A modal type theory for formalizing trusted communications

Abstract

This paper introduces a multi-modal polymorphic type theory to model epistemic processes characterized by trust, defined as a second-order relation affecting the communication process between sources and a receiver. In this language, a set of senders is expressed by a modal prioritized context, whereas the receiver is formulated in terms of a contextually derived modal judgement. Introduction and elimination rules for modalities are based on the polymorphism of terms in the language. This leads to a multi-modal nonhomogeneous version of a type theory, in which we show the embedding of the modal operators into standard group knowledge operators.

Offline and online data: on upgrading functional information to knowledge

“…Hence, at the first level of typing, one is considering the evaluation of the concrete level of meaning, obtained by performing the operation and getting 17 For the so-called 'Forget-Restore Principle', see [Sambin, Valentini, 1998]. 18 See [Primiero, 2012] for the full formal language: it is a variant interpretation of the basic system of constructive type-theory that links hypotheses and refutable contents.…”

“…18 See [Primiero, 2012] for the full formal language: it is a variant interpretation of the basic system of constructive type-theory that links hypotheses and refutable contents. It extends to a modal type-theory, variating on a theme first proposed in [Pfenning, Dvies, 2001] and later expanded in [Nanevski et al, 2008]. We shall here only focus on the appropriate introduction rules for justified and assumed contents and expand on the use of modalities in the next section.…”

“…23 A different account of the notion of epistemic modality is given in those approaches where one gets rid of truth conditions entirely and defines appropriate counterparts of the standard notions of necessity and possibility by referring to validity of alternative (accessible) assertion conditions. 24 The analysis put forward in [Primiero, 2009b] offers precisely the kind of machinery needed.…”

“…The latter is the form of judgements used for the modal extension of Martin-Löf's Type Theory in [Pfenning, Dvies, 2001] and [Nanevski et al, 2008], whereas we use the judgemental modalities both in [Primiero, 2012] and [Primiero, 2010] in order to express the contextual nature of our proof-terms. 26 See also [Bellin et al, 2001] for a formal language that requires the same kind of rules.…”

“…10 In the present paper, we address the analysis of upgrading information to knowledge from this latter epistemic perspective, starting from the ground notion of functional information characterized by locality. We shall rely on the epistemic constructive definition of information (ECDI) introduced in [Primiero, 2007] to supervene the alethic/non-alethic issue about informational contents, relying on the formal framework which uses the theory of judgements of Martin-Löf's Type Theory. 11 We define functional informational contents as syntactically correct and meaningful propositional contents.…”