By Johann A. Makowsky (auth.), Nachum Dershowitz, Andrei Voronkov (eds.)

This ebook constitutes the refereed complaints of the 14th foreign convention on good judgment for Programming, man made Intelligence, and Reasoning, LPAR 2007, held in Yerevan, Armenia, October 2007.

The 36 revised complete papers offered including 15 brief papers and 3 invited talks have been rigorously reviewed and chosen from seventy eight submissions. The papers handle all present matters in common sense programming, logic-based software manipulation, formal strategy, computerized reasoning, and numerous forms of AI logics.

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Extra resources for Logic for Programming, Artificial Intelligence, and Reasoning: 14th International Conference, LPAR 2007, Yerevan, Armenia, October 15-19, 2007. Proceedings

Example text

2. The leaf (7b) is an EX-node, but it is “blocked” from creating the desired successor containing {E(p1 U p2 ), A(⊥ B p2 )} because there is a j ∈ IN such that HCr7b [j] = HCR[j] = {E(p1 U p2 ), A(⊥ B p2 )}: namely j = 1. Thus the EX-rule computes U EV (E(p1 U p2 )) = 1 as stated above and also puts mrk7b := false. As the nodes (7a) and (6a) are marked, the function U EV is passed on to the nodes (6b), (6), and (5) according to the corresponding β- and α-rules. The crux of our procedure happens at node (4b) which is an EX-node with HCr4b = [] and hence len(HCr4b ) = 0.

This is formalized below. St 1 Vocabulary. Contains predicates, function symbols, equality symbol and atomic formulas x ∈ Im[f ] where f is a function symbol. St 1 Syntax. The formulas in St 1 are universal formulas, over a stratified vocabulary and for every function f : A1 ×. ×An → B that participates in a subformula x Im[f ] f is the only function with the range B. The semantics is as in many-sorted logic. For the new atomic formula the semantics is as for the formula ∃y1 : A1 . . ∃yn : An (x = f (y1 , .

EXϕn+m ; AXΔ ; Λ :: HCr :: mrk, uev (EX) ϕ ; Δ ϕ1 ; Δ | ··· | n :: HCr1 :: mrk1 , uev1 :: HCrn :: mrkn , uevn where: (1) (2) (3) (4) {p, ¬p} ⊆ Λ n+m≥1 ∀i ∈ {1, . . , n}. ∀j ∈ {1, . . , len(HCr)}. {ϕi } ∪ Δ = HCr[j] ∀k ∈ {n + 1, . . , n + m}. ∃j ∈ {1, . . , len(HCr)}. {ϕk } ∪ Δ = HCr[j] with: HCri := HCr @ [{ϕi } ∪ Δ] for i = 1, . . , n mrk := n i=1 mrki or ∃i ∈ {1, . . , n}. ∃ψ ∈ {ϕi } ∪ Δ. ⊥ = uevi (ψ) > len(HCr) uevk (·) := j ∈ {1, . . , len(HCr)} such that {ϕk } ∪ Δ = HCr[j] for k = n + 1, .

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