Titlebook: Mathematical Logic; Foundations for Info Wei Li Textbook 2014Latest edition Springer Basel 2014 G?del theorem.first-order language.inductiv

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Syntax of First-Order LanguagesProgramming languages such as BASIC, Pascal, and C are formal languages used for writing computer programs. A program usually implements an algorithm which describes the computational solution of a specific issue. This chapter introduces a different kind of formal language, known as a ..

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Revision CalculusIn scientific research, one usually extracts, from a large body of knowledge, the most fundamental propositions to be used as axioms. Traditionally, axiom systems for mathematics and other sciences have evolved in many stages rather than being created all at once.

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Meta-Language EnvironmentsIn the last 9 chapters we introduced the classical mathematical Logic and the basic theory of axiomatization processes. In this chapter, we shall survey these basic theories from two aspects: what these basic theories are, and how to use them.

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Mathematical Logic978-3-0348-0862-0Series ISSN 2297-0576 Series E-ISSN 2297-0584

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https://doi.org/10.1007/978-3-0348-0862-0G?del theorem; first-order language; inductive inference; language environment; revision calculus; versio

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Models of First-Order Languagesbe interpreted as elements and propositions over a domain. This semantic interpretation gives meaning to the symbol strings and is called a model of the language. In this chapter, we shall build a general theory of semantics for first-order languages.

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Formal Inference Systemsel that satisfies Γ, A is satisfied. The definition of logical consequences refers to the semantics of formulas. Essentially, it means that, however we interpret the terms in the formulas, the truth-value of A always follows the truth-value of Γ. This is consistent with our understanding of what a logical consequence is.

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