howson

8/15/26

Roll your own

• You have to use the right (unicode/html) logical symbols. Check Writing symbols

• The symbols in use here are ~ & ∨ →  

  ≡

There are the ordinary (non-modal) tree propositional rules plus

The Modal Negation (MN) rules

5/30/12

Skills to be acquired in this tutorial:

To learn about the Uniqueness quantifier (a part of identity), and to be introduced to definite descriptions.

Why this is useful:

Uniqueness is central in mathematics, and definite descriptions is a core area in philosophical logic.

12/26/13

The program, widgets, or Notes, should be accompanied by a suitable textbook, such as:

M.Bergmann, J.Moor, J.Nelson, The Logic Book
A.Hausman, H.Kahane, P.Tidman, Logic and Philosophy 
W.Hodges, Logic
C.Howson, Logic with Trees 
R.C.Jeffrey, Formal Logic: Its Scope and Limits
H.Leblanc and W.Wisdom, Deductive Logic
B.Mates, Elementary Logic
M.D.Resnick, Elementary Logic

8/12/26

Reading

Colin Howson, [1997] Logic with trees Chapter 12 Section 2

The Howson [1997] does not expand on modal logic (and modal trees) so a text like

Rod Girle [2000] Modal Logics and Philosophy

would definitely be a help here.

Tutorial

[Modal logic is a vast area, what is being presented here is the briefest of glimpses through the shop window (a book like the Girle would help you go further).]

Exercise: Finding a counter-example.

2013

The Colin Howson book uses a notation like R(a,b,c) for the application of a predicate R to the arguments or terms a, b, c.

It employs the upper case letters A-Z, perhaps followed by subscripts, to be predicates, so, for example, R, S₁, T₁₂  are all predicates.

The software supports this.

But the software makes an extension.

Often, when working informally, authors will write Red(x) to mean that the predicate Red is applied to the variable x.

12/12/20

[Howson[1997] mentions this in Chapter 5, under 'mixed domains'.]

Readings

[These might help, you need only scan them.]

K.H.Blasius et al. eds.[1990] Sorts and Types in Artificial Intelligence
Maria Manzano [1996] Extensions of First-Order Logic
John Sowa [2000] Knowledge Representation

2013

Reading

Colin Howson, [1997] Logic with trees Chapter 11

Tutorial

Set theory is an extensive topic introduced elsewhere. It can be written as a first order theory.

There is one axiom schema, Abstraction (or Comprehension), which can generate infinitely many axioms

∀y(yε{x:Φ[x]}↔Φ[y])

Axiom Schema of Abstraction (or Specification or Comprehension). The Set Builder Axiom Schema.