# The logic of defeasible argumentation

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The logic of defeasible argumentation

Rules

Overview

Rules

Rule notations

Rules

Example

Rules and arguments

Enthymematic and syllogistic arguments

Enthymematic and syllogistic arguments

Tautologies, contingencies

Tautologous rules

Implicit rules

The material implication

Strong points of the material implication

Rules as material implications

The relevance of a rule’s antecedent for the rule’s consequent

The relevance of a rule’s antecedent for the rule’s consequent

Exceptions to rules

Exceptions to rules

Exceptions to rules

Rule conflicts

Rule conflicts

Deriving rules

PPT Slide

Two types of reasoning

Dworkin on rules and principles

Rules vs. principles

Are rules and principles logically different?

A unifying view on rules and principles

Starting points for the integrated view

A rule and its underlying principles

Example

What happens when the rule applies?

A rule replaces its underlying principles when it applies

Interfering rules and principles

A typical rule applies

A typical principle applies

A hybrid rule/principle applies

Reason-Based Logic

Reason-Based Logic: an informal overview

Reason-Based Logic: an informal overview

Reason-Based Logic: an informal overview

States of affairs, sentences and terms

Sentences to terms

A translation from sentences to terms

Types of facts

Function symbols

Predicate symbols

Examples

Examples

Relations between facts

Basis: classical logic

Validity

Exclusion

Applicability

Application

Weighing

Weighing

Weighing axioms

Weighing axioms

A rule and its underlying principles

The rule of Art. 7A:1612 BW and its underlying principles

Valid(rule(sale_house, ought_to_be_done(continuation_contract)))

The fact that the principles underlie the rule of Art. 7A:1612 BW is for the first principle represented as:

Protects_inhabitants(continuation_contract)

However, the fact

The rule of Art. 7A:1612 BW replaces its underlying principles if it applies

Since we can conclude

Rules and principles (revisited)

Rules and principles (revisited)

Rules and principles (revisited)

Rules vs. principles

Three forms of reasoning to analyze reasoning by analogy

The principles underlying the rule of Art. 7A:1612 BW apply

PPT Slide

Approaches to rules

Rules as contingent rules of inference

Rules as contingent rules of inference

A dedicated connective for rules

Rule identifiers

Rule identifiers

Rule identifiers

Rule identifiers

Rules as objects

Summary

PPT Slide

Author: Bart Verheij