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The arguments of valency 1 are the first arguments of f and the last ones are of valency 0. There are separated by ’;’, like the normal/safe arguments of [3]. -Y. Moyen 1. The following program is terminating using either M P O, M P O or LM P O by setting add ≺F mult. add : Nat1 , Nat0 → Nat and [[add]](x, y) = x + y add(0; y) → y add(suc(x); y) → suc(add(x; y)) mult : Nat1 , Nat1 → Nat and [[mult]](x, y) = x × y mult(0, y; ) → 0 mult(suc(x), y; ) → add(y; mult(x, y; )) 2. The exponential program given in Example 2(2) is terminating using either MPO or M P O but not with LMPO.

Hence, we only consider normal forms in T (C) as being defined. Closed terms are interpreted by elements of the algebra T (C)/E, that is the initial algebra of the class of models of the set of program rules E. Definition 7. The semantics of a type s is the set of constructor terms whose type is s. That is [[s]] = {t : s | t ∈ T (C)}. Definition 8. Let main be a program and Γ (main) = (s1 , · · · , sn ) → s. The function computed by main is [[main]] : [[s1 ]] × · · · × [[sn ]] → [[s]] which is defined !

An Algorithm to Evaluate Quantified Boolean Formulae. In Proc. AAAI/IAAI-98, pp. 262–267, 1998. 2 5. E. Chan. A Possible Worlds Semantics for Disjunctive Databases. IEEE Trans. Knowledge and Data Engineering, 5(2):282–292, 1993. 1, 2 6. H. Decker and J. C. Casamayor. Sustained Models and Sustained Answers in First-Order Databases. In A. Oliv´e, editor, Proc. 4th International Workshop on the Deductive Approach to Information Systems and Databases (DAISD 1993), 1993, Lloret de Mar, Catalonia, pp.

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