Substitution Rules with Respect to a Context

In this paper, we deal with Leibniz’s rule of substitution of identicals, and describe how the rule can be applied in the TIL-Script language. The main goal is to introduce the algorithm of valid application of the substitution rules in all the three kinds of context that we distinguish in the TIL-Script language. The language is a computational variant of TIL, which is a hyperintensional, partial typed -calculus. Hyperintensional, because the meaning of TIL -terms are procedures producing functions rather than the denoted functions themselves. Partial, because TIL is a logic of partial functions, and typed, because all the entities of TIL ontology receive a type. Based on the results of context recognition the algorithm makes it possible to validly apply the substitution rules and derive relevant new pieces of analytic information.