# Lesson 14 - Module 6 Knowledge Representation and Logic...

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Module 6 Knowledge Representation and Logic – (First Order Logic) Version 1 CSE IIT, Kharagpur

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Lesson 14 First Order Logic - II Version 1 CSE IIT, Kharagpur
6.2.5 Herbrand Universe It is a good exercise to determine for given formulae if they are satisfied/valid on specific L-structures, and to determine, if they exist, models for them. A good starting point in this task, and useful for a number of other reasons, is the Herbrand Universe for this set of formulae. Say that {F01 . . F0n} are the individual constants in the formulae [if there are no such constants, then introduce one, say, F0]. Say that {F1 . . Fm} are all the non 0- ary function symbols occurring in the formulae. Then the set of (constant) terms obtained starting from the individual constants using the non 0-ary functions, is called the Herbrand Universe for these formulae. For example, given the formula (P x A) OR (Q y), its Herbrand Universe is just {A}. Given the formulae (P x (F y)) OR (Q A), its Herbrand Universe is {A (F A) (F (F A)) (F (F (F A))) . ..}. Reduction to Clausal Form In the following we give an algorithm for deriving from a formula an equivalent clausal form through a series of truth preserving transformations. We can state an (unproven by us) theorem: Theorem: Every formula is equivalent to a clausal form We can thus, when we want, restrict our attention only to such forms. 6.2.6 Deduction

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## Lesson 14 - Module 6 Knowledge Representation and Logic...

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