In the paper it is argued that bridging the digital divide may cause a new ethical and social dilemma. Using Hardin's Tragedy of the Commons, we show that an improper opening and enlargement of the digital environment (Infosphere) is likely to produce a Tragedy of the Digital Commons (TDC). In the course of the analysis, we explain why Adar and Huberman's previous use of Hardin's Tragedy to interpret certain recent phenomena in the Infosphere (especially peer-to-peer communication) may not be entirely (...) satisfactory. We then seek to provide an improved version of the TDC that avoids the possible shortcomings of their model. Next, we analyse some problems encountered by the application of classical ethics in the resolution of the TDC. In the conclusion, we outline the kind of work that will be required to develop an ethical approach that may bridge the digital divide but avoid the TDC. (shrink)

In the present article, we introduce a multi-type display calculus for dynamic epistemic logic, which we refer to as Dynamic Calculus. The display approach is suitable to modularly chart the space of dynamic epistemic logics on weaker-than-classical propositional base. The presence of types endows the language of the Dynamic Calculus with additional expressivity, allows for a smooth proof-theoretic treatment, and paves the way towards a general methodology for the design of proof systems for the generality of dynamic logics, and certainly (...) beyond dynamic epistemic logic. We prove that the Dynamic Calculus adequately captures Baltag–Moss–Solecki's dynamic epistemic logic, and enjoys Belnap-style cut elimination. (shrink)

In this paper we introduce three methods to approach philosophical problems informationally: Minimalism, the Method of Abstraction and Constructionism. Minimalism considers the specifications of the starting problems and systems that are tractable for a philosophical analysis. The Method of Abstraction describes the process of making explicit the level of abstraction at which a system is observed and investigated. Constructionism provides a series of principles that the investigation of the problem must fulfil once it has been fully characterised by the previous (...) two methods. For each method, we also provide an application: the problem of visual perception, functionalism, and the Turing Test, respectively. (shrink)

We introduce the logic LRC, designed to describe and reason about agents’ abilities and capabilities in using resources. The proposed framework bridges two—up to now—mutually independent strands of literature: the one on logics of abilities and capabilities, developed within the theory of agency, and the one on logics of resources, motivated by program semantics. The logic LRC is suitable to describe and reason about key aspects of social behaviour in organizations. We prove a number of properties enjoyed by LRC and (...) its associated analytic calculus. These results lay at the intersection of the algebraic theory of unified correspondence and the theory of multitype calculi in structural proof theory. Case studies are discussed which showcase several ways in which this framework can be extended and enriched while retaining its basic properties, so as to model an array of issues, both practically and theoretically relevant, spanning from planning problems to the logical foundations of the theory of organizations. (shrink)

We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be first-order definable but not modally definable. We also obtain a new definition of graded bisimulation with respect to Kripke frames by modifying the definition of monotonic bisimulation.

The present article provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. Dynamic epistemic logic is one of the best known members of a family of logical systems that have been successfully applied to diverse scientific disciplines, but the proof-theoretic treatment of which presents many difficulties. After an illustration of the proof-theoretic semantic principles most relevant to the treatment of logical connectives, we turn to illustrating the main features of display calculi, (...) a proof-theoretic paradigm that has been successfully employed to give a proof-theoretic semantic account of modal and substructural logics. Then, we review some of the most significant proposals of proof systems for dynamic epistemic logics, and we critically reflect on them in the light of the previously introduced proof-theoretic semantic principles. The contributions of the present article include a generalization of Belnap's cut-elimination metatheorem for display calculi, and a revised version of the display-style calculus D.EAK. We verify that the revised version satisfies the previously mentioned proof-theoretic semantic principles, and show that it enjoys cut-elimination as a consequence of the generalized metatheorem. (shrink)

Spiders have always fascinated humankind as whilst they are often reviled, their product, the web and its silk, are commonly viewed in awe. As such, silks’ material properties and the fear and fascination surrounding the animals that spin it are seen to play an important role in the development of many cultures and societies. More recently this is even more so with the formalization of this inspiration in scientific and technical communities through biomimetics. The aim of this work is to (...) reflect on the beginnings of our relationship with silk and discuss concepts associated with spider silks and webs in ancient Greek and Roman times whilst comparing this with our current understanding of the field. In this way, ancient texts, namely Greek and Latin ones, are found to intersect with modern advanced disciplines, ranging from architecture to medicine to physics. This allows us not only to understand how natural observation has evolved from antiquity to today, but also how such a highly interdisciplinary research network has been spun by some shared conceptual threads. (shrink)

This article considers the function and value of the mythos in Plato's Statesman. As first, I recall the context of the story and its function within the framework of diairetic inquiry about the definition of the real politician. Secondly, I point out that the formulation of the myth is based on a series of traditional stories to which a historical-reconstructive method is applied. I then highlight the ways of reasoning used by the characters in order to reconstruct a rational and (...) plausible account from the mythical tradition. Finally, I try to show that the story, even though it cannot reach the truth of the most stable objects of knowledge, displays a certain degree of plausibility, based on the internal coherence, on the respect of a series of principles admitted as true and, eventually, on its correspondence with the mythical tradition. (shrink)

Focused sequent calculi are a refinement of sequent calculi, where additional side-conditions on the applicability of inference rules force the implementation of a proof search strategy. Focused cut-free proofs exhibit a special normal form that is used for defining identity of sequent calculi proofs. We introduce a novel focused display calculus fD.LG and a fully polarized algebraic semantics FP.LG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {FP.LG}$$\end{document} for Lambek–Grishin logic by generalizing the theory of multi-type calculi and their (...) algebraic semantics with heterogenous consequence relations. The calculus fD.LG has strong focalization and it is sound and complete w.r.t. FP.LG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {FP.LG}$$\end{document}. This completeness result is in a sense stronger than completeness with respect to standard polarized algebraic semantics, insofar as we do not need to quotient over proofs with consecutive applications of shifts over the same formula. We also show a number of additional results. fD.LG is sound and complete w.r.t. LG-algebras: this amounts to a semantic proof of the so-called completeness of focusing, given that the standard (display) sequent calculus for Lambek–Grishin logic is complete w.r.t. LG-algebras. fD.LG and the focused calculus fLG of Moortgat and Moot are equivalent with respect to proofs, indeed there is an effective translation from fLG-derivations to fD.LG-derivations and vice versa: this provides the link with operational semantics, given that every fLG-derivation is in a Curry–Howard correspondence with a directional λ¯μμ~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{\lambda }\mu \widetilde{\mu }$$\end{document}-term. (shrink)

L’articolo presenta e discute gli scarni dati biografici disponibili su Rorgone Fretello, autore di una fortunata topografia della Terra Santa della prima metà del XII secolo (Descriptio de locis sanctis), e offre un quadro relativo alle due redazioni note dell’opera, inquadrando i principali aspetti legati alla loro tradizione manoscritta, alla ricezione e alla storia editoriale. Mentre la prima redazione, dedicata al vescovo boemo Enrico Sdyck, conta sei codici, la seconda, che è destinata al conte spagnolo Rodrigo di Toledo e di (...) cui in questa sede viene discussa e confermata la paternità fretelliana, godette di maggiore successo: essa è trasmessa da quarantadue testimoni e costituisce la fonte di successive opere geografiche sulla Terra Santa. In appendice si fornisce un confronto tra i testi critici dei due prologhi, allo scopo di offrire un saggio delle modifiche messe in atto nel passaggio dalla prima alla seconda redazione della Descriptio. (shrink)

In the present paper, we endow semi De Morgan logic and a family of its axiomatic extensions with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis of the variety of semi De Morgan algebras, and applies the guidelines of the multi-type methodology in the design of display calculi.