A. A. Stolyar

  • Introduction to Elementary Mathematical Logic

    A. A. Stolyar

    This introduction covers the calculus of propositions as well as quantification theory. Presupposing no more than a familiarity with the most elementary principles of logic and mathematics, the book is accessible to the high-school student or the layman desiring a clear and straightforward presentation of the subject that will prepare him to take on the standard, more advanced texts. The book is carefully designed to be self-sufficient for purposes of self-study, and the exercises following the end of each section can be used by the student to gauge the level of his understanding: they serve as “feedback signals” that tell him if he should proceed or review the material just covered.

    Of particular interest is the application of the logic of propositions to the analysis and synthesis of digital systems, which is presented at the end of the first of the three sections.

    The first section develops the fundamentals of the logic of propositions. Taken up in turn are objects and operations; formulas, equivalent formulas, and identically true formulas; applications; normal and minimum forms of functions; and applications to digital systems.

    The second section covers the calculus of propositions. Material is presented on the axiomatic approach, including the consistency, independence, and completeness of a system of axioms in the calculus of propositions.

    The logic of predicates is the subject of the last section. It treats in some detail operations section. It treats in some detail operations on sets, defects in the logic of propositions, operations on predicates, quantifiers, equivalent and generally valid formulas, aspects of traditional logic, equality relations, and the axiomatic derivation of the mathematical theory.

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