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Autour de SAT : le calcul d'impliquants P-restreints, algorithmes et applications

Abstract : Our work concernes two major problems in propositional logic : the satisfiability of a boolean formula (SAT problem) and the computation of its prime implicants/implicates. The first one is widely studied in the Artificial Intelligence community and some recent results show that SAT algorithms can be used efficiently to solve problems in domains where specialized algorithms were used (planning or diagno- sis for example). The second one is very important because it characterizes abductive reasoning (im- plicate framework). We propose to modify a SAT algorithm (the Davis and Putnam procedure) to com- pute formulas used by Assumption-based Truth Maintenance Systems. We formalize our method in terms of prime P-restricted implicants : the intersection between a model and a consistent set of liter- als. Then we apply our formalization in two examples of non-monotonic reasoning: Closed World Rea- soning and Argumentation. We introduce preference relations between P-restricted implicants. For example, in diagnosis, minimal cardinality explanations are sufficient. If other informations are avail- able (fault probabilities for each component for instance), most probable explanations are preferred. We take two examples of such preference relations in argumentation. Finally, we show that qualitative decision theory in a logical framework can also be modeled with P-restricted implicants.
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Daniel Le Berre. Autour de SAT : le calcul d'impliquants P-restreints, algorithmes et applications. Intelligence artificielle [cs.AI]. Université Toulouse III Paul Sabatier, 2000. Français. ⟨tel-02881946⟩

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