Normal forms for Answer Sets Programming

Normal forms for logic programs under stable/answer set semantics are introduced. We argue that these forms can simplify the study of program properties, mainly consistency. The first normal form, called the {\em kernel} of the program, is useful for studying existence and number of answer sets. A kernel program is composed of the atoms which are undefined in the Well-founded semantics, which are those that directly affect the existence of answer sets. The body of rules is composed of negative literals only. Thus, the kernel form tends to be significantly more compact than other formulations. Also, it is possible to check consistency of kernel programs in terms of colorings of the Extended Dependency Graph program representation which we previously developed. The second normal form is called {\em 3-kernel.} A 3-kernel program is composed of the atoms which are undefined in the Well-founded semantics. Rules in 3-kernel programs have at most two conditions, and each rule either belongs to a cycle, or defines a connection between cycles. 3-kernel programs may have positive conditions. The 3-kernel normal form is very useful for the static analysis of program consistency, i.e., the syntactic characterization of existence of answer sets. This result can be obtained thanks to a novel graph-like representation of programs, called Cycle Graph which presented in the companion article \cite{Cos04b}.Comment: 15 pages, To appear in Theory and Practice of Logic Programming (TPLP

Fluid dynamics of aortic root dilation in Marfan syndrome

Aortic root dilation and propensity to dissection are typical manifestations of the Marfan Syndrome (MS), a genetic defect leading to the degeneration of the elastic fibres. Dilation affects the structure of the flow and, in turn, altered flow may play a role in vessel dilation, generation of aneurysms, and dissection. The aim of the present work is the investigation in-vitro of the fluid dynamic modifications occurring as a consequence of the morphological changes typically induced in the aortic root by MS. A mock-loop reproducing the left ventricle outflow tract and the aortic root was used to measure time resolved velocity maps on a longitudinal symmetry plane of the aortic root. Two dilated model aortas, designed to resemble morphological characteristics typically observed in MS patients, have been compared to a reference, healthy geometry. The aortic model was designed to quantitatively reproduce the change of aortic distensibility caused by MS. Results demonstrate that vorticity released from the valve leaflets, and possibly accumulating in the root, plays a fundamental role in redirecting the systolic jet issued from the aortic valve. The altered systolic flow also determines a different residual flow during the diastole.Comment: Accepted versio

Epistemic Logic Programs: a study of some properties

Epistemic Logic Programs (ELPs), extend Answer Set Programming (ASP) with epistemic operators. The semantics of such programs is provided in terms of world views, which are sets of belief sets, i.e., syntactically, sets of sets of atoms. Different semantic approaches propose different characterizations of world views. Recent work has introduced semantic properties that should be met by any semantics for ELPs, like the Epistemic Splitting Property, that, if satisfied, allows to modularly compute world views in a bottom-up fashion, analogously to ``traditional'' ASP. We analyze the possibility of changing the perspective, shifting from a bottom-up to a top-down approach to splitting. We propose a basic top-down approach, which we prove to be equivalent to the bottom-up one. We then propose an extended approach, where our new definition: (i) is provably applicable to many of the existing semantics; (ii) operates similarly to ``traditional'' ASP; (iii) provably coincides under any semantics with the bottom-up notion of splitting at least on the class of Epistemically Stratified Programs (which are, intuitively, those where the use of epistemic operators is stratified); (iv) better adheres to common ASP programming methodology.Comment: Under consideration in Theory and Practice of Logic Programming (TPLP

Multi-context systems in time

In this paper we consider how to enhance flexibility and generality in Multi-Context Systems (MCS) by considering that contexts can evolve over time, that bridge-rule application can be proactive (according to a context's specific choice), and not instantaneous but requiring an execution mechanism. We introduce bridge-rule patterns to make bridge-rules parametric w.r.t. the involved contexts