Logic and Fixed-Domain Reasoning: Volume 1: An Empirico-Pragmatist Model Theory and Proof Theory: 67 (Trends in Logic, 67)
Logic and Fixed-Domain Reasoning : Volume 1: An Empirico-Pragmatist Model Theory and Proof Theory
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Logic and Fixed-Domain Reasoning: Volume 1: An Empirico-Pragmatist Model Theory and Proof Theory: 67 (Trends in Logic, 67)
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The author develops, incrementally over the course of several chapters, related concepts of logical system over fixed domain, both classical and nonclassical, by means of pragmatism-inspired translations into paradigmatic, infinitary, quantifier-free languages having rigidly designating constants for all elements of a fixed domain. Each concept fully accommodates both the descriptive (model-theoretic) and deductive (proof-theoretic) tasks of any logic.Chapters 1 through 7 concern first-order logics over fixed domain. Final Chapter 8 takes up second-order logics whereby standard names for each and every boolean-valued function are now introduced. Along the way, substitutional theories of first-, alternatively, second-order relations are presented following Russell. Clarification of classification questions (What is a logical vs. mathematical term? A logical law? A logical operation?) is achieved, for logics over fixed domain, in a manner that may be unattainable in the case of variable-
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