trees

2013

Reading

Colin Howson, [1997] Logic with trees Chapter 9

Tutorial

Groups can be characterized by three proper symbols {=,+,0} (ie identity, one infix operator, we will use '+', and an identify element '0') and the three proper axioms

∀x∀y∀z((x+y)+z=x+(y+z)),  (*associativity*)
∀x(x+0=x∧0+x=x),                (*identity element, right and left*) 
∀x∃y(x+y=0∧y+x=0)             (*inverse*)

6/5/12

Reading

Colin Howson, [1997] Logic with trees

Tutorial:

The word 'terms' in logic means 'names' and thus far we have met two kinds of terms: constants (or proper names), and variables.

2013

Reading

Colin Howson, [1997] Logic with trees Chapter 2

Exercises

Howson [1997] has a number of exercises. Many of them you will be able to do in the Widget below.

Here are a few hints

10/7/09

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

The Modal Negation (MN) rules

 

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

The Modal Negation (MN) rules

 

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◊ S5 world, k, must be new [here the computer will choose for you]

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∃D. The constant, a, must be new to the branch [here the computer will choose for you]

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∀D. Any closed term, stage 1, your choice

∀D. Any closed term, stage 2, a chosen

11/4/2020

Under construction

You'd want to check out the respective formation rules, to see what is a well formed formula, and what a variable, etc.

Then the tree rules are:-

7/27/08 10 Software

Skills to be acquired in this tutorial:

None really: this is merely to give you a whiff of the topic of trees for modal logic.

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.