Modal translation of substructural logics

In an article dating back in 1992, Kosta Došen initiated a project of modal translations in substructural logics, aiming at generalising the well-known Gödel–McKinsey–Tarski translation of intuitionistic logic into S4. Došen's translation worked well for (variants of) BCI and stronger systems (BCW, BCK), but not for systems below BCI. Dropping structural rules results in logic systems without distribution. In this article, we show, via translation, that every substructural (indeed, every non-distributive) logic is a fragment of a corresponding sorted, residuated (multi) modal logic. At the conceptual and philosophical level, the translation provides a classical interpretation of the meaning of the logical operators of various non-distributive propositional calculi. Technically, it allows for an effortless transfer of results, such as compactness and the Löwenheim-Skolem property and it opens up new directions for deducing properties of substructural logic systems by establishing appropriate transfer theorems. © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group

Adaptivity for knowledge content in the semantic web

The focus of this report is the adaptivity issue for Learning Objects owned by Learning (Web) Services. We address this issue based on the Concept, Resource, Order, Product (CROP) Reference Architecture that we briefly review here. Based on the essentially recursive notion of a learning object in our CROP architecture, we propose that adaptivity of learning objects is best viewed as a property of the network of learning services and the learning objects they own, i.e. as an emergent property of learning service communication and collaboration. For such a communication and collaboration to be successful with respect to an adaptive response goal, we propose that (besides adopting a standard reference architecture for learning objects) a global model of learning styles needs to be agreed upon. We contribute in this direction by presenting a basis for a global model of learning styles, by elaborating a systematic classification of the learning styles dimensions proposed in various models, uncovering relationships of concept identity or subsumption and distinguishing between base and definable concepts

Learning objects and learning services in the semantic web

With the development of the web and the intense research for a semantic web, the need arises for standardized and rigorous semantic specification both of Services on the semantic web and of the objects and processes that these Services offer to a potential client. In this report, our focus is with Learning Services, i.e. Web Services whose purpose is to offer educational services to clients. Such services are the owners of Learning Objects, which they deliver for use to their clients. Though the need for standardizing learning objects has become apparent, there is no substantial contribution towards a reference architecture for Learning Objects. We introduce here the CROP architecture, based on the notions of Concept, Resource, Order and Product. © 2008 IEEE

Representation of lattices with modal operators in two-sorted frames

We study general lattices with normal unary operators for which we prove relational representation and duality results. Similar results have appeared in print, using Urquhart's lattice representation, by the second author with Vakarelov, Radzikowska and Rewitzky. We base our approach in this article on the Hartonas and Dunn lattice duality, proven by Gehrke and Harding to deliver a canonical lattice extension, and on recent results by the first author on the relational representation of normal lattice operators. We verify that the operators at the representation level (appropriately generated by relations) are the canonical extensions of the lattice operators, in Gehrke and Harding's sense. © 2019 - IOS Press and the authors. All rights reserved

Faster and symbolic CTMC model checking

This paper reports on the implementation and the experiments with symbolic model checking of continuous-time Markov chains using multi-terminal binary decision diagrams (MTBDDs). Properties are expressed in Continuous Stochastic Logic (CSL) [7] which includes the means to express both transient and steady-state performance measures. We show that all CSL operators can be treated using standard operations on MTBDDs, thus allowing a rather straightforward implementation of symbolic CSL model checking on existing MTBDD-based platforms such as the verifier PRISM. The main result of the paper is an improvement of O(N) in the time complexity of checking time-bounded until-formulas, where N is the number of states in the CTMC under consideration. This result yields a drastic speed-up in the verification time of model checking CTMCs, both in the symbolic and non-symbolic case