Using Predicate Logic

Original article was published on Artificial Intelligence on Medium


The logical formalism of a language is useful because it immediately suggests a powerful way of deriving new knowledge from old using mathematical deduction.

In this formalism, we can conclude that a new statement is true by proving that it follows from the statements that are already known.

Proposition

A proposition is a statement, or a simple declarative sentence.

For example, “the book is expensive” is a proposition.

A proposition can be either true or false.

Propositional logic

Logical constants: true, false

Propositional symbols: P, Q, S,… (atomic sentences)

Propositions are combined by connectives:

Propositional logic is a simple language useful for showing key ideas and definitions.

User defines a set of propositional symbols, like P and Q.

User defines the semantics of each propositional symbol:

P means “It is hot”

Q means “It is humid”

R means “It is raining”

A sentence (well-formed formula) is defined as follows:

Real world facts can be represented by well-formed formulas (wffs) in propositional logic.