Showing papers by "Peter Baumgartner published in 1996"

Hyper Tableaux

Abstract: This paper introduces a variant of clausal normal form table aux that we call “hyper tableaux”. Hyper tableaux keep many desirabl e features of analytic tableaux while taking advantage of the central idea fr om (positive) hyper resolution, namely to resolve away all negative literals of a clause in a single inference step. Another feature of the proposed calculus is th e extensive use of universally quantified variables. This enables new efficient fo rward-chaining proof procedures for full first order theories as variants of table ux calculi.

Middle and Late Jurassic carbon stable-isotope stratigraphy and radiolarite sedimentation of the Umbria-Marche basin (Central Italy)

Abstract: A continuous carbon isotope curve from Middle-Upper Jurassic pelagic carbonate rocks was acquired from two sections in the southern part of the Umbria-Marche Apennines in central Italy. At the Colle Bertone section (Terni) and the Terminilletto section (Rieti), the Upper Toarcian to Bajocian Calcari e Marne a Posidonia Formation and the Aalenian to Kimmeridgian Calcari e Marne a Posidonia and Calcari Diasprigni formations were sampled, respectively. Biostratigraphy in both sections is based on rich assemblages of calcareous nannofossils and radiolarians, as well as some ammonites found in the upper Toarcian-Bajocian interval. Both sections revealed a relative minimum of delta(13)C(PDB) close to + 2 parts per thousand in the Aalenian and a maximum around 3.5 parts per thousand in early Bajocian, associated with an increase in visible chert. In basinal sections in Umbria-Marche, this interval includes the very cherry base of the Calcari Diasprigni Formation (e.g. at Valdorbia) or the chert-rich uppermost portion of the Calcari a Posidonia (e.g at Bosso). In the Terminilletto section, the Bajocian-early Barthonian interval shows a gradual decrease in delta(13)C(PDB) values and a low around 2.3 parts per thousand. This part of the section is characterised by more than 40 m of almost chart-free limestones and correlates with a recurrence of limestone-rich facies in basinal sections at Valdorbia. A double peak with values of delta(13)C(PDB) around + 3 parts per thousand was observed in the Callovian and Oxfordian, constrained by well preserved radiolarian faunas. The maxima lie in the Callovian and the middle Oxfordian, and the minimum between the two peaks should be near the Callovian/Oxfordian boundary. In the Terminilletto section, visible chert increases together with delta(13)C(PDB) values from the middle Bathonian and reaches peak values in the Callovian-Oxfordian. In basinal sections in Umbria-Marche, a sharp increase in visible chert is observed at this level within the Calcari Diasprigni. A drop of delta(13)C values towards + 2 parts per thousand occurs in the Kimmeridgian and coincides with a decrease of visible chert in outcrop. The observed delta(13)C positive anomalies during the early Bajocian and the Callovian-Oxfordian may record changes in global climate towards warmer, more humid periods characterised by increased nutrient mobilisation and increased carbon burial. High biosiliceous (radiolarians, siliceous sponges) productivity and preservation appear to coincide with the delta(13)C positive anomalies, when the production of platform carbonates was subdued and ceased in many areas, with a drastic reduction of periplatform ooze input in many Tethyan basins. The carbon and silica cycles appear to be linked through global warming and increased continental weathering. Hydrothermal events related to extensive rifting and/or accelerated oceanic spreading may be the endogenic driving force that created a perturbation of the exogenic system (excess CO2 into the atmosphere and greenhouse conditions) reflected by the positive delta(13)C shifts and biosiliceous episodes.

Linear and unit-resulting refutations for Horn theories

Abstract: We present a new transformation method by which a given Horn theory is transformed in such a way that resolution derivations can be carried out which are bot h linear (in the sense of Prologs SLD-resolution) and unit-resulting (ie the resolvents are unit clauses) Thi s is not trivial since although both strategies alone are complete, their nacombination is not Completeness is recovered by our method through a completion procedure in the spirit of Knuth-Bendix completion, however with different ordering criteria A powerful redundancy criterion helps to find a finite system quite often The transformed theory can be used in combination with linear calculi such as eg (theory) model elimination to yield sound, complete and efficient calculi for full first o rder clause logic over the given Horn theory As an example application, our method discovers a generalization of the well-known linear paramodulation calculus for the combined theory of equality and strict orderings The method has been implemented and has been tested in conjunction with a model elimination theorem prover

Hyper Tableaux and Disjunctive Logic Programming.

Abstract: For disjunctive logic programs (DLPs) there are several proposals for deening interpreters, There have also been diierent approaches to assign least xpoints to DLPs. This paper proves that there exist an eecient proof procedure, namely hyper tableaux, which can be understood as a direct implementation of some of the well known xpoint iteration techniques. We show how a hyper tableaux refutation can be transformed into a restart model elimination refutation. This result links the bottom-up to a top-down semantics for DLPs, and thus generalizes the standard result in Lloyd, 1987] saying that any nite iteration of the T-operator for deenite programs can be simulated top-town in a SLD-refutation. A diierent approach to obtain a top-down calculus is to replace all literals in the input clause set by their complements. We demonstrate that in this setting hyper tableaux generalize Rajasekar's SLO-Resolution. In the next section we give the proof theoretical part of this paper, which is based on the hyper tableaux calculus from Baumgartner et al., 1996]. In the following two sections we compare this calculus to xpoint iteration techniques: there is one seminal paper by Minker and Rajasekar Minker and Rajasekar, 1990] which introduces a consequence operator to deene a semantics for positive disjunctive logic programs by xpoint iteration over states. We will relate hyper tableaux to this iteration. Another approach by Fernandez and Minker (Fernandez and Minker, 91]), gives a bottom up evaluation of hierarchical disjunctive databases. We will demonstrate, that this approach is a special case of hyper tableaux. In Section 5 we discuss the relation of hyper tableaux to SLO-resolution, and in Section 6 we relate hyper tableaux to restart model elimination. 1 Preliminaries In what follows, we assume that the reader is familiar with the basic concepts of rst-order logic. A clause is a multiset of literals, usually written as the disjunction A 1 _ _ A m _ :B 1 _ _ :B n or the implication A 1 the variables occurring in clauses are considered implicitly as being universally quantiied, a clause is considered logically as a disjunction of literals, and a ((nite) clause set is taken as a conjunction of clauses. A ground clause is a clause containing no variables. Literal K is an instance of literal L, written as K L or L K, ii K = LL for some substitution. Let L denote the complement of a literal L. Two literals …

On Merging Theorem Proving and Logic Programming Paradigms (Poster Abstract).

Abstract: This document contains a list of 226 publications (more than 100 in refereed journals and conferences) and a list of 65 invited talks. The publications consist of 29 books and invited articles in books, 46 Journal-Publications, 10 invited Tutorials, 54 papers in refereed conferences, 48 additional papers, and 39 supervised papers. My DBLP count (http://www.informatik.uni-trier.de/~ley/ db/indices/a-tree/index.html) is currently at 108. I am mentioned in the list of the most cited authors in computer science (http://citeseer.nj.nec.com/ allcitedn.html): my current position is 3840.