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Logical Methods in Computer Science Vol. 8(4:19)2012, pp. 1–28 Submitted Oct. 27, 2011
Logical Methods in Computer Science Vol. 8(4:19)2012, pp. 1–28 Submitted Oct. 27, 2011

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lecture notes in logic - UCLA Department of Mathematics
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... The main sources of motivational examples for finite model theory are found in database theory, computational complexity, and formal languages, although in recent years connections with other areas, such as formal methods and verification, and artificial intelligence, have been discovered. The birth of ...
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... Motivation: Give an intuitive meaning to syntactic symbols. Motivation: Give the meaning of “ϕ is true” Motivation: Define a meaning of “ϕ is a logical consequence of Γ” ...
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... Denotation and type of quantifiers every dog denotes the set of all sets of which dog0 is a subset. i.e., a function which takes a function from entities to truth values and returns a truth value. For instance, every dog might denote the set {bark0 , run0 , snore0 }: ...
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... felt the need for a book concentrating on applications of these techniques to Mathematics. There was certainly enough material, but it was scattered in research journals, conference proceedings and theses. If it were collected together I hoped it might prove of interest to a wider audience than the ...
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Interpretation (logic)

An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics.The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways of presenting an interpretation. In these contexts an interpretation is a function that provides the extension of symbols and strings of symbols of an object language. For example, an interpretation function could take the predicate T (for ""tall"") and assign it the extension {a} (for ""Abraham Lincoln""). Note that all our interpretation does is assign the extension {a} to the non-logical constant T, and does not make a claim about whether T is to stand for tall and 'a' for Abraham Lincoln. Nor does logical interpretation have anything to say about logical connectives like 'and', 'or' and 'not'. Though we may take these symbols to stand for certain things or concepts, this is not determined by the interpretation function.An interpretation often (but not always) provides a way to determine the truth values of sentences in a language. If a given interpretation assigns the value True to a sentence or theory, the interpretation is called a model of that sentence or theory.
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