Deductive Reasoning using TIL

Transparent Intensional Logic (TIL) is a highly expressive logical system apt for the logical analysis of natural language. It operates with a single procedural semantics for all kinds of logical-semantic context, whether extensional, intensional or hyper-intensional, while adhering to the compositionality principle throughout. The reason why we vote for a rich procedural semantics is this. A coarse-grained analysis of assumptions yields paradoxes and puzzles, while an expressive formal system such as TIL makes it possible to build an inference machine that neither overinfers (which yields paradoxes) nor under-infers (which leads to the lack of knowledge). From the formal point of view, TIL is a hyperintensional, partial, typed lambda calculus. By way of examples we illustrate how TIL deals with particular ‘puzzles’ in a smooth way while adhering to Leibniz’s law of substitution of identicals and to the principle of compositionality.