Infinite Probabilistic Databases

Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this is not compatible with an open-world semantics (Ceylan et al., KR 2016) and with application scenarios that are modeled by continuous probability distributions (Dalvi et al., CACM 2009). We recently introduced a model of PDBs as infinite probability spaces that addresses these issues (Grohe and Lindner, PODS 2019). While that work was mainly concerned with countably infinite probability spaces, our focus here is on uncountable spaces. Such an extension is necessary to model typical continuous probability distributions that appear in many applications. However, an extension beyond countable probability spaces raises nontrivial foundational issues concerned with the measurability of events and queries and ultimately with the question whether queries have a well-defined semantics. It turns out that so-called finite point processes are the appropriate model from probability theory for dealing with probabilistic databases. This model allows us to construct suitable (uncountable) probability spaces of database instances in a systematic way. Our main technical results are measurability statements for relational algebra queries as well as aggregate queries and Datalog queries

Metric Semantics and Full Abstractness for Action Refinement and Probabilistic Choice

This paper provides a case-study in the field of metric semantics for probabilistic programming. Both an operational and a denotational semantics are presented for an abstract process language L_pr, which features action refinement and probabilistic choice. The two models are constructed in the setting of complete ultrametric spaces, here based on probability measures of compact support over sequences of actions. It is shown that the standard toolkit for metric semantics works well in the probabilistic context of L_pr, e.g. in establishing the correctness of the denotational semantics with respect to the operational one. In addition, it is shown how the method of proving full abstraction --as proposed recently by the authors for a nondeterministic language with action refinement-- can be adapted to deal with the probabilistic language L_pr as well

Loops and Knots as Topoi of Substance. Spinoza Revisited

The relationship between modern philosophy and physics is discussed. It is shown that the latter develops some need for a modernized metaphysics which shows up as an ultima philosophia of considerable heuristic value, rather than as the prima philosophia in the Aristotelian sense as it had been intended, in the first place. It is shown then, that it is the philosophy of Spinoza in fact, that can still serve as a paradigm for such an approach. In particular, Spinoza's concept of infinite substance is compared with the philosophical implications of the foundational aspects of modern physical theory. Various connotations of sub-stance are discussed within pre-geometric theories, especially with a view to the role of spin networks within quantum gravity. It is found to be useful to intro-duce a separation into physics then, so as to differ between foundational and empirical theories, respectively. This leads to a straightforward connection bet-ween foundational theories and speculative philosophy on the one hand, and between empirical theories and sceptical philosophy on the other. This might help in the end, to clarify some recent problems, such as the absence of time and causality at a fundamental level. It is implied that recent results relating to topos theory might open the way towards eventually deriving logic from physics, and also towards a possible transition from logic to hermeneutic.Comment: 42 page

A semantic foundation for hidden state

We present the first complete soundness proof of the antiframe rule, a recently proposed proof rule for capturing information hiding in the presence of higher-order store. Our proof involves solving a non-trivial recursive domain equation, and it helps identify some of the key ingredients for soundness

Pattern recognition in narrative: Tracking emotional expression in context

Using geometric data analysis, our objective is the analysis of narrative, with narrative of emotion being the focus in this work. The following two principles for analysis of emotion inform our work. Firstly, emotion is revealed not as a quality in its own right but rather through interaction. We study the 2-way relationship of Ilsa and Rick in the movie Casablanca, and the 3-way relationship of Emma, Charles and Rodolphe in the novel {\em Madame Bovary}. Secondly, emotion, that is expression of states of mind of subjects, is formed and evolves within the narrative that expresses external events and (personal, social, physical) context. In addition to the analysis methodology with key aspects that are innovative, the input data used is crucial. We use, firstly, dialogue, and secondly, broad and general description that incorporates dialogue. In a follow-on study, we apply our unsupervised narrative mapping to data streams with very low emotional expression. We map the narrative of Twitter streams. Thus we demonstrate map analysis of general narratives