Algorithmic Semantics of Ambiguous Modifiers with the Type Theory of Acyclic Recursion

With his work on formal languages of recursion, Yiannis Moschovakis initiated development of a new approach to the mathematical notion of algorithm, beginning with work on the mathematics of algorithms in 1994. One of the most exciting potentials of the approach is for applications to computational semantics of artificial and natural languages. In particular, the typed version of theory of a cyclic recursion and its language reveal crucial properties of semantic concepts such as meaning and synonymy, from computational perspective. This paper is a brief introduction to Moschovakis' Type Theory of A cyclic Recursion and its system of reduction rules from the perspective of its applications to semantics of a class of modifiers. The formal language of a cyclic recursion and its theory have potentials for applications to algorithmic semantics of natural and artificial languages. The paper demonstrates the potentials of the theory by rendering ambiguous modifiers in the formal language of recursion.