The Semantic Foundations of Logic Volume 1: Propositional Logics

✍ Scribed by Richard L. Epstein (auth.)

• Publisher: Springer Netherlands
• Year: 1990
• Tongue: English
• Leaves: 403
• Series: Nijhoff International Philosophy Series 35
• Edition: 1
• Category: Library

✦ Synopsis

This book grew out of my confusion. If logic is objective how can there be so many logics? Is there one right logic, or many right ones? Is there some underlying unity that connects them? What is the significance of the mathematical theorems about logic which I've learned if they have no connection to our everyday reasoning? The answers I propose revolve around the perception that what one pays attention to in reasoning determines which logic is appropriate. The act of abstracting from our reasoning in our usual language is the stepping stone from reasoned argument to logic. We cannot take this step alone, for we reason together: logic is reasoning which has some objective value. For you to understand my answers, or perhaps better, conjectures, I have retraced my steps: from the concrete to the abstract, from examples, to general theory, to further confirming examples, to reflections on the significance of the work.

✦ Table of Contents

Front Matter....Pages i-xxii
The Basic Assumptions of Propositional Logic....Pages 1-9
Classical Propositional Logic - PC -....Pages 11-60
Relatedness Logic: The Subject Matter of a Proposition - S and R -....Pages 61-84
A General Framework for Semantics for Propositional Logics....Pages 85-114
Dependence Logics - D, Dual D, Eq, DPC -....Pages 115-143
Modal Logics - S4, S5, S4Grz, T, B, K, QT, MSI, ML, G, G* -....Pages 145-194
Intuitionism - Int and J -....Pages 195-228
Many-Valued Logics - L 3 , L n , L ℵ , K 3 , G 3 , G n , G ℵ , S5 -....Pages 229-261
A Paraconsistent Logic: J 3 ....Pages 263-287
Translations Between Logics....Pages 289-314
The Semantic Foundations of Logic....Pages 315-321
Summary of Logics....Pages 323-349
Back Matter....Pages 351-388

✦ Subjects

Logic; Mathematical Logic and Foundations; Artificial Intelligence (incl. Robotics)