1.4. General principles of deductive reasoning

1.4.0. Overview

The properties and relations of sentence and propositions that are subject matter of deductive logic can be arranged in three groups.

1.4.1. A closer look at entailment
Entailment will be at the heart of our study and we will begin by looking in some detail at a couple ways of formulating its definition.

1.4.2. Division
It will be useful to have a special term for the kind of pattern of truth values that entailment rules out.

1.4.3. Relative exhaustiveness
Although entailment does not encompass all the concepts of deductive logic, there is a similarly defined relation that does.

1.4.4. A general framework
All the deductive properties and relations we will consider can be expressed in terms of relative exhaustiveness and expressed in a way that corresponds directly to definitions of them.

1.4.5. Reduction to entailment
Although relative exhaustiveness provides a way of thinking about deductive properties and relations, entailment is way that they are most naturally established, and we need to consider how this can be done.

1.4.6. Laws for relative exhaustiveness
The basic features of the system of relations among sets provided by relative exhaustiveness can be captured by three laws.

1.4.7. Laws for entailment
Although laws governing relative exhaustiveness are in some ways more fundamental, it is laws governing entailment that we will use most.

1.4.8. Duality
The specific principles concerning ⊤ and ⊥ display a kind of symmetry that we will also find in principles for other logical forms.