College Publications logo   College Publications title  
View Basket
Homepage Contact page
Academia Brasileira de Filosofia
Cadernos de Lógica e Computação
Cadernos de Lógica e Filosofia
Cahiers de Logique et d'Epistemologie
Communication, Mind and Language
Cuadernos de lógica, Epistemología y Lenguaje
Encyclopaedia of Logic
Historia Logicae
IfColog series in Computational Logic
Journal of Applied Logics - IfCoLog Journal
Landscapes in Logic
Logic and Semiotics
Logic PhDs
Logic, Methodology and Philosophy of Science
The Logica Yearbook
Neural Computing and Artificial Intelligence
The SILFS series
Studies in Logic
History of Logic
Logic and cognitive systems
Mathematical logic and foundations
Studies in Logic and Argumentation
Studies in Talmudic Logic
Texts in Logic and Reasoning
Texts in Mathematics
Digital Downloads
Information for authors
About us
Search for Books

Studies in Logic


Formal Logic

Classical Problems and Proofs

Luis M. Augusto

Logic is—arguably—all about proving, but proofs can be “costly,” often impossibly so, and today most are delegated to (partly) automatic provers, namely by so-called SAT solvers, software based on the (Boolean) satisfiability problem, or SAT. This is the dual of the (Boolean) validity problem, or VAL, at the core of the conception of the digital computer via Hilbert’s Entscheidungsproblem and the Universal Turing Machine. While these problems—VAL significantly less so than SAT—feature in introductory logic textbooks aimed at computer science students, they are largely or wholly absent from textbooks targeting a mathematical or philosophical studentship.

Formal logic: Classic problems and proofs corrects this—in our view—misguided state of affairs by providing the basics of formal classical logic from the central viewpoint of a formal, or computer, language that distinguishes itself from the other formal or computer languages by its ability to preserve truth, thus potentially providing solutions to decision problems formulated in terms of VAL and/or SAT. This fundamental aspect of classical logic, truth-preservation, is elaborated on from three main formal semantics, to wit, Tarskian, Herbrand, and algebraic (Boolean) semantics, which, in turn, via the adequateness results for the standard first-order logic, underlie the main proof systems of direct and indirect, or refutation, proofs, associated to VAL and SAT, respectively.

Not focusing on the history of classical logic, this book nevertheless provides discussions and quotes central passages on its origins and development, namely from a philosophical perspective. Not being a book in mathematical logic, it takes formal logic from an essentially mathematical perspective. Biased towards a computational approach, with SAT and VAL as its backbone, this is thus an introduction to logic that covers essential aspects of the three branches of logic, to wit, philosophical, mathematical, and computational.

2 September 2019


© 2005–2021 College Publications / VFH webmaster