# Semantic Foundations of Logic

This series of books is meant to present modern logic as the formalization of reasoning, and to give it a unified semantic foundation. Careful discussions of meaning, truth, and reference give the reader a basis for establishing criteria that can be used to judge formalizations of ordinary language arguments. Hundreds of worked examples illustrate the scope and limitations of modern logic, as analyzed in chapters on identity, quantifiers, descriptive names, and functions. The discussion of second-order logic shows how different conceptions of predicates and propositions do not lead to a common basis for quantification over predicates, as they do for quantification over things. Notable for their clarity of presentation and supplemented by many exercises, these volumes will be invaluable for philosophers, linguists, mathematicians, and computer scientists who wish to better understand the tools they use in formal reasoning.

This surveys and unifies the major systems of propositional logics, answering the question “If logic is the right way to reason, why are there so many logics?” It is the standard reference in the subject, as well as providing a clear and easy way to learn the subject from scratch. |
This presents the basic syntax and semantics of predicate logic motivated by attempting to formalize ordinary language reasoning. It is the only textbook that takes formalization as a serious motive for the subject and a serious constraint on the formalism. It make it clear why predicate logic is worth studying. It provides a basis for all predicate logics. |
This develops classical mathematical logic, viewing it as motivated by attempts to formalize mathematics. The scope and limitations of the formal system are explored: formalizations of theories of linear orders, arithmetic, groups, rings, fields, one- and two-dimensional Euclidean geometry, and second-order logic are all presented. It is the only place to see axiomatic geometry formulated in first-order logic where the syntax and semantics are clearly separated. |