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mustn’t: must not mustn’t’ve: must not have must’ve: must have ’neath (informal) beneath needn’t: need not nal (informal) and all ne’er (informal) never no one's: no one has / no one is nothing's: nothing has / nothing is o’clock: of the clock o’er: over ol’ old ought’ve: ought have oughtn’t: ought not oughtn’t’ve ...
A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values : as the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.
The English modal auxiliary verbs are a subset of the English auxiliary verbs used mostly to express modality, properties such as possibility and obligation. [a] They can most easily be distinguished from other verbs by their defectiveness (they do not have participles or plain forms [b]) and by their lack of the ending ‑(e)s for the third-person singular.
An auxiliary verb (abbreviated aux) is a verb that adds functional or grammatical meaning to the clause in which it occurs, so as to express tense, aspect, modality, voice, emphasis, etc. Auxiliary verbs usually accompany an infinitive verb or a participle, which respectively provide the main semantic content of the clause. [1]
We can prove that these frames produce the same set of valid sentences as do the frames where all worlds can see all other worlds of W (i.e., where R is a "total" relation). This gives the corresponding modal graph which is total complete (i.e., no more edges (relations) can be added). For example, in any modal logic based on frame conditions:
This resolution technique uses proof by contradiction and is based on the fact that any sentence in propositional logic can be transformed into an equivalent sentence in conjunctive normal form. [4] The steps are as follows. All sentences in the knowledge base and the negation of the sentence to be proved (the conjecture) are conjunctively ...
A sentence is said to be a logical consequence of a set of sentences, for a given language, if and only if, using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must be true if every sentence in the set is true. [3]
The California Job Case was a compartmentalized box for printing in the 19th century, sizes corresponding to the commonality of letters. The frequency of letters in text has been studied for use in cryptanalysis, and frequency analysis in particular, dating back to the Arab mathematician al-Kindi (c. AD 801–873 ), who formally developed the method (the ciphers breakable by this technique go ...