L
p
q
*p . q
Conjunction
p . q
* p
Simplification
A branch in formal, deductive logic in which the basic unit of thought is the proposition.
Propositional Logic
Words which combine or modify simple propositions to make compound propositions.
Logical Operators
Simple Proposition
A proposition with only one component part.
Tautology
A proposition always true due to logical structure.
Logical Equivalence
Two propositions are logically equivalent if and only if they have identical truth values
literals
simple propositions or negations of simple propositions
p
* p v q
Addition
Dilemma
A valid argument which presents a choice between 2 conditionals.
p ) q
p
* q
Modus Ponens
open branch
a path on a truth tree which includes no contradictions
p ) q
~q
*~p
Modus Tollens
decompose
break down compound propositions into simple propositions, which are called literals
Truth Tree (tool #3)
a diagram which shows a set of propositions being decomposed into their literals in order to look for contradictions
p v q
~p
*q
Disjunctive Syllogism
p ) q
q ) r
* p ) r
Hypothetical Syllogism
Defining Truth Table
A truth table that completely defines its operations on a minimum number of variables
p ) q
* p ) (p . q)
Absorption
Rules of inference
Valid argument forms which can be used to justify steps in a proof.
Reductio ad Absurdum
A special rule in a formal proof which allows us to assume the negation of a proposition, deduce a self-contradiction, then conclude the original proposition.
truth functionally complete set of operators
a set of operators from which ALL possible combinations of T and F for 2 variables can be derived
A special rule in a formal proof which allows us to assume the antecedent of a conditional and, once we deduce that consequent, to conclude the entire conditional.
Conditional Proof
Rebut the horns
Construct a counter dilemma using the same or similar components as the original dilemma.
Forms of equivalent statements, which may replace each other wherever they occur and work from left to right and right to left.
Rules of Replacement