Boolean evaluation

A Boolean valuation fixes a value for each variable, and the formula’s own value follows. It follows compositionally: the value of a complex formula is determined by the values of its immediate parts and nothing else, so the calculation climbs the parse tree from the variables to the main connective. That single property is what makes the whole semantics work — it is why a finite table can settle a formula with infinitely many possible readings behind it, and why changing one variable changes exactly the branches above it.

Scope. Boolean semantics, in the chapter’s own sense: two values, $1$ and $0$ , and the connectives of chapter 4. A many-valued valuation (chapter 10) and a first-order model (chapter 8) both evaluate formulas differently, and neither is covered here.

Type a formula, set a valuation with the $0$ and $1$ buttons, and step through the calculation.

Using it

Atoms are named, so SUN and RAIN work as well as p and q, and the usual precedence applies: $\neg$ binds tightest, then $\land$ , then $\lor$ . Node labels stay syntactic while the values sit outside them, so you can see the formula and its valuation at once. Editing the formula clears the old calculation; changing a value restarts it.

In the book

Chapter 4 · Boolean evaluations states the clauses this app applies.
Chapter 4 · Parsing and valuations runs them down a parse tree, as here.
Chapter 2 · Parsing is where the tree comes from.