Truth definitions and consistency proofs
نویسندگان
چکیده
منابع مشابه
Truth and Circular Definitions
This original and enticing book provides a fresh, unifying perspective on many old and new logico-philosophical conundrums. Its basic thesis is that many concepts central in ordinary and philosophical discourse are inherently circular and thus cannot be fully understood as long as one remains within the confines of a standard theory of definitions. As an alternative, the authors develop a revis...
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Besides their use for efficient computation, quantum computers and quantum robots form a base for studying quantum systems that create valid physical theories using mathematics and physics. If quantum mechanics is universally applicable, then quantum mechanics must describe its own validation by these quantum systems. An essential part of this process is the development of a coherent theory of ...
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The paper discusses the notion of finite model truth definitions (or FM–truth definitions), introduced by M. Mostowski as a finite model analogue of Tarski’s classical notion of truth definition. We compare FM–truth definitions with Vardi’s concept of the combined complexity of logics, noting an important difference: the difficulty of defining FM–truth for a logic L does not depend on the synta...
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Partial consistency statements can be expressed as polynomial-size propositional formulas. Frege proof systems have polynomial-size partial self-consistency proofs. Frege proof systems have polynomialsize proofs of partial consistency of extended Frege proof systems if and only if Frege proof systems polynomially simulate extended Frege proof systems. We give a new proof of Reckhow’s theorem th...
متن کاملNotes on induction proofs and recursive definitions
Most of the proof techniques we’ve talked about so far are only really useful for proving a property of a single object (although we can sometimes use generalization to show that the same property is true of all objects in some set if we weren’t too picky about which single object we started with). Mathematical induction (which mathematicians just call induction) is a powerful technique for sho...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1952
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1952-0049136-2