SETHEO V3.2: Recent developments

Goller, Christoph; Letz, Reinhold; Mayr, Klaus; Schumann, Johann

doi:10.1007/3-540-58156-1_59

Cited by 26 publications

(2 citation statements)

References 6 publications

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“…Much is known about efficient implementation techniques, and highly sophisticated implementations exist (e.g., SETHEO [14], SPASS [26]). Both theoretical issues and the design of theorem provers for first-order logic have traditionally received considerable attention.…”

Section: A Logic-based Approachmentioning

confidence: 99%

Living Book ? Deduction, Slicing, and Interaction

et al. 2004

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Living Book is a system for the management of personalized and scenario-specific teaching material. The main goal of the system is to support active, explorative, and self-determined learning in lectures, tutorials, and self-study. Living Book includes a course on "logic for computer scientists," with uniform access to various tools such as theorem provers and an interactive tableau editor. It is routinely used in teaching undergraduate courses at our university. This paper describes Living Book, together with its use of theorem-proving technology as a core component in the knowledge management system (KMS) and the use of this new concept in academic teaching. The KMS provides a scenario management component in which teachers may describe those parts of given documents that are relevant in order to achieve a certain learning goal. The task of the KMS is to assemble new documents from a database of elementary units called "slices" (definitions, theorems, and so on) in a scenario-based way (such as, "I want to prepare for an exam and need to learn about resolution"). The computation of such assemblies is carried out by a model-generating theorem prover for first-order logic with a default negation principle. Its input consists of metadata that describes the dependencies between different slices and logic-programming style rules that describe the scenario-specific composition of slices. Additionally, users may assess what units they know or don't know. This information is stored in a user model, which is taken into account to compute a model that specifies the assembly of a personalized document. This paper introduces the e-learning context we are faced with, motivates our choice of logic, and sketches the newly developed calculus used in the KMS. Furthermore, the application and evaluation of Living Book are presented.

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Section: A Logic-based Approachmentioning

confidence: 99%

Living Book ? Deduction, Slicing, and Interaction

et al. 2004

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“…Aside of clausal tableaux in the literal sense, techniques to specify and investigate such methods include model elimination [40], the connection method [11], and the Prolog technology theorem prover [57]. One of the leading first-order proving systems of the 1990s, SETHEO [26], followed that approach. The leanCoP system [50] along with its recent derivations [32,33] as well as the CM component of PIE [21,64] are implementations in active duty today.…”

Section: Introductionmentioning

confidence: 99%

Craig Interpolation and Access Interpolation with Clausal First-Order Tableaux

Wernhard

2018

Preprint

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We develop foundations for computing Craig interpolants and similar intermediates of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way include efficient machine-oriented systems based on calculi of two families: goal-oriented like model elimination and the connection method, and bottom-up like the hyper tableau calculus. The presented method for Craig-Lyndon interpolation involves a lifting step where terms are replaced by quantified variables, similar as known for resolution-based interpolation, but applied to a differently characterized ground formula and proven correct more abstractly on the basis of Herbrand's theorem, independently of a particular calculus. Access interpolation is a recent form of interpolation for database query reformulation that applies to first-order formulas with relativized quantifiers and constrains the quantification patterns of predicate occurrences. It has been previously investigated in the framework of Smullyan's non-clausal tableaux. Here, in essence, we simulate these with the more machine-oriented clausal tableaux through structural constraints that can be ensured either directly by bottom-up tableau construction methods or, for closed clausal tableaux constructed with arbitrary calculi, by postprocessing with restructuring transformations. KeywordsCraig interpolation • first-order theorem proving • clausal tableaux • connection method • hyper tableaux • interpolant lifting • query reformulation • relativized quantifiers

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Efficient Model Generation through Compilation

Schütz¹,

Geisler²

2000

Information and Computation

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SETHEO V3.2: Recent developments

Cited by 26 publications

References 6 publications

Living Book ? Deduction, Slicing, and Interaction

Living Book ? Deduction, Slicing, and Interaction

Craig Interpolation and Access Interpolation with Clausal First-Order Tableaux

Efficient Model Generation through Compilation

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