Editing Planner (programming language) (section)

==Procedural embedding of knowledge==
Planner was invented for the purposes of the procedural embedding of knowledge<ref>Hewitt 1971</ref> and was a rejection of the [[Resolution (logic)|resolution]] uniform proof procedure paradigm,<ref>Robinson 1965</ref> which
#''Converted everything to clausal form.''  Converting all information to [[clausal form]] is problematic because it hides the underlying structure of the information.
#''Then used resolution to attempt to obtain a proof by contradiction by adding the clausal form of the negation of the theorem to be proved.'' Using only resolution as the rule of inference is problematical because it hides the underlying structure of proofs.  Also, using proof by contradiction is problematical because the axiomatizations of all practical domains of knowledge are inconsistent in practice.

Planner was a kind of hybrid between the procedural and logical paradigms because it combined programmability with logical reasoning.  Planner featured a procedural interpretation of logical sentences where an implication of the form {{mono|(P implies Q)}} can be procedurally interpreted in the following ways using pattern-directed invocation:
#[[Forward chaining]] (antecedently):
#:{{mono|''If assert''  P, ''assert''  Q}}
#:{{mono|''If assert not'' Q, ''assert  not'' P}}
#[[Backward chaining]] (consequently)
#:{{mono|''If goal''  Q, ''goal''  P}}
#:{{mono|''If goal not'' P, ''goal not'' Q}}

In this respect, the development of Planner was influenced by [[natural deduction|natural deductive]] [[logical system]]s (especially the one by [[Fitch-style calculus|Frederic Fitch]] [1952]).