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 non-homogeneous version of a (...) type theory, in which we show the embedding of the modal operators into standard group knowledge operators. (shrink)

The aim of this paper is to present a logical framework in which the concepts of trust and reputation can be formally characterized and their properties studied. We start from the definition of trust proposed by Castelfranchi & Falcone . We formalize this definition in a logic of time, action, beliefs and choices. Then, we provide a refinement of C&F’s definition by distinguishing two general types of trust: occurrent trust and dispositional trust. In the second part of the paper we (...) present a definition of reputation that is structurally similar to the definition of trust but moves the basic concept of belief to a collective dimension of group belief. (shrink)

Trust may have many different informal definitions. In this work, formal definitions are proposed in Modal Logic in order to have clear rules for reasoning about trust. We start from trust in some properties of an information source, like sincerity, competence or vigilance, about a given proposition. Then, this definition is extended to trust about all the propositions which are about a given topic. A further extension is about all the propositions which inform about a given individual. Specific logics are (...) presented for reasoning about the fact that a given proposition is about a given topic and for reasoning about the fact that a proposition informs about a given individual. At the end, we give a brief extension to qualitative graded trust. (shrink)

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both (...) students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading. (shrink)