By Giovanni Sommaruga (auth.), Giovanni Sommaruga (eds.)
This booklet provides the medical consequence of a joint attempt of the pc technological know-how departments of the colleges of Berne, Fribourg and Neuchâtel.
Within an initiative dedicated to "Information and Knowledge", those study teams collaborated over a number of years on problems with good judgment, likelihood, inference, and deduction. The objective of this quantity is to check even if there's any universal floor among the several ways to the concept that of information.
The constitution of this ebook can be represented by way of a round version, with an innermost syntactical circle, comprising statistical and algorithmic methods; a moment, higher circle, the semantical one, within which "meaning" enters the level; and at last an outermost circle, the pragmatic one, casting mild on real-life logical reasoning.
These articles are complemented through philosophical contributions exploring the huge conceptual box in addition to taking inventory of the articles at the quite a few formal theories of information.
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Extra resources for Formal Theories of Information: From Shannon to Semantic Information Theory and General Concepts of Information
On June 1 Philosophical Conceptions of Information 33 1944, the BBC broadcasted a line from Verlaine’s Song of Autumn: “Les sanglots longs des violons de Autumne”. The message contained almost 1 bit of information, an increasingly likely “yes” to the question whether the D-Day invasion was imminent. The BBC then broadcasted the second line “Blessent mon coeur d’une longueur monotone”. Another almost meaningless string of letters, but almost another bit of information, since it was the other long-expected “yes” to the question whether the invasion was to take place immediately.
Noise extends the informee’s freedom of choice in selecting a message, but it is an undesirable freedom and some redundancy can help to limit it. That is why the manual of your car includes both verbal explanations and pictures to convey (slightly redundantly) the same information. We are now ready to understand Shannons two fundamental theorems. Suppose the 2-coins biased system AB produces the following message: t, h h, h t, t h, t h, t Using Fano Code we obtain: 11001111010. The next step is to send this string through a channel.
This is equivalent to the whole area delimited by the curve. Generalising to σ we have: 1 ι (σ) dx = α = 0 2 3 (14) Fig. 15 shows the graph generated by equation . The shaded area is the maximum amount of semantic information α carried by σ. Consider now V, “there will be some guests tonight”. V can be analysed as a (reasonably ﬁnite) string of disjunctions, that is V = [“there will be one guest tonight” or “there will be two guests tonight” or . . “there will be n guests tonight”], where n is the reasonable limit we wish to consider (things are more complex than this, but here we only need to grasp the general principle).