Proportional Logic|Ms.R.Vani|Asst.Prof|CS|Video Lecture Series 5

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The well-formed formulas of propositional logic are those

which we obtain by using the construction rules below, and only those,

finitely many times:

atom: Every propositional atom p, q, r,... and p1, p2, p3,... is a well-

formed formula.

It is most crucial to realize that this definition is the one a computer would

expect and that we did not make use of the binding priorities agreed upon

in the previous section.

Convention. In this section we act as if we are a rigorous computer and

we call formulas well-formed iff they can be deduced to be so using the definition above


Backus-Naur Form (BNF) is a formal notation used to describe the syntax of programming languages, data structures, or any structured language. It is a way to specify the grammar of a language in a concise and unambiguous manner. BNF consists of a set of production rules, where each rule defines how a symbol or non-terminal can be replaced with a sequence of other symbols or non-terminals.

Components of BNF
Non-terminal symbols: These are symbols that can be replaced by other symbols. They are usually written inside angle brackets.

Terminal symbols: These are the basic symbols of the language and cannot be broken down further. They are usually literals or tokens like +, *, a, b, etc.

Production rules: A production rule defines how a non-terminal symbol can be replaced with a sequence of terminals and/or non-terminals. It typically has the form: