Showing papers by "Peter Baumgartner published in 2007"

Hyper Tableaux with Equality

Abstract: In most theorem proving applications, a proper treatment of equational theories or equality is mandatory. In this paper we show how to integrate a modern treatment of equality in the hyper tableau calculus. It is based on splitting of positive clauses and an adapted version of the superposition inference rule, where equations used for paramodulation are drawn (only) from a set of positive unit clauses, the candidate model. The calculus also features a generic, semantically justified simplification rule which covers many redundancy elimination techniques known from superposition theorem proving. Our main results are soundness and completeness, but we briefly describe the implementation, too.

Abducing Coreference by Model Construction

Abstract: In this paper, we argue that the resolution of anaphoric expressions in an utterance is essentially an abductive task following [12] who use a weighted abduction scheme on horn clauses to deal with reference. We give a semantic representation for utterances containing anaphora that enables us to compute possible antecedents by abductive inference. We extend the disjunctive model construction procedure of hyper tableaux [3, 14] with a clause transformation turning the abductive task into a model generation problem and show the completeness of this transformation with respect to the computation of abductive explanations. This abductive inference is applied to the resolution of anaphoric expressions in our general model constructing framework for incremental discourse representation which we argue to be useful for computing information updates from natural language utterances.

Logical Engineering with Instance-Based Methods

Abstract: The term "instance based methods" (IMs) refers to a certain family of methods for first-order logic theorem proving. IMs share the principle of carrying out proof search by maintaining a set of instances of input clauses and analyzing it for satisfiability until completion. IMs are conceptually essentially different to well established methods like resolution or free-variable analytic tableaux. (See [Pla94] for a comparison of various calculi and strategies, including an instance based method.) Also, IMs exhibit a search space and termination behaviour (in the satisfiable case) different from those methods, which makes them attractive from a practical point of view as a complementary method.

A Unified Approach to Theory Reasoning

Abstract: Theory reasoning is a kind of two-level reasoning in automated theorem proving, where the knowledge of a given domain or theory is separated and treated by special purpose inference rules. We define a classification for the various approaches for theory reasoning which is based on the syntactic concepts of literal level — term level — variable level. The main part is a review of theory extensions of common calculi (resolution, model elimination and a connection method). In order to see the relationships among these calculi, we define a super-calculus called theory consolution. Completeness of the various theory calculi is proven. Finally, due to its relevance in automated reasoning, we describe current ways of equality handling.

Late Oligocene Larger Foraminifera From Nosara (Nicoya Península, Costa Rica) and Indward (Carriacou, Lesser Antilles), Calibrated by 87sr/ 86sr Isotope Stratigraphy

Abstract: The Late Oligocene first occurrence of Miogypsina gunteri Cole and Miogypsina tani Drooger is verified in the light of larger foraminiferal assemblages from Nosara (Nicoya Peninsula, Costa Rica) and Windward (Carriacou, Grenada, Lesser Antilles). At Windward, they co-occur with planktonic foraminifera and nannofossils studied by earlier workers. 87Sr/86Sr isotope ratios were measured in calcite of larger foraminifera at both sites to determine independent absolute ages of the two outcrops. Late Oligocene shallow water formations unconformably overlie Paleocene-Eocene distal turbidites and siliceous shales in the outcrops in Costa Rica. The shallow-water lithostratigraphy includes near shore volcanic sandstones that alternate with sandy bioclastic limestones. The latter have yielded rich assemblages of larger foraminifera that have been studied in oriented sections, SEM for split material and polished rock thin sections for transmitted light and cathodoluminescence (CL) observation. The association of larger foraminifera includes Heterostegina antillea Cushman, Miogypsina tani Drooger, Miogypsina gunteri Cole, Miogypsina c.f (Miolepidocyclina) panamensis (Cushman), Miogypsina sp., Lepidocyclina (nephrolepidina) vaughani Cushman, Lepidocyclina yurnagurensis Cushman, Lepidocyclina undosa Cushman. At Windward, scattered outcrops of the Belvedere Formation expose mass flow deposits rich in larger foraminifera associated with an early late Oligocene (NP24) planktonic foraminifa assemblage. Planktonic foraminifera and nannofossils recovered in rocks slightly downsection indicate an upper Middle Oligocene age. Larger foraminifera species collected just north of Windward include Lepidocyclina undosa Cushman and Miogypsina gunteri Cole. The 87Sr/86Sr ratio was measured in 11 specimens of megalosphaeric Lepidocyclina spp., mechanically extracted from 2 rock samples collected at Punta Peladas (Costa Rica) Ratios range from 0.709088 to 0.708196, which correspond to a model age of 27.4 to 24.94 Ma. Very similar ratios, ranging from 0.708150 to 0.708167 were obtained from Windward Village (Carriacou). All measured 87Sr/86Sr ratios fall within a Chattian (Late Oligocene) age. Nannofossils, planktonic foraminifera and identical 87Sr/86Sr ratios from Punta Peladas and Windward clearly indicate a Chattian (Upper Oligocene) first occurrence of Miogypsina gunteri and Miogypsina tani and confirm this age range for the other larger foraminifera cited above. The first occurrence of Miogypsina gunteri in the lower Aquitanian and Miogypsina tani in the upper Aquitanian as proposed by European workers cannot be confirmed.