Model Checking . Part II Kazuhisa Ishida Shinshu University Nagano , Japan

(Def. 1) CastNatx = { x, if x is a natural number, 0, otherwise. Let W1 be a set. A sequence of W1 is a function from N into W1. For simplicity, we adopt the following rules: k, n denote natural numbers, a denotes a set, D, S denote non empty sets, and p, q denote finite sequences of elements of N. Let us consider n. The functor atom. n yielding a finite sequence of elements of N is defined as follows: (Def. 2) atom. n = 〈6 + n〉. Let us consider p. The functor ¬p yielding a finite sequence of elements of N is defined by: (Def. 3) ¬p = 〈0〉 a p. Let us consider q. The functor p∧q yields a finite sequence of elements of N and is defined by: (Def. 4) p ∧ q = 〈1〉 a p a q. The functor p ∨ q yielding a finite sequence of elements of N is defined by: