SLT-Resolution for the Well-Founded Semantics

Global SLS-resolution and SLG-resolution are two representative mechanisms for top-down evaluation of the well-founded semantics of general logic programs. Global SLS-resolution is linear for query evaluation but suffers from infinite loops and redundant computations. In contrast, SLG-resolution resolves infinite loops and redundant computations by means of tabling, but it is not linear. The principal disadvantage of a non-linear approach is that it cannot be implemented using a simple, efficient stack-based memory structure nor can it be easily extended to handle some strictly sequential operators such as cuts in Prolog. In this paper, we present a linear tabling method, called SLT-resolution, for top-down evaluation of the well-founded semantics. SLT-resolution is a substantial extension of SLDNF-resolution with tabling. Its main features include: (1) It resolves infinite loops and redundant computations while preserving the linearity. (2) It is terminating, and sound and complete w.r.t. the well-founded semantics for programs with the bounded-term-size property with non-floundering queries. Its time complexity is comparable with SLG-resolution and polynomial for function-free logic programs. (3) Because of its linearity for query evaluation, SLT-resolution bridges the gap between the well-founded semantics and standard Prolog implementation techniques. It can be implemented by an extension to any existing Prolog abstract machines such as WAM or ATOAM.Comment: Slight modificatio

Linear Tabulated Resolution Based on Prolog Control Strategy

Infinite loops and redundant computations are long recognized open problems in Prolog. Two ways have been explored to resolve these problems: loop checking and tabling. Loop checking can cut infinite loops, but it cannot be both sound and complete even for function-free logic programs. Tabling seems to be an effective way to resolve infinite loops and redundant computations. However, existing tabulated resolutions, such as OLDT-resolution, SLG- resolution, and Tabulated SLS-resolution, are non-linear because they rely on the solution-lookup mode in formulating tabling. The principal disadvantage of non-linear resolutions is that they cannot be implemented using a simple stack-based memory structure like that in Prolog. Moreover, some strictly sequential operators such as cuts may not be handled as easily as in Prolog. In this paper, we propose a hybrid method to resolve infinite loops and redundant computations. We combine the ideas of loop checking and tabling to establish a linear tabulated resolution called TP-resolution. TP-resolution has two distinctive features: (1) It makes linear tabulated derivations in the same way as Prolog except that infinite loops are broken and redundant computations are reduced. It handles cuts as effectively as Prolog. (2) It is sound and complete for positive logic programs with the bounded-term-size property. The underlying algorithm can be implemented by an extension to any existing Prolog abstract machines such as WAM or ATOAM.Comment: To appear as the first accepted paper in Theory and Practice of Logic Programming (http://www.cwi.nl/projects/alp/TPLP

Knowledge of Holocene hydro-climatic conditions in northern China from high temporal resolution stalagmites collected from Lianghua Cave

Our understanding of hydro-climatic dynamics in the East Asian monsoon region during the Holocene was obstructed by very few absolutely dated and high temporally resolved proxy records in northern China. Here we present duplicated carbonate δ18O records of six stalagmites with sub-decadal to multi-decadal temporal resolutions from Lianhua cave to reveal a detailed transition of the East Asian Summer Monsoon (EASM) intensity in northern China from 11.5 thousand years ago (hereafter, ka BP, before 1950 AD). Our composite records show that solar forcing dominated hydro-climatic changes, including an intensified monsoon at the Holocene Optimum from the end of Younger Dryas to 6.5 ka BP, and a subsequent multi-millennial weakening of monsoon intensity, that agree with cave records in central and southern China. However, the EASM has retreated southwards more rapidly than the Indian summer monsoon after ∼6.5 ka BP, resulting in some rapid onset of dry conditions occurring at 4.0 ka BP in northern China, which is ∼2000 years earlier than in central and southern China. This asynchrony may be related to the different regional responses among the coupling of the EASM, Indian summer monsoon, the solar forcing, and the differences in thermal forcing due to complex geographical configurations. In addition, a relative enrichment of 1h in our δ18O data of Lianhua record from 9.5 to 8.1 ka BP shows that the Holocene Optimum was punctuated by a millennial-long weak monsoon interval, which is not registered among previous cave records in central and southern China. The freshwater-induced cold climate conditions in the North Atlantic region could create stronger East Asian winter monsoon and induce a weakened EASM and a southward shift of precipitation band in northern China. Therefore, it shall not be surprised that there are strong heterogeneities among regional hydro-climatic conditions across monsoonal China in the Holocene, given the complex interplay between external and internal forcing mechanisms over the entire Holocene