John Barwise and John Etchemendy, [1999] Language, Proof and Logic
LP&L [1999] has a number of exercises. Many of them you will be able to do in the Widget below.
Here are a few hints
2013
Colin Howson, [1997] Logic with trees Chapter 11
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.
8/12/26
Colin Howson, [1997] Logic with trees Chapter 9 & 11
It is common in this setting (which is arithmetic) to use functional terms like s(x), s(1), s(0) to mean the successor of x, 1, and 0, respectively. Equally common is the notation x', 1', and 0' to mean the same thing. The latter is quicker and shorter (though not semi-nmemonic)-- we will use it here.
To learn about the Uniqueness quantifier (a part of identity), and to be introduced to definite descriptions.
Uniqueness is central in mathematics, and definite descriptions is a core area in philosophical logic.
2013
Colin Howson, [1997] Logic with trees Chapter 9
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*)
Colin Howson, [1997] Logic with trees
The word 'terms' in logic means 'names' and thus far we have met two kinds of terms: constants (or proper names), and variables.
8/16/2026
Colin Howson, [1997] Logic with trees Chapter 2
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
