Time Aware Knowledge Extraction for Microblog Summarization on Twitter

Microblogging services like Twitter and Facebook collect millions of user generated content every moment about trending news, occurring events, and so on. Nevertheless, it is really a nightmare to find information of interest through the huge amount of available posts that are often noise and redundant. In general, social media analytics services have caught increasing attention from both side research and industry. Specifically, the dynamic context of microblogging requires to manage not only meaning of information but also the evolution of knowledge over the timeline. This work defines Time Aware Knowledge Extraction (briefly TAKE) methodology that relies on temporal extension of Fuzzy Formal Concept Analysis. In particular, a microblog summarization algorithm has been defined filtering the concepts organized by TAKE in a time-dependent hierarchy. The algorithm addresses topic-based summarization on Twitter. Besides considering the timing of the concepts, another distinguish feature of the proposed microblog summarization framework is the possibility to have more or less detailed summary, according to the user's needs, with good levels of quality and completeness as highlighted in the experimental results.Comment: 33 pages, 10 figure

On the Notion of Proposition in Classical and Quantum Mechanics

The term proposition usually denotes in quantum mechanics (QM) an element of (standard) quantum logic (QL). Within the orthodox interpretation of QM the propositions of QL cannot be associated with sentences of a language stating properties of individual samples of a physical system, since properties are nonobjective in QM. This makes the interpretation of propositions problematical. The difficulty can be removed by adopting the objective interpretation of QM proposed by one of the authors (semantic realism, or SR, interpretation). In this case, a unified perspective can be adopted for QM and classical mechanics (CM), and a simple first order predicate calculus L(x) with Tarskian semantics can be constructed such that one can associate a physical proposition (i.e., a set of physical states) with every sentence of L(x). The set $P^{f}$ of all physical propositions is partially ordered and contains a subset $P^{f}_{T}$ of testable physical propositions whose order structure depends on the criteria of testability established by the physical theory. In particular, $P^{f}_{T}$ turns out to be a Boolean lattice in CM, while it can be identified with QL in QM. Hence the propositions of QL can be associated with sentences of L(x), or also with the sentences of a suitable quantum language $L_{TQ}(x)$, and the structure of QL characterizes the notion of testability in QM. One can then show that the notion of quantum truth does not conflict with the classical notion of truth within this perspective. Furthermore, the interpretation of QL propounded here proves to be equivalent to a previous pragmatic interpretation worked out by one of the authors, and can be embodied within a more general perspective which considers states as first order predicates of a broader language with a Kripkean semantics.Comment: 22 pages. To appear in "The Foundations of Quantum Mechanics: Historical Analysis and Open Questions-Cesena 2004", C. Garola, A. Rossi and S. Sozzo Eds., World Scientific, Singapore, 200

Coherent Multi-Sentence Video Description with Variable Level of Detail

Humans can easily describe what they see in a coherent way and at varying level of detail. However, existing approaches for automatic video description are mainly focused on single sentence generation and produce descriptions at a fixed level of detail. In this paper, we address both of these limitations: for a variable level of detail we produce coherent multi-sentence descriptions of complex videos. We follow a two-step approach where we first learn to predict a semantic representation (SR) from video and then generate natural language descriptions from the SR. To produce consistent multi-sentence descriptions, we model across-sentence consistency at the level of the SR by enforcing a consistent topic. We also contribute both to the visual recognition of objects proposing a hand-centric approach as well as to the robust generation of sentences using a word lattice. Human judges rate our multi-sentence descriptions as more readable, correct, and relevant than related work. To understand the difference between more detailed and shorter descriptions, we collect and analyze a video description corpus of three levels of detail.Comment: 10 page

Morphisms and Duality for Polarities and Lattices with Operators

Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of morphism between polarity-based structures that generalises the theory of bounded morphisms for Boolean modal logics. It defines a category of such structures that is contravariantly dual to a given category of lattice-based algebras whose additional operations preserve either finite joins or finite meets. Two different versions of the Goldblatt-Thomason theorem are derived in this setting

A theory of concepts and their combinations I: The structure of the sets of contexts and properties

We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts