Syntax and semantics

1. Predicates are verb-like: adored(), boy() etc. which have values true for false.
2. Terms are the only things that can appear as the arguments to predicates: predicate(term,term,...). Terms come in three flavours:

a. Objects: these are specific - Marilyn-Monroe, BigBen
b. Variables: x
c. Functions: function() must return a term

3. Atomic formulae are the predicates and arguments, eg adored(Marilyn-Monroe,x)
4. Literals are atomic formulae and their negations, eg, huge(BigBen).
5. Well-formed formulae are defined recursively. Literals are wffs, wffs connected by connectives are wffs, wffs surrounded by quantifiers are wffs.
6. Sentences are wffs in which all the variables (if any) are inside the scope of the corresponding quantifiers: eg,

"x[elephant(x) =>has-trunk(x)]
elephant(Nellie) => has-trunk(Nellie)

are both sentences.
7. Bound variables are those that appear within the scope of a quantifier, otherwise they are free variables.

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