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The article was the founding work of the field of information theory. It was later published in 1949 as a book titled The Mathematical Theory of Communication (ISBN 0-252-72546-8), which was published as a paperback in 1963 (ISBN 0-252-72548-4).
The Shannon–Weaver model is one of the earliest models of communication. [2] [3] [4] It was initially published by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication". [5] The model was further developed together with Warren Weaver in their co-authored 1949 book The Mathematical Theory of Communication.
For a theory T ∈ A, let Mod(T ) be the set of all structures that satisfy the axioms T ; for a set of mathematical structures S ∈ B, let Th(S ) be the minimum of the axiomatizations that approximate S (in first-order logic, this is the set of sentences that are true in all structures in S).
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). [1]
A structure on a set, or more generally a type, consists of additional mathematical objects that in some manner attach (or are related) to the set, making it easier to visualize or work with, or endowing the collection with meaning or significance.
Given a structure or interpretation, a sentence will have a fixed truth value. A theory is satisfiable when it is possible to present an interpretation in which all of its sentences are true. The study of algorithms to automatically discover interpretations of theories that render all sentences as being true is known as the satisfiability ...
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines).
In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.