@article{CabalarFandinnoSchaubetal.2019, author = {Cabalar, Pedro and Fandinno, Jorge and Schaub, Torsten H. and Schellhorn, Sebastian}, title = {Gelfond-Zhang aggregates as propositional formulas}, series = {Artificial intelligence}, volume = {274}, journal = {Artificial intelligence}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0004-3702}, doi = {10.1016/j.artint.2018.10.007}, pages = {26 -- 43}, year = {2019}, abstract = {Answer Set Programming (ASP) has become a popular and widespread paradigm for practical Knowledge Representation thanks to its expressiveness and the available enhancements of its input language. One of such enhancements is the use of aggregates, for which different semantic proposals have been made. In this paper, we show that any ASP aggregate interpreted under Gelfond and Zhang's (GZ) semantics can be replaced (under strong equivalence) by a propositional formula. Restricted to the original GZ syntax, the resulting formula is reducible to a disjunction of conjunctions of literals but the formulation is still applicable even when the syntax is extended to allow for arbitrary formulas (including nested aggregates) in the condition. Once GZ-aggregates are represented as formulas, we establish a formal comparison (in terms of the logic of Here-and-There) to Ferraris' (F) aggregates, which are defined by a different formula translation involving nested implications. In particular, we prove that if we replace an F-aggregate by a GZ-aggregate in a rule head, we do not lose answer sets (although more can be gained). This extends the previously known result that the opposite happens in rule bodies, i.e., replacing a GZ-aggregate by an F-aggregate in the body may yield more answer sets. Finally, we characterize a class of aggregates for which GZ- and F-semantics coincide.}, language = {en} } @misc{Fandinno2019, author = {Fandinno, Jorge}, title = {Founded (auto)epistemic equilibrium logic satisfies epistemic splitting}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1060}, issn = {1866-8372}, doi = {10.25932/publishup-46968}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-469685}, pages = {671 -- 687}, year = {2019}, abstract = {In a recent line of research, two familiar concepts from logic programming semantics (unfounded sets and splitting) were extrapolated to the case of epistemic logic programs. The property of epistemic splitting provides a natural and modular way to understand programs without epistemic cycles but, surprisingly, was only fulfilled by Gelfond's original semantics (G91), among the many proposals in the literature. On the other hand, G91 may suffer from a kind of self-supported, unfounded derivations when epistemic cycles come into play. Recently, the absence of these derivations was also formalised as a property of epistemic semantics called foundedness. Moreover, a first semantics proved to satisfy foundedness was also proposed, the so-called Founded Autoepistemic Equilibrium Logic (FAEEL). In this paper, we prove that FAEEL also satisfies the epistemic splitting property something that, together with foundedness, was not fulfilled by any other approach up to date. To prove this result, we provide an alternative characterisation of FAEEL as a combination of G91 with a simpler logic we called Founded Epistemic Equilibrium Logic (FEEL), which is somehow an extrapolation of the stable model semantics to the modal logic S5.}, language = {en} } @misc{AguadoCabalarFandinnoetal.2019, author = {Aguado, Felicidad and Cabalar, Pedro and Fandinno, Jorge and Pearce, David and Perez, Gilberto and Vidal, Concepcion}, title = {Revisiting explicit negation in answer set programming}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1104}, issn = {1866-8372}, doi = {10.25932/publishup-46969}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-469697}, pages = {908 -- 924}, year = {2019}, abstract = {A common feature in Answer Set Programming is the use of a second negation, stronger than default negation and sometimes called explicit, strong or classical negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular operator. In this paper we consider the arbitrary combination of explicit negation with nested expressions, as those defined by Lifschitz, Tang and Turner. We extend the concept of reduct for this new syntax and then prove that it can be captured by an extension of Equilibrium Logic with this second negation. We study some properties of this variant and compare to the already known combination of Equilibrium Logic with Nelson's strong negation.}, language = {en} } @article{AguadoCabalarFandinnoetal.2019, author = {Aguado, Felicidad and Cabalar, Pedro and Fandinno, Jorge and Pearce, David and Perez, Gilberto and Vidal, Concepcion}, title = {Forgetting auxiliary atoms in forks}, series = {Artificial intelligence}, volume = {275}, journal = {Artificial intelligence}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0004-3702}, doi = {10.1016/j.artint.2019.07.005}, pages = {575 -- 601}, year = {2019}, abstract = {In this work we tackle the problem of checking strong equivalence of logic programs that may contain local auxiliary atoms, to be removed from their stable models and to be forbidden in any external context. We call this property projective strong equivalence (PSE). It has been recently proved that not any logic program containing auxiliary atoms can be reformulated, under PSE, as another logic program or formula without them - this is known as strongly persistent forgetting. In this paper, we introduce a conservative extension of Equilibrium Logic and its monotonic basis, the logic of Here-and-There, in which we deal with a new connective '|' we call fork. We provide a semantic characterisation of PSE for forks and use it to show that, in this extension, it is always possible to forget auxiliary atoms under strong persistence. We further define when the obtained fork is representable as a regular formula.}, language = {en} } @misc{CabalarFandinnoSchaubetal.2019, author = {Cabalar, Pedro and Fandinno, Jorge and Schaub, Torsten H. and Schellhorn, Sebastian}, title = {Lower Bound Founded Logic of Here-and-There}, series = {Logics in Artificial Intelligence}, volume = {11468}, journal = {Logics in Artificial Intelligence}, publisher = {Springer}, address = {Cham}, isbn = {978-3-030-19570-0}, issn = {0302-9743}, doi = {10.1007/978-3-030-19570-0_34}, pages = {509 -- 525}, year = {2019}, abstract = {A distinguishing feature of Answer Set Programming is that all atoms belonging to a stable model must be founded. That is, an atom must not only be true but provably true. This can be made precise by means of the constructive logic of Here-and-There, whose equilibrium models correspond to stable models. One way of looking at foundedness is to regard Boolean truth values as ordered by letting true be greater than false. Then, each Boolean variable takes the smallest truth value that can be proven for it. This idea was generalized by Aziz to ordered domains and applied to constraint satisfaction problems. As before, the idea is that a, say integer, variable gets only assigned to the smallest integer that can be justified. In this paper, we present a logical reconstruction of Aziz' idea in the setting of the logic of Here-and-There. More precisely, we start by defining the logic of Here-and-There with lower bound founded variables along with its equilibrium models and elaborate upon its formal properties. Finally, we compare our approach with related ones and sketch future work.}, language = {en} }