Isn't it all just math in the end?
Richard Holaj
Masaryk University in Brno
In typed formal logics, we use type restrictions along with lambda calculus, to describe semantic relations. We apply arguments to functions to replace lambda with values and get the compound meaning, when binary branching occurs. We also use general quantifiers to make the interaction more general. In this presentation I would like to show, how bringing in one extra general quantifier, which is cartesian product can help us making things more simple. The reason for this, is that cartesian product is simple set operation (and we like sets in semantics) and it allows us to bring n-tuples, thus relations into game. Whole computation is then base on principle of modifying sets by different set modification operations (like union, intersection), creating relations (by cartesian product) and testing if one set is subset of another (by subset operators). All our semantics are thus described as sets (n-tuples are also sets below the surface) and set operations.