Lecture 8

Part 1: Review of Sets, Logic, and Probability

Clinical decision support systems, data analysis, healthcare programming, and other areas crucial in health informatics, require representing domain knowledge. Regardless if the knowledge is represented using rules, equations, computer algorithm or a flowchart, some basic principles apply. Among things that are the most widely used are sets, logic, and probability. This lecture is intended to briefly review these three areas.

In order to deal with healthcare data and knowledge, it is important to know basic set operations. These are: intersection, union, inclusion, and difference. Here are some examples of these operators:
A = {a, b, c, d}
B = {a, b, d}
C = {a, c, e}

Intersection: A ∩ B = {a, b, d}
Union: A ∪ C = {a,b,c,d,e}
Difference: A \ B = {c}, A \ C = {b,d}
B ⊂ A
a ∈ A

If the above video does not work, download this file: Lecture Part 1.mp4


By far the most popular is Boolean logic (although other logics exist). In Boolean logic, everything is either true or false. These can be represented by 1 and 0, T and F, Y and N, and whatever else is convenient. The most popular logic operators are listed below.
Conjunction: a AND b, a ∩ b, a & b, a && b
True only if both a and b are true
Disjunction: a OR b, a ∪ b, a || b ,
False only if both a and b are false
Negation: NOT a
True only if a is false
Implication: a IMPLIES b
False only when a true and b false
Equivalence: a IS EQUIVALENT TO b, a = b, a == b ,
True when a and b are the same

Another important issue related to logic is rules. Rules typically take form IF then ELSE . Most clinical decision support systems use rules to represent clinical knowledge.

If the above video does not work, download this file: Lecture Part 2.mp4


Probability is the most common way of presenting uncertain situations. It provides strict methods of calculation. Many methods, formulas, theorems, etc. are available along with software that allows for making calculations. Uncertainty in most CDSS is modelled using probability. Basic probability concepts are important for this class: joint probability, independence, conditional probability, conditional independence, Bayesian formula.

If the above video does not work, download this file: Lecture Part 3.mp4