fight', 'realise', etc., we look at what distributional and morphosyntactic features they have. Unlike the structuralists, though, we don't treat them as necessary and sufficient conditions. Instead, we treat them as violable rules. A verb will be like most other verbs in most ways - but there will always be outliers which lack one or two morphosyntactic features!
For some of these criteria (there are a plenty in the literature), verbs in English can be put in the syntactic frame 'They will _' (for intransitive verbs) and 'They will _ it' (for transitive verbs), they can inflect for past tense and for the third person singular in the present, they can take perfect and progressive forms, and they take on at least one argument except in imperatives.
Some verbs don't satisfy all of these criteria and are therefore less prototypical verbs. Often, these are verbs that have experienced a high degree of grammaticalisation, such as the auxiliary verbs 'can, should, may', etc.
In the American structuralist tradition (Bloomfield and his followers - Hockett, Bloch, etc.), meaning was not thought to be part of the language, and syntactic categories had to be uncovered through 'discovery procedures', and that means, according to their extreme empiricist views, that there must be a set of distributional criteria picking out all and only members of a particular word class. For them, as Prof. Lee mentioned, verbs must all have something in common.
But this is no longer believed to be the case in the linguistic community. There is nothing that all verbs have in common. As Donohue (2008) noted,
Word classes (syntactic categories, parts of speech) are aggregate patterns of morpho-syntactic behaviours corresponding in some way to semantic prototypes
(with greater or lesser amounts of overlap between categories in different languages).
Donohue, M. (2008). Covert word classes: Seeking your own syntax in Tukang Besi. Studies in Language, 32(3), 590-609
Givón, T. (2001). Syntax: an introduction (Vol. 1). John Benjamins Publishing.