Precedence

!, &, |, ⇒, ⇐>

CNF and DNF

• false = both, formulas consisting only true and false are both CNF and DNF
• a | !b = neither, true and false may only appear if they are the entire formula
• a & b & c = both
• a & !(b | C) : neither because negation can only be on a single term

CNF: ( OR ) & ( OR ) DNF:

Satisfiable, contingent, tautology or contradiction

Predicate Logic

wffs in typed and untyped predicate logic

Untyped Predicate Logic

• the question tells us which symbols are constants, predicates, and functions
• the formula must satisfy the grammar rules, which include that function symbols applied to terms produce terms, and predicate symbols applied to terms produce formulas
• the arity of a fcn/predicate symbol must be consistent throughout the formula

Typed Predicate Logic

• there is no distinction between function and predicate symbols → they are all considered function symbols and a function applied to terms that returns a boolean type is a formula
• the formula must satisfy the grammar rules
• some information about types of the symbols or quantified variables may be given
• there must be a consistent typing of the symbols (whic