Presupposition

Presupposition is first assumption that appears in speaker's mind in conversation that the hearer can understand what the speaker is talking about.  Presupposition is assumption that the addressee is able to understand what the speaker means because the speaker's utterance has certain sign, context, and reference that is understood by interlocutor.

In addition, Palmer (1989: 181) tries to explain this by giving an example "the king of France is bald", Palmer tries to compare the notion of Russell (1905) and Strawson in which according to Russell, considered by Palmer as the first notion appeared, the sentence "the king of France is bald" indicates two things, first, the existence of king of France and the king is bald. If essentially the king of France does not exist, the sentence is judged as fake or false sentence, and conversely. The second notion comes from Strawson, he states that in sentence "the king of France is bald", the speaker supposes that the hearer is able to recognize exactly the man or thing in the sentence uttered by him exists. So that the speaker is not necessary to confirm whether the man or thing is really exist, however the speaker only makes presupposition about the existence of it. If the man or thing does not exist, so it will appear what is called 'the failure of presupposition', and the sentence is not true or false. Simpler we can say that, if sentence (a) presuppose sentence (b), the truth of the sentence (b) must follow from the truth of sentence (a), but if sentence (b) is false, then the sentence (a) will has no truth value. 

In addition presupposition is divided into two categories, they are: logic presupposition and pragmatic presupposition. Logic presupposition is presupposition which deals with the arrangement and understanding of message in which as the part of semantics has logic relationship with form of expression, both in coding and structuring of relationship. In addition, pragmatic presupposition is presupposition which deals with context, both in the relation between the users and social-situational surrounded it.

In the study of logic of language, we know about the term propositional calculus. This term basically involve two concepts, they are: calculus and proposition. Calculus is 'taking conclusion determining truth' and proposition is 'statement which suitable with abstraction in the consciousness of the user'. So that, propositional calculus deals with characteristics abstraction of reference when it is in the conceptualization of expression, taking conclusion of the characteristic of relationship of abstraction result is signed by connective sign, such as: which, that, to be, and, not, or. For instance, '"Malang is beautiful city", when the speaker abstracts Malang city for instance, he has known well about Malang city so that he is able to give earmark' beautiful'.  
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See also:

• Formal Semantics
• Analytic Sentence
• Synthetic Sentence
• Entailment
• Presupposition