On Probabilistic Logical Argumentation

In this paper, we introduce a framework for probabilistic logic-based argumentation inspired on the DeLP formalism and an extensive use of conditional probability. We define probabilistic arguments built from possibly inconsistent probabilistic knowledge bases and study the notions of attack, defeat and preference between these arguments. Finally, we discuss consistency properties of admissible extensions of the Dung’s abstract argumentation graphs obtained from sets of probabilistic arguments and the attack relations between them.

Analysing Probability Teaching Practices in Primary Education: What Tasks Do Teachers Implement?

This study analyses probability tasks proposed by primary education teachers to promote probabilistic literacy. To this end, eight class sessions at various levels of the Chilean educational system were recorded on video and analysed through the ”probability tasks” dimension from the “Observation Instrument for Probability Classes” (IOC-PROB), which includes five components: use of resources, probabilistic contexts, cognitive challenge, procedures and strategies, and probability meanings. The results show that probability tasks focus mainly on technical knowledge, causing the probability class to become an arithmetic class in which only formulas are applied, mechanically and with no meaning. As a result, we see no use of technological resources, a low use of physical materials, and an absolute predominance of solving decontextualised exercises. We conclude that it is necessary to enhance the probability teaching practices based on lesson plans that consider a wide variety of resources and contexts to gradually advance towards a representation of probabilistic knowledge that relies on conventional procedures and notations.

The alternation between exterior locative cases and postpositions in Estonian web texts

A probabilistic grammar approach to language assumes that grammatical knowledge has a probabilistic component and that this probabilistic knowledge of language is derived from language experience. It is assumed that the extent and nature of grammatical knowledge is reflected in language variation. In the present paper, the probabilistic variation patterns of the Estonian exterior locative cases and the corresponding postpositions are determined by exploring a large, manually annotated dataset of Estonian web texts. It is proposed that there are both similarities and differences in the morphosyntactic knowledge on the part of Estonian speakers as pertains to the three alternations: allative ~ peale ‘onto’, adessive ~ peal ‘on’, ablative ~ pealt ‘off’. The study points towards the stability and direction of the factors that have been found significant in the previous studies. Multivariate analysis of corpus data shows that the grammatical knowledge of Estonian exterior cases and the corresponding postpositions is probabilistic and regulated by both morphosyntactic and semantic factors. Kokkuvõte. Jane Klavan: Eesti keele väliskohakäänete ja kaassõnade peal, peale, pealt kasutus eestikeelses veebis. Tõenäosusliku grammatika raamistikus eeldatakse, et grammatiline teadmine hõlmab endas tõenäosuslikku komponenti ja et see tõenäosuslik komponent pärineb suures osas keele kasutuse kogemusest. Sellistelt põhimõtetelt lähtuvate uurimuste eesmärgiks on mõõta grammatilise teadmise ulatust ja olemust nagu see peegeldub keelelises varieeruvuses. Esitan suuremahulise korpusuurimuse eesti keele väliskohakäänete ja nendega rööpselt tarvitatavate kaassõnade (peale, peal, pealt) paralleelsest kasutusest eestikeelsetel veebilehtedel. Korpusandmete multifaktoriaalne analüüs näitab, et grammatiline teadmine sellest rööpsest kasutusest on tõenäosuslik ja et seda reguleerivad nii morfosüntaktilised kui semantilised tegurid.

On the Progression of Belief

Based on weighted possible-world semantics, Belle and Lakemeyer recently proposed the logic DS, a probabilistic extension of a modal variant of the situation calculus with a model of belief. The logic has many desirable properties like full introspection and it is able to precisely capture the beliefs of a probabilistic knowledge base in terms of the notion of only-believing. While the proposal is intuitively appealing, it is unclear how to do planning with such logic. The reason behind this is that the logic lacks projection reasoning mechanisms. Projection reasoning, in general, is to decide what holds after actions. Two main solutions to projection exist: regression and progression. Roughly, regression reduces a query about the future to a query about the initial state while progression, on the other hand, changes the initial state according to the effects of actions and then checks whether the formula holds in the updated state. In this paper, we study projection by progression in the logic DS. It is known that the progression of a categorical knowledge base wrt a noise-free action corresponds to what is only-known after that action. We show how to progress a type of probabilistic knowledge base wrt noisy actions by the notion of only-believing after actions. Our notion of only-believing is closely related to Lin and Reiter's notion of progression.

Hierarchical Self-supervised Augmented Knowledge Distillation

Knowledge distillation often involves how to define and transfer knowledge from teacher to student effectively. Although recent self-supervised contrastive knowledge achieves the best performance, forcing the network to learn such knowledge may damage the representation learning of the original class recognition task. We therefore adopt an alternative self-supervised augmented task to guide the network to learn the joint distribution of the original recognition task and self-supervised auxiliary task. It is demonstrated as a richer knowledge to improve the representation power without losing the normal classification capability. Moreover, it is incomplete that previous methods only transfer the probabilistic knowledge between the final layers. We propose to append several auxiliary classifiers to hierarchical intermediate feature maps to generate diverse self-supervised knowledge and perform the one-to-one transfer to teach the student network thoroughly. Our method significantly surpasses the previous SOTA SSKD with an average improvement of 2.56% on CIFAR-100 and an improvement of 0.77% on ImageNet across widely used network pairs. Codes are available at https://github.com/winycg/HSAKD.

Reasoning about Beliefs and Meta-Beliefs by Regression in an Expressive Probabilistic Action Logic

In a recent paper Belle and Lakemeyer proposed the logic DS, a probabilistic extension of a modal variant of the situation calculus with a model of belief based on weighted possible worlds. Among other things, they were able to precisely capture the beliefs of a probabilistic knowledge base in terms of the concept of only-believing. While intuitively appealing, the logic has a number of shortcomings. Perhaps the most severe is the limited expressiveness in that degrees of belief are restricted to constant rational numbers, which makes it impossible to express arbitrary belief distributions. In this paper we will address this and other shortcomings by extending the language and modifying the semantics of belief and only-believing. Among other things, we will show that belief retains many but not all of the properties of DS. Moreover, it turns out that only-believing arbitrary sentences, including those mentioning belief, is uniquely satisfiable in our logic. For an interesting class of knowledge bases we also show how reasoning about beliefs and meta-beliefs after performing noisy actions and sensing can be reduced to reasoning about the initial beliefs of an agent using a form of regression.

Could probability be out of proportion? Self-explanation and example-based practice help students with lower proportional reasoning skills learn probability

Proportional reasoning failures seem to constitute most errors in probabilistic reasoning, yet there is little empirical evidence about its role for attaining probabilistic knowledge and how to effectively intervene with students who have less proportional reasoning skills. We examined the contributions of students' proportional reasoning skill and example-based practice when learning about probabilities from a reformed seventh grade curriculum. Teachers in their regular classrooms were randomly assigned to instruct with a reformed textbook (control) or a version revised to incorporate correct and incorrect example problems with prompts to explain (treatment). Students' prior knowledge in proportional reasoning skill separately predicted probabilistic knowledge at posttest, regardless of their prior knowledge in probability or minority status. Overall, students in the treatment condition improved more in their probabilistic knowledge, if they started with less proportional reasoning skills. Our findings suggest that example-based practice is beneficial for students with less prior knowledge of proportions, likely a key concept for developing probabilistic knowledge.