Learning path

Knowledge representation and reasoning (KRR)

Represent what a system knows in logic and networks, and derive new facts with entailment, chaining, resolution, unification, and probability.

About this subject

Knowledge representation and reasoning is about writing down what an agent knows in a form a program can use, then drawing conclusions from it. Different representations suit different needs: logic for precise rules, networks of concepts for categories and defaults, and probability for uncertain evidence.

This path covers propositional entailment by model checking, forward chaining on definite clauses, resolution refutation, semantic networks with default reasoning, first-order unification, and Bayes' rule with a small Bayesian network. Each lesson uses a small, complete program that runs on its own. Python has the full sequence. The other languages listed below add lessons that use that language's own idioms and standard library, such as Java threads, C++ smart pointers, C# LINQ, or Node.js streams, and appear only for the topics the language supports. The programs are simplified models chosen to make an idea visible, so they are a foundation for further study rather than a replacement for a full course or for production-grade software.

Before you start: Boolean logic, sets, and recursion.

1
Python
Readable code for automation, data, and first programs.
Propositional logic and entailment by model checking
Decide whether a knowledge base entails a conclusion by checking every truth assignment.
Forward chaining with definite clauses
Derive new facts from if-then rules until the query is proved or nothing new follows.
Resolution and proof by refutation
Prove a conclusion by adding its negation to the clauses and deriving the empty clause.
Semantic networks, inheritance, and default reasoning
Represent categories and properties as a network, and let specific knowledge override general defaults.
First-order unification
Find the substitution that makes two logical terms identical, including the occurs check.
Reasoning under uncertainty: Bayes' rule
Update beliefs with Bayes' rule and compute a posterior from a small Bayesian network by enumeration.
2
C
Learn memory, pointers, and efficient systems programming.
C: forward chaining with bit sets
Store facts as bits of an integer and apply if-then rules with bitwise operations.
C: resolution refutation with clauses as bit masks
Represent each clause by two masks, one for positive and one for negative literals, and resolve until a contradiction appears.
3
C++
Build fast applications with modern types and classes.
C++: entailment by enumerating models
Test whether a knowledge base entails a query by checking every truth assignment.
C++: backward chaining from a goal
Prove a goal by finding a rule that concludes it and then proving that rule's conditions.
4
Java
Understand object oriented programs and the JVM.
Java: propositional entailment by model checking
Enumerate every truth assignment to decide whether a knowledge base entails a query.
Java: forward chaining with if-then rules
Repeatedly apply rules whose conditions are known until no new facts can be derived.
5
C#
Build typed applications on .NET.
C#: first-order unification
Find a substitution that makes two logical terms identical, including the occurs check.
C#: semantic networks with default reasoning
Inherit properties up an is-a hierarchy and let more specific nodes override defaults.
6
JavaScript
Add behavior to the web and build applications.
JavaScript: querying facts stored as triples
Represent knowledge as subject–predicate–object triples and answer queries with variables.
JavaScript: proof by resolution refutation
Show that a knowledge base entails a query by deriving a contradiction from the knowledge base plus the negated query.
7
TypeScript
JavaScript with static types for dependable code.
TypeScript: propositional formulas as a discriminated union
Represent formulas as trees, evaluate them for any assignment, and test for tautologies.

About this subject

Python

Propositional logic and entailment by model checking

Forward chaining with definite clauses

Resolution and proof by refutation

Semantic networks, inheritance, and default reasoning

First-order unification

Reasoning under uncertainty: Bayes' rule

C

C: forward chaining with bit sets

C: resolution refutation with clauses as bit masks

C++

C++: entailment by enumerating models

C++: backward chaining from a goal

Java

Java: propositional entailment by model checking

Java: forward chaining with if-then rules

C#

C#: first-order unification

C#: semantic networks with default reasoning

JavaScript

JavaScript: querying facts stored as triples

JavaScript: proof by resolution refutation

TypeScript

TypeScript: propositional formulas as a discriminated union