By Gerhard Brewka (auth.), Pedro Cabalar, Tran Cao Son (eds.)

This quantity comprises the refereed court cases of the twelfth overseas convention on good judgment Programming and Nonmonotonic Reasoning, LPNMR 2013, held in September 2013 in Corunna, Spain. The 34 revised complete papers (22 technical papers, nine software description, and three method descriptions) and 19 brief papers (11 technical papers, three software descriptions, and five process descriptions) awarded including 2 invited talks, have been rigorously reviewed and chosen from ninety one submissions. Being a discussion board for replacing rules on declarative common sense programming, nonmonotonic reasoning, and data illustration, the convention goals to facilitate interactions among these researchers and practitioners attracted to the layout and implementation of logic-based programming languages and database structures, and those that paintings within the zone of data illustration and nonmonotonic reasoning.

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**Sample text**

It is not difficult to see that, by exhaustively applying these equivalences from left to right, we can always rewrite a formula into an equivalent one in strong negation normal form (SNNF), that is, guaranteeing that the operator ‘∼’ only affects to atoms in P. Given an infinite word σ ∈ Σ ω , we define a valuation function V as a mapping V : pref (σ) → 2LitS assigning a set of literals to each finite prefix of σ. A valuation function V is consistent if, for any τ ∈ pref (σ), V (τ ) does not contain a pair of opposite literals of the form p and ∼p simultaneously.

However, the definition of TAS uses a syntactic transformation (analogous to Gelfond & Lifschitz’s program reduct [8]) that is only defined for theories with a rather restricted syntax. A first natural question is whether it is possible to get the advantages from both approaches: the richer temporal semantics provided by DLTL together with a complete logical characterisation applicable to arbitrary DLTL theories. A second important question is whether TEL and TAS can be formally related, especially if we consider the syntactic fragment in which both are defined: TAS-like logic programs limited to LTL operators.

Consider now the following formula obtained from α: α = G ∧ t(α) ∧ ♦ (l ∧ ¬l ) def l∈LitS α characterises the non-total DLTLHT models of the formula α. While G ∧ t(α) alone would charaterise all DLTLHT models, the disjunction of expressions ♦(l ∧ ¬l ) guarantees that, at some time point, Hi is a strict subset of Ti , Hi ⊂ Ti . In other words, for any H = (σ, U ) such that H ≈ M with M = (σ, Vh , Vt ), we have that H , |= l∈LitS ♦ (l ∧ ¬l ) if, and only if, there exists l ∈ LitS with l ∈ Vt (τ ) \ Vh (τ ) for some τ ∈ pref (σ).