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By Marvin I. Knopp

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Additional info for Analytic number theory. Proceedings conference, Temple Univ., Philadelphia, 1980

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Given a logic L, consider the syntactic pre-interpretation IL given by 44 Gianluca Amato and Giorgio Levi – IL (S) = P(SchS ), ⊆ for each sequent S; – IL (r) is the semantic function corresponding to r ∈ R, as in (6). Interpretations for IL are called syntactical interpretations. In the following, these will be denoted by subsets of Sch. The convention does not rise any ambiguities, since if S1 = S2 , then SchS1 ∩ SchS2 = ∅. A syntactical model, therefore, is a set of proof schemas closed under application of inference rules.

Sn ) just replacing Si in the hypotheses of p with the inference rule r. We write p −→p when the above conditions are satisfied. In general, it is possible to replace more than one hypothesis, hence we have the following transition rule p −→p(r1 , . . , rn ) when p : S1 , . . , Sn S, ri ∈ R ∪ and th(ri ) = Si for each 1 ≤ i ≤ n. (21) We call complete operational semantics of L the interpretation Oc (L) = {p ∈ Sch | ∃S. S −→ p} . (22) It is possible to give a collecting variant of the operational semantics construction, via a fixpoint operator UL on interpretations which uses the gluing semantic operator: UL (I) = I ¿ (R ∪ ) .

R(x) ← x = ε This rule can be generalized to any set of clauses specifying a finite automaton that accepts only words ending with the letter a (here, q1 , . . , qn are new). y, q2 (y) .. y, q2 (y) .. y, qn (y)     qn (x) ← x = ε This schematic inference rule is used by Boigelot and Godefroid (see [2,3]). Model Checking as Constraint Solving 7 35 Related Work and Conclusion Since a fixpoint equation is a constraint over sets of states, the existence of a characterization of a temporal property by a second-order Constraint is not surprising.

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