Subset Spaces Modeling Knowledge-Competitive Agents
Bernhard Heinemann · Lecture notes in computer science · 2015
The bi-modal logic of subset spaces, LSS, was originally designed for revealing the intrinsic relationship between knowledge and topology. In recent years, it has been developed in several directions, not least towards a comprehensive knowledge-theoretic formalism. As to that, subset spaces have been shown to be smoothly combinable with various epistemic concepts, at least as long as attention is restricted to the single-agent case. Adjusting LSS to general multi-agent scenarios, however, has brought about few results only, presumably due to reasons inherent in the system. This is why one is led to consider more special cases. In the present paper, LSS is extended to a particular two-agent setting, where the peculiarity is given by the case that the agents are competitive in a sense; in fact, it is assumed here that one agent is always able to go ahead of another one regarding knowledge (or, the other one is possibly lagging behind in this respect), and vice versa. It turns out that such circumstances can be modeled in corresponding logical terms to a considerable extent.