ABSTRACT

In this volume, logic starts from the observation that in everyday arguments, as brought forward by say a lawyer, statements are transformed linguistically, connecting them in formal ways irrespective of their contents. Understanding such arguments as deductive situations, or "sequents" in the technical terminology, the transformations between them

chapter |4 pages

Introduction

chapter 1|3 pages

Positive Rules for Deductive Situations

chapter 2|3 pages

The Calculus KsP

chapter 3|8 pages

The Calculi KtP and KuP

chapter 4|2 pages

Inversion Operators

chapter 5|6 pages

Tableaux

part 2|2 pages

Cuts

chapter 1|15 pages

Cut Elimination with Exchange Operators

chapter 2|2 pages

Arithmetization

chapter 1|5 pages

Explicit Retracing as a Motivation

chapter 2|12 pages

The Reduction Operator R0

chapter 1|2 pages

Negation in Deductive Situations

chapter 3|5 pages

The Intermediary Calculi KM1, KJ1

chapter 4|8 pages

The Calculi LM and LJ

chapter 5|3 pages

K–Calculi for the Connective

chapter 6|2 pages

Tableaux

part 5|3 pages

Sequent Calculi for Classical Logic

chapter 1|6 pages

The Multiple Calculus MK

chapter 3|6 pages

MK as a Calculus for Classical Logic

chapter 4|2 pages

The Calculi MP, MM and MJ

chapter 5|10 pages

The Peirce Rule

chapter 6|7 pages

Tableaux

chapter 1|8 pages

d–Algebras and d–Frames

chapter 4|6 pages

m–Algebras, m–Frames and m–Lattices

part 7|6 pages

Calculi of Formulas

chapter 1|7 pages

Modus Ponens Calculi for Positive Logic

chapter 3|11 pages

Modus Ponens Calculi for Classical Logic

chapter |6 pages

Historical Notes to Chapters 1 – 7

chapter 1|2 pages

Quantifier Rules for Deductive Situations

chapter 2|8 pages

Sequent Calculi with Q–rules

chapter 5|5 pages

The Sets SUB

chapter 6|5 pages

The Substitution Theorem Resumed

chapter 7|2 pages

Cut Elimination Resumed

chapter 8|3 pages

Inversion Rules

chapter 1|4 pages

The Calculi cxqt and cxqs

chapter 2|3 pages

The Variants cxqt0 of cxqt

chapter 3|2 pages

The Variants cxqt1 and cxqt2 of cxqt

chapter 4|3 pages

The Calculi cxqsi

chapter 6|2 pages

Tautologies of Positive Quantifier Logic

chapter 7|1 pages

Tautologies of Minimal Quantifier Logic

chapter 8|3 pages

Tautologies of Classical Quantifier Logic

chapter 3|7 pages

Equality Logic

chapter 7|10 pages

The Midsequent Theorem

chapter 8|7 pages

Herbrand’s Theorem for Prenex Formulas

chapter 9|12 pages

Tableaux