In ownership-based access control frameworks with the possibility of delegating permissions and administrative rights, chains of delegated accesses will form. There are different ways to treat these delegation chains when revoking rights, which give rise to different revocation schemes. Hagström et al. [8] proposed a framework for classifying revocation schemes, in which the different revocation schemes are defined graph-theoretically; they motivate the revocation schemes in this framework by presenting various scenarios in which the agents have different reasons for revocating. This paper is based on the observation that there are some problems with Hagström et al.'s definitions of the revocation schemes, which have led us to propose a refined framework with new graph-theoretic definitions of the revocation schemes. In order to formally study the merits and demerits of various definitions of revocation schemes, we propose to apply the axiomatic method originating in social choice theory to revocation schemes. For formulating an axiom, i.e. a desirable property of revocation frameworks, we propose a logic, Trust Delegation Logic (TDL), with which one can formalize the different reasons an agent may have for performing a revocation. We show that our refined graph-theoretic definitions of the revocation schemes, unlike Hagström et al.'s original definitions, satisfy the desirable property that can be formulated using TDL.
Abstract. This paper discusses the semi-formal language of mathematics and presents the Naproche CNL, a controlled natural language for mathematical authoring. Proof Representation Structures, an adaptation of Discourse Representation Structures, are used to represent the semantics of texts written in the Naproche CNL. We discuss how the Naproche CNL can be used in formal mathematics, and present our prototypical Naproche system, a computer program for parsing texts in the Naproche CNL and checking the proofs in them for logical correctness.
In abstract argumentation, multiple argumentation semantics have been proposed that allow to select sets of jointly acceptable arguments from a given argumentation framework, i.e. based only on the attack relation between arguments. The existence of multiple argumentation semantics raises the question which of these semantics predicts best how humans evaluate arguments. Previous empirical cognitive studies that have tested how humans evaluate sets of arguments depending on the attack relation between them have been limited to a small set of very simple argumentation frameworks, so that some semantics studied in the literature could not be meaningfully distinguished by these studies. In this paper we report on an empirical cognitive study that overcomes these limitations by taking into consideration twelve argumentation frameworks of three to eight arguments each. These argumentation frameworks were mostly more complex than the argumentation frameworks considered in previous studies. All twelve argumentation framework were systematically instantiated with natural language arguments based on a certain fictional scenario, and participants were shown both the natural language arguments and a graphical depiction of the attack relation between them. Our data shows that grounded and CF2 semantics were the best predictors of human argument evaluation. A detailed analysis revealed that part of the participants chose a cognitively simpler strategy that is predicted very well by grounded semantics, while another part of the participants chose a cognitively more demanding strategy that is mostly predicted well by CF2 semantics. Argumentation Framework 11Argument W (48): Islander Walter says that islander Xavier is not trustworthy and that there is a treasure buried between the ponds. So we should not trust what Xavier says, and we should dig up the sand between the ponds. Argument X (49): Islander Xavier says that islander Yanis and islander Zoe are not trustworthy and that there is a treasure buried next to the temple. So we should not trust what Yanis and Zoe say, and we should dig up the sand next to the temple. Argument Y (50):Islander Yanis says that islander Walter and islander Zoe are not trustworthy and that there is a treasure buried to the east of the lake. So we should not trust what Walter and Zoe say, and we should dig up the sand to the east of the lake. Argument Z (51):Islander Zoe says that islander Anna is not trustworthy, and that there is a treasure buried between the two highest mountains. So we should not trust what Anna says, and we should dig up the sand between the two highest mountains.Argument A (52): Islander Anna says that there is a treasure buried to the west of the lake. So we should dig up the sand to the west of the lake. Argumentation Framework 12Argument C (53): Islander Charlie says that islander Dorothy is not trustworthy and that there is a treasure buried to the south of the high mountain. So we should not trust what Dorothy says, and we should dig up the sand to the south of the high m...
The frame concept from linguistics, cognitive science and artificial intelligence is a theoretical tool to model how explicitly given information is combined with expectations deriving from background knowledge. In this paper, we show how the frame concept can be fruitfully applied to analyze the notion of mathematical understanding. Our analysis additionally integrates insights from the hermeneutic tradition of philosophy as well as Schmid’s ideal genetic model of narrative constitution. We illustrate the practical applicability of our theoretical analysis through a case study on extremal proofs. Based on this case study, we compare our analysis of proof understanding to Avigad’s ability-based analysis of proof understanding.
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