Artificial intelligence unity algorithm?

In order to apply inference rules (e.g., take-form hypothetical inference), the inference system must be able to determine when two expressions are the same, i.e., when the two expressions match. In propositional arithmetic, this is obvious: two expressions are matched if and only if they are identical in statement composition. In predicate arithmetic, the presence of variables in an expression complicates the process of matching two statements. Holomorphic instantiation allows the replacement of holomorphically quantified variables with terms in the definitional domain. This requires a decision process to determine whether the two or more expressions resulting from variable substitution can be made identical (usually for the purpose of applying inference rules). Uniformity is an algorithm for determining what substitutions can be made so that the two predicate arithmetic expressions produced match. We saw this process in the previous -section, where the × substitution in VX( man(X)=mortal(X)) was replaced by soc-rates in man( socrates). unity and inference rules like hypothetical reasoning allow us to reason about a set of logical assertions. In order to do this, the logical database must be represented in a suitable form. A fundamental feature of this form is the requirement that all variables are fully quantified. This permits complete freedom in the computation of substitutions. Existentially quantified variables can be eliminated from a database statement by replacing them with constants that make this statement true. For example, 3× parent( X, tom) can be replaced with the expressions parent( bob, tom) or parent( mary , tom), assuming that bob and mary are both parents of tom under the current interpretation. The handling of eliminating the presence of quantified variables is complicated by the fact that the values of these substitutions may depend on other variables in the expression.