A Distributed and Trusted Web of Formal Proofs

International audienceMost computer checked proofs are tied to the particular technology of a prover's software. While sharing results between proof assistants is a recognized and desirable goal, the current organization of theorem proving tools makes such sharing an exception instead of the rule. In this talk, I argue that we need to turn the current architecture of proof assistants and formal proofs inside-out. That is, instead of having a few mature theorem provers include within them their formally checked theorems and proofs, I propose that proof assistants should sit on the edge of a web of formal proofs and that proof assistant should be exporting their proofs so that they can exist independently of any theorem prover. While it is necessary to maintain the dependencies between definitions, theories, and theorems, no explicit library structure should be imposed on this web of formal proofs. Thus a theorem and its proofs should not necessarily be located at a particular URL or within a particular prover's library. While the world of symbolic logic and proof theory certainly allows for proofs to be seen as global and permanent objects, there is a lot of research and engineering work that is needed to make this possible. I describe some of the required research and development that must be done to achieve this goal

Multiagent Deontic Logic and its Challenges from a Normative Systems Perspective

This article gives an overview of several challenges studied in deontic logic, with an emphasis on challenges involving agents. We start with traditional modal deontic logic using preferences to address the challenge of contrary-toduty reasoning, and STIT theory addressing the challenges of non-deterministic actions, moral luck and procrastination. Then we turn to alternative normbased deontic logics detaching obligations from norms to address the challenge of Jørgensen’s dilemma, including the question how to derive obligations from a normative system when agents cannot assume that other agents comply with their norms. We discuss also some traditional challenges from the viewpoint of normative systems: when a set of norms may be termed ‘coherent’, how to deal with normative conflicts, how to combine normative systems and traditional deontic logic, how various kinds of permission can be accommodated, how meaning postulates and counts-as conditionals can be taken into account,how sets of norms may be revised and merged, and how normative systems can be combined with game theory. The normative systems perspective means that norms, not ideality or preference, should take the central position in deontic semantics, and that a semantics that represents norms explicitly provides a helpful tool for analysing, clarifying and solving the problems of deontic logic. We focus on the challenges rather than trying to give full coverage of related work, for which we refer to the handbook of deontic logic and normative systems