Language Proof And Logic

Rev. ed. of: Language, proof, and logic / Jon Barwise & John Etchemendy.

LANGUAGE, TRUTH AND LOGIC is the classic work of philosophy by Alfred Jules Ayer published in 1936 when Ayer was 26 (though it was in fact completed by age 25). This book defines, explains, and argues for the verification principle of logical positivism, as it relates to the use of objectives and methods in determining truths and probabilities. And whether or not one agrees that emperical evidence is the only basis for proof, there is no denying that this is a brilliant book in how it explains in what ways the principle of verifiability may be applied to the problems of philosophy itself.

Forallx is an introduction to sentential logic and first-order predicate logic with identity, logical systems that significantly influenced twentieth-century analytic philosophy. After working through the material in this book, a student should be able to understand most quantified expressions that arise in their philosophical reading. This book treats symbolization, formal semantics, and proof theory for each language. The discussion of formal semantics is more direct than in many introductory texts. Although forall x does not contain proofs of soundness and completeness, it lays the groundwork for understanding why these are things that need to be proven. Contents: What is logic? Sentential logic Truth tables Quanti ed logic Formal semantics Proofs Other symbolic notation Solutions to selected exercises

This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).

This Festschrift was published in honor of Andre Scedrov on the occasion of his 65th birthday. The 11 technical papers and 3 short papers included in this volume show the many transformative discoveries made by Andre Scedrov in the areas of linear logic and structural proof theory; formal reasoning for networked systems; and foundations of information security emphasizing cryptographic protocols. These papers are authored by researchers around the world, including North America, Russia, Europe, and Japan, that have been directly or indirectly impacted by Andre Scedrov. The chapter “A Small Remark on Hilbert's Finitist View of Divisibility and Kanovich-Okada-Scedrov's Logical Analysis of Real-Time Systems” is available open access under a CC BY 4.0 license at link.springer.com.

Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical properties; and how to construct and strategically use derivation rules in proofs.

The mathematical proof is the most important form of justification in mathematics. It is not, however, the only kind of justification for mathematical propositions. The existence of other forms, some of very significant strength, places a question mark over the prominence given to proof within mathematics. This collection of essays, by leading figures working within the philosophy of mathematics, is a response to the challenge of understanding the nature and role of the proof.