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Awareness has been shown to be a useful addition to standard epistemic logic for many applications. However, standard propositional logics for knowledge and awareness cannot express the fact that an agent knows that there are facts of which he is unaware without there being an explicit fact that the agent knows he is unaware of. We propose a logic for… (More)

Standard game theory assumes that the structure of the game is common knowledge among players. We relax this assumption by considering extensive games where agents may be unaware of the complete structure of the game. In particular, they may not be aware of moves that they and other agents can make. We show how such games can be represented; the key idea is… (More)

In earlier work [Halpern and Rêgo 2006b], we proposed a logic that extends the Logic of General Awareness of Fagin and Halpern [1988] by allowing quantification over primitive propositions. This makes it possible to express the fact that an agent knows that there are some facts of which he is unaware. In that logic, it is not possible to model an agent… (More)

There has been a great deal of work on characterizing the complexity of the satisfiability and validity problem for modal logics. In particular, Ladner showed that the satisfiability problem for all logics between K and S4 is PSPACE-hard, while for S5 it is NP-complete. We show that it is negative intro-spection, the axiom ¬Kp ⇒ K¬Kp, that causes the gap:… (More)

A Chaotic Probability model is a usual set of probability measures, M, the totality of which is endowed with an objective, frequentist interpretation as opposed to being viewed as a statistical compound hypothesis or an imprecise behavioral subjective one. In the prior work of Fierens and Fine, given finite time series data, the estimation of the Chaotic… (More)

We analyze a model of interactive unawareness introduced by Heifetz, Meier and Schipper (HMS). We consider two axiomatizations for their model, which capture different notions of validity. These axiomatizations allow us to compare the HMS approach to both the standard (S5) epistemic logic and two other approaches to unawareness: that of Fagin and Halpern… (More)

Most work in game theory assumes that players are perfect reasoners and have common knowledge of all significant aspects of the game. In earlier work [Halpern and Rêgo 2006], we proposed a framework for representing and analyzing games with possibly unaware players, and suggested a generalization of Nash equilibrium appropriate for games with unaware… (More)

- Simon Grant, John Quiggin, Joseph Halpern, Je Kline, Mamuro Kaneko, Benoît Menoni +3 others
- 2013

We develop a model of games with awareness that allows for di¤erential levels of awareness. We show that, for the standard modal logical interpretations of belief and awareness, a player cannot believe there exist propositions of which he is unaware. Nevertheless, we argue that a boundedly rational individual may regard the possibility that there exist… (More)

Candida is an opportunistic pathogen that affects high-risk patients who are either immunocompromised or critically ill and is associated with almost 80% of all nosocomial fungal infections, representing the major cause of fungemia with high mortality rates (40%). Candida albicans is the main cause of candidemia and among the non-albicans species C.… (More)