By Franz Baader, Andrei Voronkov

This e-book constitutes the refereed complaints of the eleventh overseas convention on common sense for Programming, synthetic Intelligence, and Reasoning, LPAR 2004, held in Montevideo, Uruguay in March 2005.

The 33 revised complete papers provided including abstracts of four invited papers have been rigorously reviewed and chosen from seventy seven submissions. The papers tackle all present matters in common sense programming, computerized reasoning, and AI logics particularly description logics, fuzzy good judgment, linear good judgment, multi-modal common sense, facts concept, formal verification, protocol verification, constraint good judgment programming, programming calculi, theorem proving, and so forth.

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Additional info for Logic for Programming, Artificial Intelligence, and Reasoning: 11th International Workshop, LPAR 2004, Montevideo, Uruguay, March 14-18, 2005, Proceedings

Example text

KB if and only if the set of closures Γ = Ξ(KB ) ∪ {¬Q(a, y)} is unsatisfiable, where ¬Q(a, y) is the closure obtained by negating each conjunct of Q(a, y). A conjunctive query Q(a, y) is weakly connected if its literals cannot be decomposed into two subsets not sharing common variables. g. we assume that Q(a, y) is weakly connected: if Q(a, y) can be split into n weakly connected mutually variable-disjoint subqueries Q1 (a1 , y1 ), . . , Qn (an , yn ), then π(KB ) |= 1≤i≤n ∃yi : Qi (ai , yi ) if and only if π(KB ) |= ∃yi : Qi (ai , yi ) for all 1 ≤ i ≤ n.

Adding an additional literal to a previous decision level, even if all the work done in later decision levels is “thrown away”. Note that it is not trivial to check whether a state is final, because of the Backjump rule. But in practice Backjump is applied only if there is a conflict. , there are no undefined literals in M ), then one can of course stop because M is a model of F . Lemma 6. Assume that ∅ || F =⇒∗ M || F and that M |= ¬D for some clause D in F . Then either Fail or Backjump applies to M || F .

The notion of variable irreducibility is a central concept in the completeness proof of basic superposition. t. a ground and convergent rewrite system R if substitution positions in C ·ρτ are not reducible by rewrite rules in R. We use this to prove completeness, by showing that decomposition is compatible with the usual notion of redundancy for BS [3,14], as shown by Lemma 3. We do so in two steps. First, the eligibility criterion ensures that (*) ground instances of C1 · ρ ∨ Q([t]) and C2 · θ ∨ ¬Q(x) are smaller than the corresponding ground instances of Dm · η.

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