Descriptive dynamic logic and its application to reflective architectures

The aim of this paper is to propose dynamic logic as a common logical framework to describe and identify the most relevant formal characteristics of multi-language logical architectures (MLA) in order to investigate the expressive power of the knowledge bases that can be built upon them. In general, a MLA allows to build knowledge bases as a set of units with initial local theories written in possible different logical languages. Each unit is also usually allowed to have its own intra-unit deductive system. Moreover, the whole knowledge base is equipped with an additional set of deductive rules, called bridge rules, to control the information flow among the different units of the knowledge base. The set of bridge rules act as an inter-unit deductive system. The reasoning dynamics of a knowledge base on top of a MLA can therefore be described by how the local theories of the units evolve during execution.Peer Reviewe

The Philosophical Foundations of PLEN: A Protocol-theoretic Logic of Epistemic Norms

In this dissertation, I defend the protocol-theoretic account of epistemic norms. The protocol-theoretic account amounts to three theses: (i) There are norms of epistemic rationality that are procedural; epistemic rationality is at least partially defined by rules that restrict the possible ways in which epistemic actions and processes can be sequenced, combined, or chosen among under varying conditions. (ii) Epistemic rationality is ineliminably defined by procedural norms; procedural restrictions provide an irreducible unifying structure for even apparently non-procedural prescriptions and normative expressions, and they are practically indispensable in our cognitive lives. (iii) These procedural epistemic norms are best analyzed in terms of the protocol (or program) constructions of dynamic logic. I defend (i) and (ii) at length and in multi-faceted ways, and I argue that they entail a set of criteria of adequacy for models of epistemic dynamics and abstract accounts of epistemic norms. I then define PLEN, the protocol-theoretic logic of epistemic norms. PLEN is a dynamic logic that analyzes epistemic rationality norms with protocol constructions interpreted over multi-graph based models of epistemic dynamics. The kernel of the overall argument of the dissertation is showing that PLEN uniquely satisfies the criteria defended; none of the familiar, rival frameworks for modeling epistemic dynamics or normative concepts are capable of satisfying these criteria to the same degree as PLEN. The overarching argument of the dissertation is thus a theory-preference argument for PLEN