8 papers
Cryptographic certificates of validity for trustworthy AI
Murdoch J. Gabbay
We propose cryptographic certificates of validity for agentic AI systems. The core idea is to formally specify a correctness or policy condition as a logical predicate, compile thi…
Declarative distributed algorithms as axiomatic theories in three-valued modal logic over semitopologies
Murdoch J. Gabbay
We illustrate how to formally specify distributed algorithms as declarative axiomatic theories in a modal logic, using as illustrative examples a simple voting protocol, a simple b…
Nominal techniques as an Agda library
Murdoch J. Gabbay, Orestis Melkonian
Nominal techniques provide a mathematically principled approach to dealing with names and variable binding in programming languages. This paper explores an attempt to make nominal…
Semiframes: the algebra of semitopologies and actionable coalitions
Murdoch J. Gabbay
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent dev…
Semitopology: distributed collaborative action via topology, algebra, and logic
Murdoch J. Gabbay
We introduce semitopologies, a generalisation of point-set topology that removes the restriction that intersections of open sets need necessarily be open. The intuition is that poi…
Decentralised collaborative action: cryptoeconomics in space
Murdoch J. Gabbay
Blockchains and peer-to-peer systems are part of a trend towards computer systems that are "radically decentralised", by which we mean that they 1) run across many participants, 2)…