By Miki Hermann, Andrei Voronkov

This ebook constitutes the refereed court cases of the thirteenth overseas convention on common sense for Programming, man made Intelligence, and Reasoning, LPAR 2006, held in Phnom Penh, Cambodia in November 2006.

The 38 revised complete papers offered including 1 invited speak have been rigorously reviewed and chosen from ninety six submissions. The papers tackle all present matters in common sense programming, logic-based application manipulation, formal approach, computerized reasoning, and numerous forms of AI logics.

**Read Online or Download Logic for Programming, Artificial Intelligence, and Reasoning: 13th International Conference, LPAR 2006, Phnom Penh, Cambodia, November 13-17, 2006, PDF**

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**Extra resources for Logic for Programming, Artificial Intelligence, and Reasoning: 13th International Conference, LPAR 2006, Phnom Penh, Cambodia, November 13-17, 2006, **

**Example text**

Sn ) πLP O f (t1 , . . , tn ) = list(π(f )) π,lex τ ( s1 , . . , s n LP O,f t1 , . . , tn ) (π(f ) − j) → τ (f (s1 , . . , sn ) πLP O tj ) 1≤j≤n τ2 (f (s1 , . . , sn ) ⎛ π LP O t) = (π(f ) = i) 1≤i≤n ⎝list(π(f )) ∧ 1≤i≤n (π(f ) − i) ∧ τ (si π LP O τ (si ⎞ π LP O t) ∨ t)⎠ Encoding II: π,lex τ ( si , . . , s n LP O,f ti , . . , tn ) = false if n = 0 else ((π(f ) − i) τ (si πLP O ti )) ( (π(f ) − i) → τ (si π LP O ti ) ) τ ( si+1 , . . , sn π,lex LP O,f ti+1 , . . , tn ) Fig. 1. Encoding LPO with Argument Filterings We proceed to describe how partial order and argument ﬁltering constraints are transformed into propositional logic.

Xm ]) ⇐ G, G be an NGSPR clause where G = { P (x, x) | x ∈ {x1 , . . , xm } and x occurs once in G, G } RR(C) = fP (t1 , . . , tn−1 ) → C[x1 , . . , xm ]σ ⇐ equat(G ) where σ = { x → term(P (x, x)) | P (x, x) ∈ G }. For an NGSPR logic program P, let RR(P) denote the CTRS consisting of the rules { RR(H ⇐ G) | H ⇐ G ∈ P }. For example, Pf (s(x1 , y), s(x2 , y), s(z1 , z2 )) ⇐ Pf (x2 , x1 , z1 ), Pf (x1 , x1 , x2 ) is transformed into f (s(x1 , y), s(x2 , y)) → s(f (x2 , x1 ), z2 ) ⇐ f (x1 , x1 ) ↓R x2 .

2. Then SAT solving can search for an LPO satisfying (11) for the given ﬁltering π. However, this approach is hopelessly ineﬃcient, potentially calling the SAT solver for each of the exponentially many argument ﬁlterings. Even if one considers the less naive enumeration algorithms implemented in [14] and [18], for many examples the SAT solver would be called exponentially often. A contribution of this paper is to show instead how to encode the argument ﬁlterings into the propositional formula and delegate the search for an argument ﬁltering to the SAT solver.